The orbital period is simply how long an orbiting body takes to complete one orbit.
Specifying orbits
It turns out that it takes a minimum 6 numbers to specify an orbit about a body, and this can be done in several ways. For example, specifying the 3 numbers specifying location and 3 specifying the velocity of a body gives a unique orbit that can be calculated forwards (or backwards). 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 Kepler's laws. The Keplerian elements are six:
- Inclination (
)
- Longitude of the ascending node (
)
- Argument of periapsis (
)
- Eccentricity (
)
- Semimajor axis (
)
- Mean anomaly at epoch (
)
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 forces other than gravity due to the central body and thus the orbital elements change over time.
Orbital 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, 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 given 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.
Orbital decay
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 solar maxima, the Earth's atmosphere causes drag up to a hundred kilometres higher than during solar minima.
Some satellites with long conductive tethers can also decay because of electromagnetic drag from the Earth's magnetic field. Basically, the wire cuts the magnetic field, and acts as a generator. The wire moves electrons from the near vacuum on one end to the near-vacuum on the other end. The orbital energy is converted to heat in the wire.
Orbits can be artificially influenced through the use of rocket motors 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 also 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.
Finally, 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.
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 quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body.
The general effect of this is to change the orbital parameters over time; predominantly this gives a rotation of the orbital plane around the rotational pole of the central body (it perturbs the argument of perigee) in a way that is dependent on the angle of orbital plane to the equator as well as altitude at perigee.
Multiple gravitating bodies
The effects of other gravitating bodies can be very large. For example, the orbit of the Moon cannot in any way be accurately described without allowing for the action of the Sun's gravity as well as the Earth's.
In general 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 there are number of special cases.
Light radiation and stellar wind
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 quite significant. Of the planetary bodies, the motion of asteroids is particularly affected over large periods when the asteroids are rotating relative to the Sun.
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