what do you call the point farthest from a satellite's orbit to a planet

As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.)

Orbit

In physics, an orbit is the gravitationally curved trajectory of an object,[1] such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the central mass being orbited at a focal point of the ellipse,[2] as described by Kepler's laws of planetary motion.

Current understanding of the mechanics of orbital motion is based on Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics. For ease of calculation, in most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse square law.[3]

Historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached. It assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets' motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became increasingly unwieldy. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model. The model was further challenged during the 16th century, as comets were observed traversing the spheres.[4][5]

The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus.[6] Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits.

Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common center of mass. Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.

Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange (1736â€“1813) developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus.

Albert Einstein (1879-1955) in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions (except where there are very strong gravity fields and very high speeds) but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate.

Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet.

Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune.

In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and that energy is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.

There are a few common ways of understanding orbits:

As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). This is a 'thought experiment', in which a cannon on top of a tall mountain is able to fire a cannonball horizontally at any chosen muzzle speed. The effects of air friction on the cannonball are ignored (or perhaps the mountain is high enough that the cannon will be above the Earth's atmosphere, which comes to the same thing).[7]

If the cannon fires its ball with a low initial speed, the trajectory of the ball curves downward and hits the ground (A). As the firing speed is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense – they are describing a portion of an elliptical path around the center of gravity – but the orbits are interrupted by striking the Earth.

If the cannonball is fired with sufficient speed, the ground curves away from the ball at least as much as the ball falls â€“ so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity and mass of the planet, there is one specific firing speed (unaffected by the mass of the ball, which is assumed to be very small relative to the Earth's mass) that produces a circular orbit, as shown in (C).

As the firing speed is increased beyond this, non-interrupted elliptic orbits are produced; one is shown in (D). If the initial firing is above the surface of the Earth as shown, there will also be non-interrupted elliptical orbits at slower firing speed; these will come closest to the Earth at the point half an orbit beyond, and directly opposite the firing point, below the circular orbit.

At a specific horizontal firing speed called escape velocity, dependent on the mass of the planet, an open orbit (E) is achieved that has a parabolic path. At even greater speeds the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space" never to return.

The velocity relationship of two moving objects with mass can thus be considered in four practical classes, with subtypes:

It is worth noting that orbital rockets are launched vertically at first to lift the rocket above the atmosphere (which causes frictional drag), and then slowly pitch over and finish firing the rocket engine parallel to the atmosphere to achieve orbit speed.

Once in orbit, their speed keeps them in orbit above the atmosphere. If e.g., an elliptical orbit dips into dense air, the object will lose speed and re-enter (i.e. fall). Occasionally a space craft will intentionally intercept the atmosphere, in an act commonly referred to as an aerobraking maneuver

In most situations relativistic effects can be neglected, and Newton's laws give a sufficiently accurate description of motion. The acceleration of a body is equal to the sum of the forces acting on it, divided by its mass, and the gravitational force acting on a body is proportional to the product of the masses of the two attracting bodies and decreases inversely with the square of the distance between them. To this Newtonian approximation, for a system of two point masses or spherical bodies, only influenced by their mutual gravitation (called a two-body problem), their trajectories can be exactly calculated. If the heavier body is much more massive than the smaller, as in the case of a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate enough and convenient to describe the motion in terms of a coordinate system that is centered on the heavier body, and we say that the lighter body is in orbit around the heavier. For the case where the masses of two bodies are comparable, an exact Newtonian solution is still sufficient and can be had by placing the coordinate system at the center of mass of the system.

Energy is associated with gravitational fields. A stationary body far from another can do external work if it is pulled towards it, and therefore has gravitational potential energy. Since work is required to separate two bodies against the pull of gravity, their gravitational potential energy increases as they are separated, and decreases as they approach one another. For point masses the gravitational energy decreases to zero as they approach zero separation. It is convenient and conventional to assign the potential energy as having zero value when they are an infinite distance apart, and hence it has a negative value (since it decreases from zero) for smaller finite distances.

When only two gravitational bodies interact, their orbits follow a conic section. The orbit can be open (implying the object never returns) or closed (returning). Which it is depends on the total energy (kinetic + potential energy) of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, the speed is always less than the escape velocity. Since the kinetic energy is never negative, if the common convention is adopted of taking the potential energy as zero at infinite separation, the bound orbits will have negative total energy, the parabolic trajectories zero total energy, and hyperbolic orbits positive total energy.

An open orbit will have a parabolic shape if it has velocity of exactly the escape velocity at that point in its trajectory, and it will have the shape of a hyperbola when its velocity is greater than the escape velocity. When bodies with escape velocity or greater approach each other, they will briefly curve around each other at the time of their closest approach, and then separate, forever. This may be the case with most comets if they come from outside the solar system.

All closed orbits have the shape of an ellipse. A circular orbit is a special case, wherein the foci of the ellipse coincide. The point where the orbiting body is closest to Earth is called the perigee, and is called the periapsis (less properly, "perifocus" or "pericentron") when the orbit is about a body other than Earth. The point where the satellite is farthest from Earth is called the apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part.

Bodies following closed orbits repeat their paths with a certain time called the period. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows:

Note that while bound orbits of a point mass or a spherical body with a Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects (such as caused by the slight oblateness of the Earth, or by relativistic effects, thereby changing the gravitational field's behavior with distance) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion. The two-body solutions were published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a converging infinite series that solves the three-body problem; however, it converges too slowly to be of much use. Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.

Rather than an exact closed form solution, orbits with many bodies can be approximated with arbitrarily high accuracy. These approximations take two forms:

Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large assemblages of objects have been simulated.[citation needed]

The Earth follows an ellipse round the sun. But unlike the ellipse followed by a pendulum or an object attached to a spring, the sun is at a focal point of the ellipse and not at its centre.

The following derivation applies to such an elliptical orbit. We start only with the Newtonian law of gravitation stating that the gravitational acceleration towards the central body is related to the inverse of the square of the distance between them, namely

Where F2 is the force acting on the mass m2 caused by the gravitational attraction mass m1 has for m2, G is the universal gravitational constant, and r is the distance between the two masses centers.

From Newton's Second Law, the summation of the forces acting on m2 related to that bodies acceleration:

Where A2 is the acceleration of m2 caused by the force of gravitational attraction F2 of m1 acting on m2.

Combining Eq 1 and 2:

Solving for the acceleration, A2:

where

μ

{\displaystyle \mu \,}

 is the standard gravitational parameter, in this case

G

m

1

{\displaystyle Gm_{1}}

. It is understood that the system being described is m2, hence the subscripts can be dropped.

We assume that the central body is massive enough that it can be considered to be stationary and we ignore the more subtle effects of general relativity.

When a pendulum or an object attached to a spring swings in an ellipse, the inward acceleration/force is proportional to the distance

A
=
F

/

m
=
−
k
r
.

{\displaystyle A=F/m=-kr.}

 Due to the way vectors add, the component of the force in the

x

^

{\displaystyle {\hat {\mathbf {x}}}}

 or in the

y

^

{\displaystyle {\hat {\mathbf {y}}}}

 directions are also proportionate to the respective components of the distances,

r

x

″

=

A

x

=
−
k

r

x

{\displaystyle r''_{x}=A_{x}=-kr_{x}}

. Hence, the entire analysis can be done separately in these dimensions. This results in the harmonic parabolic equations

x
=
A
cos

(
t
)

{\displaystyle x=A\cos(t)}

 and

y
=
B
sin

(
t
)

{\displaystyle y=B\sin(t)}

 of the ellipse. In contrast, with the decreasing relationship

A
=
μ

/

r

2

{\displaystyle A=\mu /r^{2}}

, the dimensions cannot be separated.[citation needed]

The location of the orbiting object at the current time

t

{\displaystyle t}

 is located in the plane using Vector calculus in polar coordinates both with the standard Euclidean basis and with the polar basis with the origin coinciding with the center of force. Let

r

{\displaystyle r}

 be the distance between the object and the center and

θ

{\displaystyle \theta }

 be the angle it has rotated. Let

x

^

{\displaystyle {\hat {\mathbf {x}}}}

 and

y

^

{\displaystyle {\hat {\mathbf {y}}}}

 be the standard Euclidean bases and let

r

^

=
cos

(
θ
)

x

^

+
sin

(
θ
)

y

^

{\displaystyle {\hat {\mathbf {r}}}=\cos(\theta ){\hat {\mathbf {x}}}+\sin(\theta ){\hat {\mathbf {y}}}}

 and

θ
^

=
−
sin

(
θ
)

x

^

+
cos

(
θ
)

y

^

{\displaystyle {\hat {\boldsymbol {\theta }}}=-\sin(\theta ){\hat {\mathbf {x}}}+\cos(\theta ){\hat {\mathbf {y}}}}

 be the radial and transverse polar basis with the first being the unit vector pointing from the central body to the current location of the orbiting object and the second being the orthogonal unit vector pointing in the direction that the orbiting object would travel if orbiting in a counter clockwise circle. Then the vector to the orbiting object is

We use

r
˙

{\displaystyle {\dot {r}}}

 and

θ
˙

{\displaystyle {\dot {\theta }}}

 to denote the standard derivatives of how this distance and angle change over time. We take the derivative of a vector to see how it changes over time by subtracting its location at time

t

{\displaystyle t}

 from that at time

t
+
δ
t

{\displaystyle t+\delta t}

 and dividing by

δ
t

{\displaystyle \delta t}

. The result is also a vector. Because our basis vector

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 moves as the object orbits, we start by differentiating it. From time

t

{\displaystyle t}

 to

t
+
δ
t

{\displaystyle t+\delta t}

, the vector

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 keeps its beginning at the origin and rotates from angle

θ

{\displaystyle \theta }

 to

θ
+

θ
˙

δ
t

{\displaystyle \theta +{\dot {\theta }}\ \delta t}

 which moves its head a distance

θ
˙

δ
t

{\displaystyle {\dot {\theta }}\ \delta t}

 in the perpendicular direction

θ
^

{\displaystyle {\hat {\boldsymbol {\theta }}}}

 giving a derivative of

θ
˙

θ
^

{\displaystyle {\dot {\theta }}{\hat {\boldsymbol {\theta }}}}

.

We can now find the velocity and acceleration of our orbiting object.

The coefficients of

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 and

θ
^

{\displaystyle {\hat {\boldsymbol {\theta }}}}

 give the accelerations in the radial and transverse directions. As said, Newton gives this first due to gravity is

−
μ

/

r

2

{\displaystyle -\mu /r^{2}}

 and the second is zero.

r
¨

−
r

θ
˙

2

=
−

μ

r

2

{\displaystyle {\ddot {r}}-r{\dot {\theta }}^{2}=-{\frac {\mu }{r^{2}}}}

r

θ
¨

+
2

r
˙

θ
˙

=
0

{\displaystyle r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}=0}

Equation (2) can be rearranged using integration by parts.

We can multiply through by

r

{\displaystyle r}

 because it is not zero unless the orbiting object crashes. Then having the derivative be zero gives that the function is a constant.

r

2

θ
˙

=
h

{\displaystyle r^{2}{\dot {\theta }}=h}

which is actually the theoretical proof of Kepler's second law (A line joining a planet and the Sun sweeps out equal areas during equal intervals of time). The constant of integration, h, is the angular momentum per unit mass.

In order to get an equation for the orbit from equation (1), we need to eliminate time.[8] (See also Binet equation.) In polar coordinates, this would express the distance

r

{\displaystyle r}

 of the orbiting object from the center as a function of its angle

θ

{\displaystyle \theta }

. However, it is easier to introduce the auxiliary variable

u
=
1

/

r

{\displaystyle u=1/r}

 and to express

u

{\displaystyle u}

 as a function of

θ

{\displaystyle \theta }

. Derivatives of

r

{\displaystyle r}

 with respect to time may be rewritten as derivatives of

u

{\displaystyle u}

 with respect to angle.

Plugging these into (1) gives

So for the gravitational force – or, more generally, for any inverse square force law – the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The solution is:

where A and θ0 are arbitrary constants. This resulting equation of the orbit of the object is that of an ellipse in Polar form relative to one of the focal points. This is put into a more standard form by letting

e
≡

h

2

A

/

μ

{\displaystyle e\equiv h^{2}A/\mu }

 be the eccentricity, letting

a
≡

h

2

/

(
μ
(
1
−

e

2

)
)

{\displaystyle a\equiv h^{2}/(\mu (1-e^{2}))}

 be the semi-major axis. Finally, letting

θ

0

≡
0

{\displaystyle \theta _{0}\equiv 0}

 so the long axis of the ellipse is along the positive x coordinate.

The above classical (Newtonian) analysis of orbital mechanics assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible. Relativistic effects cease to be negligible when near very massive bodies (as with the precession of Mercury's orbit about the Sun), or when extreme precision is needed (as with calculations of the orbital elements and time signal references for GPS satellites.[9])

The analysis so far has been two dimensional; it turns out that an unperturbed orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved.

The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles.

The orbital period is simply how long an orbiting body takes to complete one orbit.

Six parameters are required to specify a Keplerian orbit about a body. For example, the three numbers that specify the body's initial position, and the three values that specify its velocity will define a unique orbit that can be calculated forwards (or backwards) in time. However, traditionally the parameters used are slightly different.

The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his laws. The Keplerian elements are six:

In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. However, in practice, orbits are affected or perturbed, by other forces than simple gravity from an assumed point source (see the next section), and thus the orbital elements change over time.

An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time.

A small radial impulse given to a body in orbit changes the eccentricity, but not the orbital period (to first order). A prograde or retrograde impulse (i.e. an impulse applied along the orbital motion) changes both the eccentricity and the orbital period. Notably, a prograde impulse at periapsis raises the altitude at apoapsis, and vice versa, and a retrograde impulse does the opposite. A transverse impulse (out of the orbital plane) causes rotation of the orbital plane without changing the period or eccentricity. In all instances, a closed orbit will still intersect the perturbation point.

If an orbit is about a planetary body with significant atmosphere, its orbit can decay because of drag. Particularly at each periapsis, the object experiences atmospheric drag, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body.

The bounds of an atmosphere vary wildly. During a solar maximum, the Earth's atmosphere causes drag up to a hundred kilometres higher than during a solar minimum.

Some satellites with long conductive tethers can also experience orbital decay because of electromagnetic drag from the Earth's magnetic field. As the wire cuts the magnetic field it acts as a generator, moving electrons from one end to the other. The orbital energy is converted to heat in the wire.

Orbits can be artificially influenced through the use of rocket engines which change the kinetic energy of the body at some point in its path. This is the conversion of chemical or electrical energy to kinetic energy. In this way changes in the orbit shape or orientation can be facilitated.

Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input other than that of the Sun, and so can be used indefinitely. See statite for one such proposed use.

Orbital decay can occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years.

Orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely.

The standard analysis of orbiting bodies assumes that all bodies consist of uniform spheres, or more generally, concentric shells each of uniform density. It can be shown that such bodies are gravitationally equivalent to point sources.

However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body. In the general case, the gravitational potential of a rotating body such as, e.g., a planet is usually expanded in multipoles accounting for the departures of it from spherical symmetry. From the point of view of satellite dynamics, of particular relevance are the so-called even zonal harmonic coefficients, or even zonals, since they induce secular orbital perturbations which are cumulative over time spans longer than the orbital period.[10][11][12] They do depend on the orientation of the body's symmetry axis in the space, affecting, in general, the whole orbit, with the exception of the semimajor axis.

The effects of other gravitating bodies can be significant. For example, the orbit of the Moon cannot be accurately described without allowing for the action of the Sun's gravity as well as the Earth's. One approximate result is that bodies will usually have reasonably stable orbits around a heavier planet or moon, in spite of these perturbations, provided they are orbiting well within the heavier body's Hill sphere.

When there are more than two gravitating bodies it is referred to as an n-body problem. Most n-body problems have no closed form solution, although some special cases have been formulated.

For smaller bodies particularly, light and stellar wind can cause significant perturbations to the attitude and direction of motion of the body, and over time can be significant. Of the planetary bodies, the motion of asteroids is particularly affected over large periods when the asteroids are rotating relative to the Sun.

Mathematicians have discovered that it is possible in principle to have multiple bodies in non-elliptical orbits that repeat periodically, although most such orbits are not stable regarding small perturbations in mass, position, or velocity. However, some special stable cases have been identified, including a planar figure-eight orbit occupied by three moving bodies. Further studies have discovered that nonplanar orbits are also possible, including one involving 12 masses moving in 4 roughly circular, interlocking orbits topologically equivalent to the edges of a cuboctahedron.[13]

Finding such orbits naturally occurring in the universe is thought to be extremely unlikely, because of the improbability of the required conditions occurring by chance.[13]

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun).

The gravitational constant G has been calculated as:

Thus the constant has dimension density−1 time−2. This corresponds to the following properties.

Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence velocities are halved and orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the Earth.

Scaling of distances while keeping the masses the same (in the case of point masses, or by reducing the densities) gives similar orbits; if distances are multiplied by 4, gravitational forces and accelerations are divided by 16, velocities are halved and orbital periods are multiplied by 8.

When all densities are multiplied by 4, orbits are the same; gravitational forces are multiplied by 16 and accelerations by 4, velocities are doubled and orbital periods are halved.

When all densities are multiplied by 4, and all sizes are halved, orbits are similar; masses are divided by 2, gravitational forces are the same, gravitational accelerations are doubled. Hence velocities are the same and orbital periods are halved.

In all these cases of scaling. if densities are multiplied by 4, times are halved; if velocities are doubled, forces are multiplied by 16.

These properties are illustrated in the formula (derived from the formula for the orbital period)

for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density Ïƒ, where T is the orbital period. See also Kepler's Third Law.

The application of certain orbits or orbital maneuvers to specific useful purposes have been the subject of patents.[17]


what are the leaf like parts in simple flowers

In botany, a bract is a modified or specialized leaf, especially one associated with a reproductive structure such as a flower, inflorescence axis or cone scale. Bracts are often (but not always) different from foliage leaves. They may be smaller, larger, or of a different color, shape, or texture. Typically, they also look different from the parts of the flower, such as the petals or sepals. The state of having bracts is referred to as bracteate[1] or bracteolate, and conversely the state of lacking them is referred to as ebracteate[2] and ebracteolate, without bracts.

Bract

Some bracts are brightly colored and serve the function of attracting pollinators, either together with the perianth or instead of it. Examples of this type of bract include Euphorbia pulcherrima (poinsettia) and Bougainvillea: both of these have large colourful bracts surrounding much smaller, less colourful flowers.

In grasses, each floret (flower) is enclosed in a pair of papery bracts, called the lemma (lower bract) and palea (upper bract), while each spikelet (group of florets) has a further pair of bracts at its base called glumes. These bracts form the chaff removed from cereal grain during threshing and winnowing.

Bats may detect acoustic signals from dish-shaped bracts such as those of Marcgravia evenia.[3]

A prophyll is a leaf-like structure, such as a bracteole, subtending (extending under) a single flower or pedicel. The term can also mean the lower bract on a peduncle.

The frequently showy pair of bracts of Euphorbia species in subgenus Lacanthis are the cyathophylls.

Bracts subtend the cone scales in the seed cones of many conifers, and in some cases, such as Pseudotsuga, they extend beyond the cone scales.

Bracts of Bougainvillea glabra, differ in colour from the non-bract leaves, and attract pollinators.

Bracts along a banana flower stalk surround the rows of flowers

Euphorbia milii var. vulcanii cyathia bearing a pair of pinkish cyathophylls.

Colourful bracts of Ananas bracteatus.

Bracts, Taraxacum officinale.

Dogwood species Cornus florida inflorescence showing four large white bracts and central flower cluster.

Cornus Florida dogwood with pink bracts surrounding small flower cluster.

A small bract is called a bracteole or bractlet. Technically this is any bract that arises on a pedicel instead of subtending it.

Bracts that appear in a whorl subtending an inflorescence are collectively called an involucre. An involucre is a common feature beneath the inflorescences of many Apiaceae, Asteraceae, Dipsacaceae and Polygonaceae. Each flower in an inflorescence may have its own whorl of bracts, in this case called an involucel. In this case they may be called chaff, paleas, or receptacular bracts and are usually minute scales or bristles. Many asteraceous plants have bracts at the base of each inflorescence.

The term involucre is also used for a highly conspicuous bract or bract pair at the base of an inflorescence. In the family Betulaceae, notably in the genera Carpinus and Corylus, the involucre is a leafy structure that protects the developing nuts. Beggar-tick (Bidens comosa) has narrow involucral bracts surrounding each inflorescence, each of which also has a single bract below it. There is then a pair of leafy bracts on the main stem and below those a pair of leaves.

An epicalyx, which forms an additional whorl around the calyx of a single flower, is a modification of bracteoles[4] In other words, the epicalyx is a group of bracts resembling a calyx or bracteoles forming a whorl outer to the calyx.[5] It is a calyx-like extra whorl of floral appendages. Each individual segment of the epicalyx is called an episepal because they resemble the sepals.[6] They are present in family Malvaceae, the Hibiscus family. Fragaria (strawberries) may or may not have an epicalyx.

A spathe is a large bract or pair of bracts forming a sheath to enclose the flower cluster of such plants as palms, arums, Irises,[7] Crocuses,[8] and dayflowers. In many arums (Araceae family), the spathe is petal-like, attracting pollinators to the flowers arranged on a type of spike called a spadix.


what animal is big pete from mickey mouse

Pete (also called Peg-Leg Pete, Pistol Pete and Black Pete, among other names) is an anthropomorphic cartoon character created in 1925 by Walt Disney and Ub Iwerks. He is a character of The Walt Disney Company and often appears as a nemesis and the main antagonist in Mickey Mouse universe stories. He was originally an anthropomorphic bear but with the advent of Mickey Mouse in 1928, he was defined as a cat.[1][2] Pete is the oldest continuing Disney character, having debuted three years before Mickey Mouse in the cartoon Alice Solves the Puzzle (1925).

Pete (Disney)

Pete has appeared in more than 40 animated short films between 1925 and 1954, having been featured in the Alice Comedies and Oswald the Lucky Rabbit cartoons, and later in the Mickey Mouse, Donald Duck, and Goofy cartoons. Pete's final appearance during this era was The Lone Chipmunks (1954), which was the final installment of a three-part Chip an' Dale series. He also appeared in the short films Mickey's Christmas Carol (1983), The Prince and the Pauper (1990), Mickey, Donald, Goofy: The Three Musketeers (2004), and Get a Horse! (2013).

Pete has also made many appearances in Disney comics, and often appeared as Sylvester Shyster's dimwitted sidekick in the Mickey Mouse comic strip. In the Italian comic production he has come to be the central character in comics from time to time. Pete later made several appearances in television, most extensively in Goof Troop (1992–1993) where he was given more continuity, having a family and a regular job as a used car salesman and is a friend (albeit a poor one) to Goofy. He reprises this incarnation in 1999's Mickey's Once Upon a Christmas. Pete also appears in House of Mouse (2001–03) as the greedy property owner who's always trying devious ways and loop holes to get the club shut down.

Although Pete is often typecast as a villain, he has shown great versatility within the role, playing everything from a hardened criminal (The Dognapper, The Lone Chipmunks) to a legitimate authority figure (Moving Day, Donald Gets Drafted, Mr. Mouse Takes a Trip), and from a menacing trouble maker (Building a Building, Trombone Trouble) to a victim of mischief himself (Timber, The Vanishing Private). On some occasions, Pete has even played a sympathetic character, all the while maintaining his underlying menacing nature. (Symphony Hour, How to Be a Detective) He seems to have lost much of his antagonistic demeanor in his Mickey Mouse Clubhouse appearances and is today a largely friendly character, although his antics can occasionally prove an annoyance.

Comic book stories have depicted Pete as being descended from a long line of villains, highwaymen and outlaws. Even historical figures such as Attila the Hun, Blackbeard, Antonio López de Santa Anna, Billy The Kid, and Cao Cao have been included among his ancestors. His mother is known only as Maw Pete and was mentioned in the story "Donald Duck Finds Pirate Gold" by Carl Barks and Jack Hannah (first published October 1942) as a resident of Pittsburgh, Pennsylvania, USA. Her first actual appearance however was in "The River Pirates" (first published September 1968) by Carl Fallberg and Paul Murry. The same story introduced Li'l Pete, Black Pete's fraternal twin brother who seems to be afflicted with dwarfism. In December 1998, the Mickey Mouse comic strip introduced an older sister of Pete. Petula is the television host of the cooking show Petula's Pantry. She finds time, however, to seek revenge against Mickey for condemning her "baby brother" to life imprisonment.

Better-known and more enduring as characters are two figures created by Romano Scarpa for Italian Disney comics. The first, Trudy Van Tubb, was introduced in Topolino e la collana Chirikawa (Mickey Mouse and the Chirikawa Necklace, first published on March 10, 1960). This female partner of Pete was presented as a childhood acquaintance of his: they are even shown as kids kidnapping Mickey when he was a baby.[3] However, Trudy soon became Pete's girlfriend, his partner-in-crime and roommateâ€”whenever they hold residence out of prison, that is. Their relationship seems to have evolved to a long-standing common-law marriage. This is occasionally used in contrast to Mickey's eternal engagement to Minnie Mouse and Goofy's determination to remain a bachelor. Trudy and Pete also have two hellion nephews named Pierino and Pieretto who often serve as foils for Mickey or Mickey's nephews Morty and Ferdie Fieldmouse.[4]

The second to be introduced is a cousin, the criminal scientist Portis (Plottigat in the original Italian version; English name first used in Walt Disney's Comics and Stories 695, 2008). Portis first appeared in Topolino e il Pippo-lupo" (approximately Mickey Mouse and the Weregoof; January 9, 1977).[5] Portis is a firm believer in the saying "knowledge is power". He considers himself superior to most others in both intellect and education, therefore a rightful leader. However, Portis often finds himself employed by gangs under Pete or even the Phantom Blot. Both of the latter are considered better connected within the Mouseton version of organized crime.

Ed Nofziger is responsible for a third recurring character, an alternative girlfriend of Pete named Chirpy Bird. She first appeared in Topolino e i piccioni "poliziotti" (Mickey Mouse and the Pidgeon Police, first published in December 1981) and starred as Pete's partner-in-crime in eight stories from 1981 to 1984.[6] In France, she and Trudy are presented as the same character, being both renamed Gertrude, despite Trudy being a cat and Chirpy being a canary.

In Mickey Mouse Works, Pete has another cousin named Zeke. Zeke is a criminal like Pete, but is wary of his cousin's attempts to double-cross him "Just like old Times". Mickey often uses this distrust to turn the two against one-another.

In Goof Troop, Pete has a wife, Peg, and two children, PJ and Pistol. Alternatively, the comic book story "Mickey's Strange Mission" from Walt Disney's Comics & Stories #245 (1961, by Carl Fallberg and Paul Murry) suggests a cultured ancestry for Pete, giving his full name as the genteel Percy P. Percival.

In the Italian comic story of 1998, Topolino e il diario di zia Topolinda (Mickey Mouse and aunt Topolinda's diary) we meet Pete's grandma, depicted as the only honest member of his family.

Pete first appeared in the Walt Disney-produced 1920s Alice Comedies short subject series. He first appeared in Alice Solves the Puzzle (February 15, 1925) as Bootleg Pete. His nickname is a reference to his career of bootlegging alcoholic beverages during Prohibition in the United States (January 16, 1920 - December 5, 1933). His activities brought him at a[beach in time to see Alice playing with a crossword puzzle. Pete happened to be a collector of crossword puzzles and identified Alice's puzzle being a rare one missing from his collection. The rest of the short focused on his antagonizing Alice and her drunk-on-moonshine cat Julius in order to steal it. The menacing, bear villain commanded quite a presence on the screen and was destined to return.

Disney needed a villain to place against his new star Oswald the Lucky Rabbit, and Pete was introduced to his new adversary in the sixth Oswald short The Ocean Hop (September 8, 1927). Apparently inspired by Charles Lindbergh, the two enter an aeroplane race across the Atlantic Ocean. Hugh Harman and Rollin Hamilton were responsible for animating several inventive gags during the film. At least one became a classic. At some point Oswald runs off a cliff and continues to walk on air without the effect of gravity until realizing there is no ground to stand on. The gag would be reused in many cartoon shorts. Charles Lindbergh also served as the inspiration for Plane Crazy (May 15, 1927), the first cartoon to feature Mickey Mouse and Minnie Mouse.[7]

By the time producer Charles Mintz took away the Oswald series from Disney, Pete had been established as the most consistently appearing supporting character to Oswald. He continued to appear in that role in the Oswald films directed and produced by Walter Lantz until 1933. His most notable non-Disney appearance was arguably as a captain in Permanent Wave (September 29, 1929).

Animation historian David Gerstein speculates that when Disney stopped working on the Oswald cartoons for Universal he separated from the character and his cast including Pete. Disney and his team created a cat villain for their new protagonist Mickey Mouse. Originally called "Terrible Tom", the villain was named "Pegleg Pete" by 1930 as the Disney crew felt that he was essentially a continuation of their earlier villain, albeit a different species.[12] Animator Norm Ferguson, known for developing Pluto, also developed Pete's character in several shorts and he was made to resemble actor Wallace Beery.[2][13]

Pete appeared as Mickey's enemy beginning with the cartoons The Gallopin' Gaucho and Steamboat Willie. In the cartoons of the 1930s, Pete would be Mickey Mouse's nemesis, but would vary in professions, from an all-out outlaw (Gallopin' Gaucho and the cartoon within a cartoon Gallopin Romance in Mickey's Gala Premier) to a brutal law-enforcer (such as Moving Day in which he is a sheriff who serves Mickey and Donald Duck with an eviction notice). On the other hand, Pete is seen in the audience in the 1932 Mickey's Revue in which the antagonist is not Pete but "Dippy Dawg" aka Goofy; in the 1942 cartoon Symphony Hour, Pete is a sympathetic impresario who sponsors Mickey's orchestra in a concert, which goes terribly wrong, but is a great success.

In addition, Pete is featured in the Mickey Mouse cartoons The Barn Dance (1928), The Barnyard Battle (1929), The Cactus Kid (1930), The Chain Gang (1930), Traffic Troubles (1931), The Mad Dog (1932), Barnyard Olympics (1932), Mickey in Arabia (1932), Touchdown Mickey (1932), The Klondike Kid (1932), Building a Building (1933), The Mail Pilot (1933), Mickey's Gala Premier (1933), Shanghaied (1934), The Dognapper (1934), Two-Gun Mickey (1934), Mickey's Service Station (1935), Moving Day (1936), The Worm Turns (1937), Mickey's Amateurs (1937), Mr. Mouse Takes a Trip (1940), Symphony Hour (1942), and Get a Horse (2013).

Pete is a featured character in the Donald Duck cartoons Donald's Lucky Day (1939), Officer Duck (1939), The Riveter (1940), Timber (1941), Donald Gets Drafted (1942), The Vanishing Private (1942), Sky Trooper (1942), Bellboy Donald (1942), The Old Army Game (1943), Trombone Trouble (1944), The New Neighbor (1953) and Canvas Back Duck (1953, where he fights a semi-pro boxing match with Donald Duck).

Pete appears in three Goofy cartoons: Two Gun Goofy (1952), How to be a Detective (1952), and Father's Day Off (1953). He appears in Goof Troop, A Goofy Movie and its sequel An Extremely Goofy Movie.

Pete appears in one Chip 'n' Dale cartoon, as the main antagonist of The Lone Chipmunks (1954).

During World War II, Pete was "drafted" by Walt Disney and appeared as the official mascot of the United States Merchant Marine. He appeared in Donald Duck's series of army films where he plays Donald's Drill Sergeant and later Sergeant and Jumpmaster. In the comic strips he was a spy for Nazi Germany as Mickey discovered in Mickey Mouse on a Secret Mission (1943) his motivation being the money.

In comic strips and comic books, Pete is consistently depicted as a hardened criminal. In the 1943 comic strip story Mickey Mouse on a Secret Mission, he was an agent of Nazi Germany, working as the henchman of Gestapo spy Von Weasel. In the 1950 comic strip story The Moook Treasure, he's even portrayed as the Beria-like deputy chief of intelligence in a totalitarian state on the other side of the iron curtain.

Pete often teams up with Mickey Mouse enemies Sylvester Shyster, Eli Squinch, or The Phantom Blot. In earlier comic strips, starting with Mickey Mouse in Death Valley (1930) Pete was portrayed as Sylvester Shyster's henchman, but he gradually started to work on his own. Sometimes, Pete also teams up with other bad guys in the Disney universe, such as Scrooge McDuck's enemies (the Beagle Boys and Magica De Spell), Mad Madam Mim, Captain Hook, and the Evil Queen. In Italian comics, his girlfriend Trudy (Trudy Van Tubb) is his frequent partner-in-crime. His cousin the "mad scientist" Plottigat is another, less frequent, accomplice.

In his earlier comic strip appearances, Pete sported a knee-high pegleg, which was later reduced to a foot-high prosthesis. In Mickey Mouse in Death Valley, Floyd Gottfredson occasionally committed goofs, with the pegleg switching from Pete's right leg to his left one. In Gottfredson's story The Mystery at Hidden River (1941â€“42), the pegleg disappeared, with Pete having two normal legs: when Mickey expressed surprise at this, Pete described one of his legs as a new, "streamlined, modern" artificial leg. Pete has since been consistently depicted as having two legs; except in the 2004 feature film Mickey, Donald, Goofy: The Three Musketeers.

His name in Italy has remained "Pietro Gambadilegno" ("Pegleg Peter"), or simply "Gambadilegno" ("Pegleg") even though it has been a long time since he was actually depicted with a pegleg in either comics or animated cartoons. In an Italian story by Romano Scarpa, "Topolino e la dimensione Delta" ("Mickey Mouse and the Delta Dimension", first published in 1959), Pete briefly removes his artificial leg, revealing his old foot-high pegleg underneath. Usually, Gambadilegno is depicted as the rival of Chief Seamus O'Hara ("commissario Adamo Basettoni"), Detective Casey ("ispettore Manetta") and Phantom Blot ("Macchia Nera").

In the first season of the 1987 TV series DuckTales, Pete appeared in a few episodes. However, he was portrayed as a different character in each of his appearances. Because of this, he wasn't always a true villain, but sometimes just a selfish individual with no evil agenda. In a few episodes, he even makes peace with Scrooge's group in the end. The various Petes appear to be their own characters, as two of them lived in different time periods, and because Scrooge never "recognizes" him, despite any previous encounters he may have had with any of the other Petes. In all of his appearances Pete was voiced by Will Ryan.

In the 1992 TV series Goof Troop, Pete has a family who includes his wife Peg, their two children Pete Junior (or PJ for short) and Pistol, and their dog Chainsaw with Pete taking on a more canine-like appearance. They live next door to Goofy and his son Max. In the series, Pete is the major antagonist and the main antihero. Pete is often the victim of Goofy's clumsiness and mishaps, usually resulting in the destruction of his property or great personal injury. Pete owns a used-car dealership, and though no longer openly villainous, is still conniving (as well as abrasive, obnoxious, truculent and suspicious) and often exploits his good-hearted and somewhat addled friend Goofy. Often, his schemes backfire, or he feels guilty about his oafish behavior and works to set things right. His wife Peg often attempts to rid Pete of his uncouth attitude, and his son PJ is a complete opposite of his father in behavior, as he is good friends with Goofy's son Max in the series and its spin-off movies A Goofy Movie (1995) and An Extremely Goofy Movie (2000) as a good character. Jim Cummings provided Pete's booming bass voice starting from that series, and to date is still the character's voice in all media. It is eventually revealed in the series' pilot episode "Forever Goof" that one of the reasons why Pete dislikes Goofy so much is that when Pete was a high school quarterback in a big football game, it was Goofy who accidentally caused Pete to fumble the ball and lose the game by hitting him in the face with a pom pom (Goofy was on the cheerleading squad).

After Goof Troop, Pete reverted to his evil ways on Mickey Mouse Works, where he frequently bullied the other characters and occasionally kidnapped Minnie Mouse. He would also play an average criminal (i.e. a house burglar). Then in House of Mouse, he plays the role of the evil landlord. Several episodes involved his attempts to close the club by sabotaging the show, though there were times when he helped out the crew.

Pete appears in numerous episodes of Mickey Mouse Clubhouse, Disney's newest 3D-animated children's series. He maintains his protagonist and semi-antagonist role, but is significantly toned down for its preschool audience—he is less malicious and more mischievous. Viewers will find that Mickey and gang are very forgiving of Pete and his escapades. He often appears as a seller of objects the gang needs, and will give them an item in exchange for beans. He is much nicer than his previous incarnations—in one episode, he invites the group to a Halloween party; in "Pete's Beach Blanket Luau", he even invites everyone to the titular party.

While Clubhouse has a great deal of fun at Pete's expense (or "expanse", as he's the biggest and fattest character; they use his overalls for a sail in "Mickey and Minnie's Jungle Safari"), it also depicts him in a sympathetic light; he's openly sentimental in "Clarabelle's Clubhouse Carnival", not wanting to part with his "Petey doll" prizes. He even changes Baby Goofy's diaper (willingly) in "Goofy Baby".

The Carnival episode also gives us the closest approximation of Pete's weight; he's shown to be the same size and weight as a brown bear.

In Mickey's Great Clubhouse Hunt, he is the only character not invited to the Easter Egg Hunt (or so he thinks), so he tries to gatecrash, but messes up the secret word, causing the clubhouse to float away. At the end, he apologizes and is invited to the egg hunt after all. He is also revealed as the owner of Butch the Bulldog, who is friends with Mickey's dog, Pluto.

Pete appears in the 2013 Mickey Mouse cartoon series. In the show, he is designed based on his appearances in the early Mickey Mouse cartoons, complete with a peg-leg. Like Mickey Mouse Works and House of Mouse, in the series he has revert to his evil ways, and again his booming bass voice provided by Jim Cummings.

In the 1983 short film Mickey's Christmas Carol, an adaptation of Charles Dickens' novel A Christmas Carol featuring Disney characters, Pete was cast as the Ghost of Christmas Yet to Come, who reveals himself by removing his hood and lighting a cigar, which also lights up the engraving on Scrooge's grave, and having only one line ("Why yours, Ebenezer. The richest man in the cemetery!", in response to Scrooge's question about whose grave it was) and laughing cruelly while Scrooge struggles to escape from his open grave as the gates of Hell are opening. Pete also made a cameo appearance as a Toontown police officer in the very final scene of Who Framed Roger Rabbit - he is viewed from the back, alongside Tom and Jerry's Spike and Horace Horsecollar in security uniforms; this can be seen just before Porky Pig and Tinkerbell close the movie. This was a non-speaking role. Pete later appeared in A Goofy Movie and its sequel where he was shown in a much lighter tone as these movies are based on Goof Troop. He was Goofy's best friend and confidante in the films making him a minor character. However, he was still arrogant and somewhat grouchy.

In this Disney version of Mark Twain's The Prince and the Pauper, Pete once again played as the primary villain, this time as the English king's captain of the guard. When he saw that his ruler's life was slowly diminishing, he and his henchmen, a band of anthropomorphic weasels (from The Wind in the Willows) who now act as the king's guards, seized the opportunity to terrorize England's citizens and rob them of their goods in "favor" of the king. After kicking out a disguised Prince, whom he mistook for the peasant boy Mickey Mouse, out of his kingdom, he later receives word from one of his guards that the Prince was seen a causing a commotion in the village, as the guard claimed that he "acted like a nobleman and he had the royal ring!" Pete suddenly realizes that it was indeed the Prince he "booted out" and seizes another opportunity out of this. That night, after the king passes away, Pete finds the "phony prince" (Mickey), threatening the life of his dog, Pluto, unless Mickey follows his commands. In the village, he soon finds and captures the real Prince and takes him to the castle's dungeon to lock him up. On the day of the Prince's coronation, Pete plots to get Mickey crowned as king, though Mickey is still subservient to Pete's orders. His plan, however, is thwarted when the Prince suddenly appears in the throne room, having busted out of the dungeon and evading the guards with the help of Goofy (Mickey's peasant friend) and Donald Duck (the Prince's valet). A sudden battle in the throne room (Mickey and the Prince vs. Pete; Goofy and Donald vs. the Weasel Guards) results in Pete's defeat, as Goofy's bumbling antics cause a chandelier to fall on the weasels, bundle them together, and send them rolling towards Pete. Pete, seeing this, tries to flee but is slowed down by his ripped-down pants (courtesy of the Prince's swashbuckling skills) and tripped by both the Prince and Mickey, causing him to get rolled over and caught on the chandelier, which sends him and his men rolling through a stain-glass window and falling out of the castle.

In the 2002 direct-to-video House of Mouse spinoff film Mickey's House of Villains, Pete and other Disney villains' guest appearances from House of Mouse are featured. He takes part in the musical number "It's Our House Now."

In the 2004 made-for-video animated film The Three Musketeers (with Mickey, Donald Duck, and Goofy playing the title roles), Pete again appeared under the name Peg-Leg Pete. He served as the main antagonist of the film. Here, he was the Captain of the Musketeers, aiming to take over France, with the help of his lieutenant, Clarabelle Cow, and the Beagle Boys. To do so, he must get Princess Minnie out of the way, but it proves to be difficult for him, even when he hires the film's titular trio to be her bodyguards, believing they won't do a good job protecting her. He received his own "bad guy song", using the classic music piece In the Hall of the Mountain King.

Pete is depicted as a recurring villain within the Kingdom Hearts video game series. He was originally a steamboat captain, with Mickey Mouse as his deck hand (as they were seen in Steamboat Willie), and later the captain of the Royal Musketeers until his plans for a coup were foiled by Mickey (as they were seen in The Three Musketeers). After Disney Castle was built in their world, with Mickey its new king, Pete began causing all sorts of mischief until he was banished to another dimension. He was subsequently freed by Maleficent, to whom he became indebted, and vowed to amass an army of Heartless, creatures born from the darkness of people's hearts, to return the favor.


liquid produced by the interaction of rainwater with solid waste

Leachate from a landfill varies widely in composition depending on the age of the landfill and the type of waste that it contains.[1][2] It usually contains both dissolved and suspended material. The generation of leachate is caused principally by precipitation percolating through waste deposited in a landfill. Once in contact with decomposing solid waste, the percolating water becomes contaminated, and if it then flows out of the waste material it is termed leachate.[3] Additional leachate volume is produced during this decomposition of carbonaceous material producing a wide range of other materials including methane, carbon dioxide and a complex mixture of organic acids, aldehydes, alcohols and simple sugars.

Leachate

A leachate is any liquid that, in the course of passing through matter, extracts soluble or suspended solids, or any other component of the material through which it has passed.

Leachate is a widely used term in the environmental sciences where it has the specific meaning of a liquid that has dissolved or entrained environmentally harmful substances that may then enter the environment. It is most commonly used in the context of land-filling of putrescible or industrial waste.

In the narrow environmental context leachate is therefore any liquid material that drains from land or stockpiled material and contains significantly elevated concentrations of undesirable material derived from the material that it has passed through.

The risks of leachate generation can be mitigated by properly designed and engineered landfill sites, such as those that are constructed on geologically impermeable materials or sites that use impermeable liners made of geomembranes or engineered clay. The use of linings is now mandatory within the United States, Australia and the European Union except where the waste is deemed inert. In addition, most toxic and difficult materials are now specifically excluded from landfilling. However, despite much stricter statutory controls, leachates from modern sites are often found to contain a range of contaminants stemming from illegal activity or legally discarded household and domestic products.

When water percolates through waste, it promotes and assists the process of decomposition by bacteria and fungi. These processes in turn release by-products of decomposition and rapidly use up any available oxygen, creating an anoxic environment. In actively decomposing waste, the temperature rises and the pH falls rapidly with the result that many metal ions that are relatively insoluble at neutral pH become dissolved in the developing leachate. The decomposition processes themselves release more water, which adds to the volume of leachate. Leachate also reacts with materials that are not prone to decomposition themselves, such as fire ash, cement-based building materials and gypsum-based materials changing the chemical composition. In sites with large volumes of building waste, especially those containing gypsum plaster, the reaction of leachate with the gypsum can generate large volumes of hydrogen sulfide, which may be released in the leachate and may also form a large component of the landfill gas.

In a landfill that receives a mixture of municipal, commercial, and mixed industrial waste but excludes significant amounts of concentrated chemical waste, landfill leachate may be characterized as a water-based solution of four groups of contaminants: dissolved organic matter (alcohols, acids, aldehydes, short chain sugars etc.), inorganic macro components (common cations and anions including sulfate, chloride, iron, aluminium, zinc and ammonia), heavy metals (Pb, Ni, Cu, Hg), and xenobiotic organic compounds such as halogenated organics, (PCBs, dioxins, etc.).[4]

The physical appearance of leachate when it emerges from a typical landfill site is a strongly odoured black-, yellow- or orange-coloured cloudy liquid. The smell is acidic and offensive and may be very pervasive because of hydrogen-, nitrogen- and sulfur-rich organic species such as mercaptans.

In older landfills and those with no membrane between the waste and the underlying geology, leachate is free to leave the waste and flow directly into the groundwater. In such cases, high concentrations of leachate are often found in nearby springs and flushes. As leachate first emerges it can be black in colour, anoxic, and possibly effervescent, with dissolved and entrained gases. As it becomes oxygenated it tends to turn brown or yellow because of the presence of iron salts in solution and in suspension. It also quickly develops a bacterial flora often comprising substantial growths of Sphaerotilus natans.

In the UK, in the late 1960s, central Government policy was to ensure new landfill sites were being chosen with permeable underlying geological strata to avoid the build-up of leachate. This policy was dubbed "dilute and disperse". However, following a number of cases where this policy was seen to be failing, and an exposee in The Sunday Times of serious environmental damage being caused by inappropriate disposal of industrial wastes, both policy and the law were changed. The Deposit of Poisonous Wastes Act 1972,[5] together with The 1974 Local Government Act, made local government responsible for waste disposal and for the enforcement of environmental standards regarding waste disposal. Proposed landfill locations also had to be justified not only by geography but also scientifically. Many European countries decided to select landfill sites in groundwater-free clay geological conditions or to require that the site have an engineered lining. In the wake of European advancements, the United States increased its development of leachate retaining and collection systems. This quickly led from lining in principle to the use of multiple lining layers in all landfills (excepting those truly inert).[6]

The primary criterion for design of the leachate system is that all leachate be collected and removed from the landfill at a rate sufficient to prevent an unacceptable hydraulic head occurring at any point over the lining system.

There are many components to a collection system including pumps, manholes, discharge lines and liquid level monitors. However, there are four main components which govern the overall efficiency of the system. These four elements are liners, filters, pumps and sumps.

Natural and synthetic liners may be utilized as both a collection device and as a means for isolating leachate within the fill to protect the soil and groundwater below. The chief concern is the ability of a liner to maintain integrity and impermeability over the life of the landfill. Subsurface water monitoring, leachate collection, and clay liners are commonly included in the design and construction of a waste landfill. To effectively serve the purpose of containing leachate in a landfill, a liner system must possess a number of physical properties. The liner must have high tensile strength, flexibility, and elongation without failure. It is also important that the liner resist abrasion, puncture, and chemical degradation by leachate. Lastly, the liner must withstand temperature variation and be black (to resist UV light), easily installed, and economical.

There are several types of liners used in leachate control and collection. These types include geomembranes, geosynthetic clay liners, geotextiles, geogrids, geonets, and geocomposites. Each style of liner has specific uses and abilities. Geomembranes are used to provide a barrier between mobile polluting substances released from wastes and the groundwater. In the closing of landfills, geomembranes are used to provide a low-permeability cover barrier to prevent the intrusion of rain water. Geosynthetic clay liners (GCLs) are fabricated by distributing sodium bentonite in a uniform thickness between woven and non-woven geotextiles. Sodium bentonite has a low permeability, which makes GCLs a suitable alternative to clay liners in a composite liner system. Geotextiles are used as separation between two different types of soils to prevent contamination of the lower layer by the upper layer. Geotextiles also act as a cushion to protect synthetic layers against puncture from underlying and overlaying rocks. Geogrids are structural synthetic materials used in slope veneer stability to create stability for cover soils over synthetic liners or as soil reinforcement in steep slopes. Geonets are synthetic drainage materials that are often used in lieu of sand and gravel. Radz can take 12 in (30 cm) of drainage sand, thus increasing the landfill space for waste. Geocomposites are a combination of synthetic materials that are ordinarily used singly. A common type of geocomposite is a geonet that is heat-bonded to two layers of geotextile, one on each side. The geocomposite serves as a filter and drainage medium.

Geosynthetic clay liners are a type of combination liner. One advantage to using a geosynthetic clay liner (GCL) is the ability to order exact amounts of the liner. Ordering precise amounts from the manufacturer prevents surplus and over-spending. Another advantage to GCLs is that the liner can be used in areas without an adequate clay source. On the other hand, GCLs are heavy and cumbersome, and their installation is very labor-intensive. In addition to being arduous and difficult under normal conditions, installation can be cancelled during damp conditions because the bentonite would absorb the moisture, making the job even more burdensome and tedious.

The leachate drainage system is responsible for the collection and transport of the leachate collected inside the liner. The pipe dimensions, type, and layout must all be planned with the weight and pressure of waste, and transport vehicles in mind. The pipes are located on the floor of the cell. Above the network lies an enormous amount of weight and pressure. To support this, the pipes can either be flexible or rigid, but the joints to connect the pipes yield better results if the connections are flexible. An alternative to placing the collection system underneath the waste is to position the conduits in trenches or above grade.

The collection pipe network of a leachate collection system drains, collects, and transports leachate through the drainage layer to a collection sump where it is removed for treatment or disposal. The pipes also serve as drains within the drainage layer to minimize the mounding of leachate in the layer. These pipes are designed with cuts that are inclined to 120 degrees, preventing entry of solid particles.[7]

The filter layer is used above the drainage layer in leachate collection. There are two types of filters typically used in engineering practices: granular and geotextile. Granular filters consist of one or more soil layers or multiple layers having a coarser gradation in the direction of the seepage than the soil to be protected.

As liquid enters the landfill cell, it moves down the filter, passes through the pipe network, and rests in the sump. As collection systems are planned, the number, location, and size of the sumps are vital to an efficient operation. When designing sumps, the amount of leachate and liquid expected is the foremost concern. Areas in which rainfall is higher than average typically have larger sumps. A further criterion for sump planning is accounting for the pump capacity. The relationship of pump capacity and sump size is inverse. If the pump capacity is low, the volume of the sump should be larger than average. It is critical for the volume of the sump to be able to store the expected leachate between pumping cycles. This relationship helps maintain a healthy operation. Sump pumps can function with preset phase times. If the flow is not predictable, a predetermined leachate height level can automatically switch the system on. Other conditions for sump planning are maintenance and pump drawdown. Collection pipes typically convey the leachate by gravity to one or more sumps, depending upon the size of the area drained. Leachate collected in the sump is removed by pumping to a vehicle, to a holding facility for subsequent vehicle pickup, or to an on-site treatment facility. Sump dimensions are governed by the amount of leachate to be stored, pump capacity, and minimum pump drawdown. The volume of the sump must be sufficient to hold the maximum amount of leachate anticipated between pump cycles, plus an additional volume equal to the minimum pump drawdown volume. Sump size should also consider dimensional requirements for conducting maintenance and inspection activities. Sump pumps may operate with preset cycling times or, if leachate flow is less predictable, the pump may be automatically switched on when the leachate reaches a predetermined level.

More modern landfills in the developed world have some form of membrane separating the waste from the surrounding ground, and in such sites there is often a leachate collection series of pipes laid on the membrane to convey the leachate to a collection or treatment location. An example of a treatment system with only minor membrane use is the Nantmel Landfill Site.

All membranes are porous to a limited extent so that, over time, low volumes of leachate will cross the membrane. The design of landfill membranes is at such low volumes that they should never have a measurable adverse impact on the quality of the receiving groundwater. A more significant risk may be the failure or abandonment of the leachate collection system. Such systems are prone to internal failure as landfills suffer large internal movements as waste decomposes unevenly and thus buckles and distorts pipes. If a leachate collection system fails, leachate levels will slowly build in a site and may even over-top the containing membrane and flow out into the environment. Rising leachate levels can also wet waste masses that have previously been dry, triggering further active decomposition and leachate generation. Thus, what appears to be a stabilised and inactive site can become re-activated and restart significant gas production and exhibit significant changes in finished ground levels.

One method of leachate management that was more common in uncontained sites was leachate re-circulation, in which leachate was collected and re-injected into the waste mass. This process greatly accelerated decomposition and therefore gas production and had the impact of converting some leachate volume into landfill gas and reducing the overall volume of leachate for disposal. However, it also tended to increase substantially the concentrations of contaminant materials, making it a more difficult waste to treat.[8]

The most common method of handling collected leachate is on-site treatment. When treating leachate on-site, the leachate is pumped from the sump into the treatment tanks. The leachate may then be mixed with chemical reagents to modify the pH and to coagulate and settle solids and to reduce the concentration of hazardous matter. Traditional treatment involved a modified form of activated sludge to substantially reduce the dissolved organic content. Nutrient imbalance can cause difficulties in maintaining an effective biological treatment stage. The treated liquor is rarely of sufficient quality to be released to the environment and may be tankered or piped to a local sewage treatment facility; the decision depends on the age of the landfill and on the limit of water quality that must be achieved after treatment. With high conductivity, leachate is hard to treat with biological treatment or chemical treatment.

Treatment with reverse osmosis is also limited, resulting in low recoveries and fouling of the RO membranes. Reverse osmosis applicability is limited by conductivity, organics, and scaling inorganic elements such as CaSO4, Si, and Ba.

In some older landfills, leachate was directed to the sewers, but this can cause a number of problems. Toxic metals from leachate passing through the sewage treatment plant concentrate in the sewage sludge, making it difficult or dangerous to dispose of the sludge without incurring a risk to the environment. In Europe, regulations and controls have improved in recent decades, and toxic wastes are now no longer permitted to be disposed of in the Municipal Solid Waste landfills, and in most developed countries the metals problem has diminished. Paradoxically, however, as sewage treatment plant discharges are being improved throughout Europe and many other countries, the plant operators are finding that leachates are difficult waste streams to treat. This is because leachates contain very high ammoniacal nitrogen concentrations, are usually very acidic, are often anoxic and, if received in large volumes relative to the incoming sewage flow, lack the Phosphorus needed to prevent nutrient starvation for the biological communities that perform the sewage treatment processes. The result is that leachates are a difficult-to-treat waste stream. However, within aging municipal solid waste landfills, this may not be a problem as the pH returns close to neutral after the initial stage of acidogenic leachate decomposition. Many sewer undertakers limit maximum ammoniacal nitrogen[10] concentration in their sewers to 250Â mg/l to protect sewer maintenance workers, as the WHO's maximum occupational safety limit would be exceeded at above pH 9 to 10, which is often the highest pH allowed in sewer discharges.

Many older leachate streams also contained a variety of synthetic organic species and their decomposition products, some of which had the potential to be acutely damaging to the environment.

The risks from waste leachate are due to its high organic contaminant concentrations and high concentration of ammonia. Pathogenic microorganisms that might be present in it are often cited as the most important, but pathogenic organism counts reduce rapidly with time in the landfill, so this only applies to the freshest leachate. Toxic substances may, however, be present in variable concentrations, and their presence is related to the nature of the waste deposited.

Most landfills containing organic material will produce methane, some of which dissolves in the leachate. This could, in theory, be released in poorly ventilated areas in the treatment plant. All plants in Europe must now be assessed under the EU ATEX Directive and zoned where explosion risks are identified to prevent future accidents. The most important requirement is the prevention of the discharge of dissolved methane from untreated leachate into public sewers, and most sewage treatment authorities limit the permissible discharge concentration of dissolved methane to 0.14Â mg/l, or 1/10 of the lower explosive limit. This entails methane stripping from the leachate.

The greatest environmental risks occur in the discharges from older sites constructed before modern engineering standards became mandatory and also from sites in the developing world where modern standards have not been applied. There are also substantial risks from illegal sites and ad-hoc sites used by organizations outside the law to dispose of waste materials. Leachate streams running directly into the aquatic environment have both an acute and chronic impact on the environment, which may be very severe and can severely diminish bio-diversity and greatly reduce populations of sensitive species. Where toxic metals and organics are present this can lead to chronic toxin accumulation in both local and far distant populations. Rivers impacted by leachate are often yellow in appearance and often support severe overgrowths of sewage fungus.

The contemporary research in the field of assessment techniques and remedial technology of environmental issues originating from landfill leachate has been reviewed in an article published in Critical Reviews in Environmental Science and Technology journal [11].

Leachate collection systems can experience many problems including clogging with mud or silt. Bioclogging can be exacerbated by the growth of micro-organisms in the conduit. The conditions in leachate collection systems are ideal for micro-organisms to multiply. Chemical reactions in the leachate may also cause clogging through generation of solid residues. The chemical composition of leachate can weaken pipe walls, which may then fail.

Leachate can also be produced from land that was contaminated by chemicals or toxic materials used in industrial activities such as factories, mines or storage sites. Composting sites in areas of high rainfall also produce leachate.[clarification needed]

Leachate is also associated with stockpiled coal and with waste materials from metal ore mining and other rock extraction processes, especially those in which sulfide containing materials are exposed to air producing sulfuric acid, often with elevated metal concentrations.

In the context of civil engineering (more specifically reinforced concrete design), leachate refers to the effluent of pavement wash-off (that may include melting snow and ice with salt) that permeates through the cement paste onto the surface of the steel reinforcement, thereby catalyzing its oxidation and degradation. Leachates can be genotoxic in nature.[12]


where is johnson shut in state park in mo

Johnson's Shut-Ins State Park is a state-owned, public recreation area covering 8,647 acres (3,499 ha) on the East Fork Black River in Reynolds County, Missouri. The state park is jointly administered with adjoining Taum Sauk Mountain State Park, and together the two parks cover 16,050 acres (6,500 ha) in the St. Francois Mountains region of the Missouri Ozarks.

Johnson's Shut-Ins State Park

The term "shut-in" refers to a place where the river's breadth is limited by hard rock that is resistant to erosion. In these shut-ins, the river cascades in many rivulets over and around igneous rocks worn smooth over many eons. It is used by park visitors as a natural water park when the water is not so high as to be dangerous.[6]

The bedrock of the area is an erosion resistant rhyolite porphyry and dark colored diabase dikes of Proterozoic age. Waters of the East Fork Black River became confined, or "shut-in," to a narrow channel following fractures and joints within the hard igneous rock. Water-borne sand and gravel cut deeply even into this erosion-resistant rock, carving potholes, chutes and canyon-like gorges.[7]

Most of the park, including the shut-ins and two miles of river frontage, was assembled over the course of 17 years and donated to the state in 1955 by Joseph Desloge[8] (1889â€“1971), a St. Louis civic leader and conservationist from the prominent Desloge lead mining family, which has continued over the years to donate funds for park improvements.

On December 14, 2005, the park was devastated by a catastrophic flood caused by the failure of the Taum Sauk pumped storage plant reservoir atop a neighboring mountain. Damage included eradication of the park's campground, which was unoccupied at the time. The only people at the park were the park's superintendent and his family, who survived, sustaining some injuries.[9] The park was closed because of the extent of the damage it received.

The park partly reopened in the summer of 2006 for limited day use, but due to dangerous conditions, swimming in the river and exploring the rock formations was prohibited. In 2009, the river and shut-ins were reopened for water recreation. A new campground opened in 2010.[10] Park restoration and improvements are funded with $52 million of a $180 million settlement to the state from AmerenUE, the owner and operator of the failed reservoir.[11]

Some areas of forest in the park and the surrounding region were severely damaged by the May 2009 derecho windstorm. Straight-line wind speeds in this part of Reynolds County reached 60 to 70 mi/h (97 to 113 km/h) with microbursts estimated up to 100 mi/h (161 km/h).[12]

Camping, hiking, swimming, and rock climbing are available at the park.[6] A paved quarter-mile (0.4Â km) walkway takes visitors to an observation deck overlooking the shut-ins.[13] A section of the Ozark trail also crosses the park, and the Goggins Mountain Equestrian Trail provides a 10-mile loop for those who bring their own horses.[14]

An extension to the park provides an auto tour that passes by the ongoing recovery effort, as well as the recovered endangered fens area,[8] terminating at a shaded overlook of the flood path accessible from the park entrance. From this one can walk a path through the boulder field created by the flood. The boulder field contains many examples of the minerals and rocks that make up the St. Francois Mountains of the Ozarks.[14][15]