Editing Orbital mechanics (section)

===Rules of thumb===
The following rules of thumb are useful for situations approximated by [[classical mechanics]] under the standard assumptions of astrodynamics outlined below. The specific example discussed is of a satellite orbiting a planet, but the rules of thumb could also apply to other situations, such as orbits of small bodies around a star such as the Sun.

*[[Kepler's laws of planetary motion]]:
**Orbits are [[ellipse|elliptical]], with the heavier body at one [[focus (geometry)|focus]] of the ellipse. A special case of this is a circular orbit (a circle is a special case of ellipse) with the planet at the center.
**A line drawn from the planet to the satellite sweeps out ''equal areas in equal times'' no matter which portion of the orbit is measured.
**The square of a satellite's orbital period is proportional to the cube of its average distance from the planet.
*Without applying force (such as firing a rocket engine), the period and shape of the satellite's orbit will not change.
*A satellite in a low orbit (or a low part of an elliptical orbit) moves more quickly with respect to the surface of the planet than a satellite in a higher orbit (or a high part of an elliptical orbit), due to the stronger gravitational attraction closer to the planet.
*If thrust is applied at only one point in the satellite's orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change. Thus one cannot move from one circular orbit to another with only one brief application of thrust.
*From a circular orbit, thrust applied in a direction opposite to the satellite's motion changes the orbit to an elliptical one; the satellite will descend and reach the lowest orbital point (the [[periapse]]) at 180 degrees away from the firing point; then it will ascend back. The period of the resultant orbit will be less than that of the original circular orbit.  Thrust applied in the direction of the satellite's motion creates an elliptical orbit with its highest point ([[apoapse]]) 180 degrees away from the firing point. The period of the resultant orbit will be longer than that of the original circular orbit.

The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecrafts are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster. This will change the shape of its orbit, causing it to gain altitude and actually slow down relative to the leading craft, missing the target. The [[space rendezvous]] before docking normally takes multiple precisely calculated engine firings in multiple orbital periods, requiring hours or even days to complete.

To the extent that the standard assumptions of astrodynamics do not hold, actual trajectories will vary from those calculated. For example, simple [[atmospheric drag]] is another complicating factor for objects in [[low Earth orbit]].

These rules of thumb are decidedly inaccurate when describing two or more bodies of similar mass, such as a [[binary star system]] (see [[n-body problem]]). [[Celestial mechanics]] uses more general rules applicable to a wider variety of situations. Kepler's laws of planetary motion, which can be mathematically derived from Newton's laws, hold strictly only in describing the motion of two gravitating bodies in the absence of non-gravitational forces; they also describe parabolic and hyperbolic trajectories. In the close proximity of large objects like stars the differences between [[classical mechanics]] and [[general relativity]] also become important.