In astrodynamics (*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 law of universal gravitation; it is a core discipline within space-mission design and control), the orbital manoeuvres made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit are called orbital station-keeping.

For many Earth satellites, the effects of the *non-Keplerian forces* (orbital perturbation analysis is the activity of determining why a satellite’s orbit differs from the mathematical ideal orbit. A satellite’s orbit in an ideal two-body system describes a conic section, usually an ellipse. In reality, there are several factors that cause the conic section to continually change. These deviations from the ideal Kepler’s orbit are called perturbations), like the deviations of the gravitational force of the Earth from that of a homogeneous sphere, the gravitational forces from Sun/Moon, solar radiation pressure and air drag, must be counteracted.

### Orbital perturbation

All celestial bodies of the Solar System follow in first approximation a *Kepler orbit* around a *central body*. In celestial mechanics, a Kepler orbit (or *Keplerian orbit*) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also form a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on.

In most applications, there is a large central body, the centre of mass of which is assumed to be the centre of mass of the entire system. By decomposition, the orbits of two objects of similar mass can be described as Kepler orbits around their common centre of mass, their barycentre.

For a satellite (artificial or natural), this *central body* is a planet. But both due to gravitational forces caused by the Sun and other celestial bodies, and due to the flattening of its planet (caused by its rotation which makes the planet slightly oblate and therefore the result of the *Shell theorem* not fully applicable), the satellite will follow an orbit around the Earth that deviates more than the Kepler orbits observed for the planets.

For man-made spacecraft orbiting the Earth at comparatively low altitudes, the deviations from a Kepler orbit are much larger than for the Moon. The approximation of the gravitational force of the Earth to be that of a homogeneous sphere gets worse the closer one gets to the Earth surface, and the majority of the artificial Earth satellites are in orbits that are only a few hundred kilometres over the Earth surface. Furthermore, they are (as opposed to the Moon) significantly affected by the solar radiation pressure because of their large cross-section-to-mass ratio; this applies in particular to 3-axis stabilised spacecraft with large solar arrays, and is allowed for in calculation of graveyard orbits.

### Orbital station-keeping

The deviation of Earth’s gravity field from that of a homogeneous sphere and gravitational forces from Sun/Moon will in general perturb the orbital plane. For a *Sun-synchronous orbit*, the precession of the orbital plane caused by the oblateness of the Earth is a desirable feature that is part of the mission design, but the inclination change caused by the gravitational forces of Sun/Moon is undesirable. For *geostationary spacecraft*, the inclination change caused by the gravitational forces of the Sun/Moon must be counteracted by a rather large expense of fuel, as the inclination should be kept sufficiently small for the spacecraft to be tracked by a non-steerable antenna.

For spacecraft in Low Earth Orbits (LEOs), the effects of atmospheric drag must often be compensated for. For some missions, this is needed simply to avoid re-entry; for other missions, typically missions for which the orbit should be accurately synchronised with Earth rotation, this is necessary to avoid the orbital period shortening.

Solar radiation pressure will in general perturb the eccentricity. For some missions, this must be actively counter-acted with manoeuvres. For geostationary spacecraft, the eccentricity must be kept sufficiently small for a spacecraft to be tracked with a non-steerable antenna. Also for Earth observation spacecraft, for which a very repetitive orbit with a fixed ground track is desirable, the eccentricity vector should be kept as fixed as possible. A large part of this compensation can be done by using a frozen orbit design, but for the fine control manoeuvres with thrusters are needed.

For spacecraft in a *halo orbit* (resulting from an interaction between the gravitational pull of two planetary bodies, like the Earth and the Moon, and the *Coriolis* and centrifugal accelerations on a spacecraft) around a *Lagrangian point*, usually space telescopes (most satellites in halo orbit serve scientific purposes), station-keeping is even more fundamental, as such an orbit is unstable. Without an active control with thruster burns, the smallest deviation in position/velocity would result in the spacecraft leaving the orbit completely.

#### Orbital station-keeping in Low Earth Orbit (LEO)

For a spacecraft in a very low orbit the *atmospheric drag* is sufficiently strong to cause a re-entry before the intended end of mission if orbit raising manoeuvres are not executed from time to time. An example of this is the *International Space Station* (ISS), operating in Low Earth Orbit (LEO): due to atmospheric drag the space station is constantly losing orbital energy; in order to compensate for this loss, which would eventually lead to a re-entry of the station, it has from time to time been re-boosted to a higher orbit.

#### Orbital station-keeping for Earth observation spacecraft

For *Earth observation spacecraft* (an Earth observation satellite or *Earth remote sensing satellite* is a satellite specifically designed for Earth observation from orbit, similar to spy satellites, but intended for non-military uses such as environmental monitoring, meteorology, map-makingâ€¦) typically operated in an altitude above the Earth surface of about seven hundred kilometres, the air-drag is very faint and a re-entry due to air-drag is not a concern. But if the orbital period should be synchronous with the Earth’s rotation to maintain a fixed ground track, the faint air-drag at this high altitude must also be counter-acted by orbit raising manoeuvres in the form of thruster burns tangential to the orbit.

#### Orbital station-keeping in geostationary orbit

For geostationary spacecraft, thruster burns orthogonal to the orbital plane must be executed to compensate for the effect of the lunar/solar gravitation that perturbs the orbit pole.

#### Orbital station-keeping at libration points

Orbits around libration points are dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use propulsion systems to perform orbital station-keeping.