Editing Orbit (section)

==Perturbations==
{{main|Perturbation (astronomy)}}
{{further|Osculating orbit#Perturbations|Orbit modeling#Perturbations}}

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.

===Radial, prograde and transverse perturbations===
A small radial impulse given to a body in orbit changes the [[Eccentricity (mathematics)|eccentricity]], but not the [[orbital period]] (to first order). A [[Direct motion|prograde]] or [[Retrograde motion|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 (astronomy)|orbital plane]] without changing the [[Orbit (dynamics)|period]] or eccentricity. In all instances, a closed orbit will still intersect the perturbation point.

===Orbital decay===
{{Main|Orbital decay}}
If an orbit is about a planetary body with a significant atmosphere, its orbit can decay because of [[drag (physics)|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 sail]]s or [[magnetic sail]]s. 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 force]]s for objects below the [[synchronous orbit]] for the body they're orbiting. The gravity of the orbiting object raises [[tidal bulge]]s 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 with 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 (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 wave]]s. 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 hole]]s or [[neutron star]]s that are orbiting each other closely.

===Oblateness===
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 [[Quadropole#Gravitational quadrupole|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.<ref>{{cite journal
|last1=Iorio
|first1=L.
|date=2011
|title=Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis
|journal=[[Physical Review D]]
 |volume=84
|issue=12
|pages=124001
|bibcode=2011PhRvD..84l4001I
 |doi=10.1103/PhysRevD.84.124001
 |arxiv = 1107.2916 |s2cid=118305813
}}</ref><ref>{{cite journal
|last1=Renzetti
|first1=G.
|date=2013
|title=Satellite Orbital Precessions Caused by the Octupolar Mass Moment of a Non-Spherical Body Arbitrarily Oriented in Space
|journal=[[Journal of Astrophysics and Astronomy]]
 |volume=34
|issue=4
|pages=341–348
|bibcode=2013JApA...34..341R
 |doi=10.1007/s12036-013-9186-4
 |s2cid=120030309
}}</ref><ref>{{cite journal
|last1=Renzetti
|first1=G.
|date=2014
|title=Satellite orbital precessions caused by the first odd zonal J3 multipole of a non-spherical body arbitrarily oriented in space
|journal=[[Astrophysics and Space Science]]
 |volume=352
|issue=2
|pages=493–496
|bibcode=2014Ap&SS.352..493R
 |doi=10.1007/s10509-014-1915-x
 |s2cid=119537102
}}</ref> 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.

===Multiple gravitating bodies===
{{Main|n-body problem}}
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 expression|closed form solution]], although some special cases have been formulated.

===Light radiation and stellar wind===
For smaller bodies particularly, light and [[stellar wind]] can cause significant perturbations to the [[attitude (geometry)|attitude]] and direction of motion of the body, and over time can be significant. Of the planetary bodies, the motion of [[asteroid]]s is particularly affected over large periods when the asteroids are rotating relative to the Sun.