Orbital Mechanics

Is basically the application of ballistics and celestial mechanics (separate post coming later) to practical problems, such as the motion of rockets or other spacecraft. Newton’s laws of motion and universal gravitation are used in calculation of these problems.

Main focus of orbital mechanics is spacecraft trajectories. There’s plenty of mathematical formulae for different situations, but for these purposes I’m just going to skip the maths (I’m really bad at math, so I’d just screw things up if I tried). You can find them online if you want to know. The practical applications of all the math are mostly orbital maneuvers, orbit plane changes and interplanetary transfers.

If two spacecraft want to dock in orbit the trailing craft cannot just fire its engines to go faster (because the trajectory will change). Multiple precisely calculated engine firings in multiple orbital periods may be required (may take anything from hours to days).

Basic transfer orbit is ellipticalAlso other options available (bi-elliptical, general).

There are a few basic points I’m going to put up here just so I have them on hand, as follows:

  • Kepler’s laws of planetary motion (abridged)
    • orbits are elliptical with the heavier body always at the center (think of the Earth and Moon) – circles are also a special case of ellipse!
    • the square of a satellite’s orbital period is proportional to the cube of it’s average distance from the planet (or sun or whatever one’s orbiting)
  • without applying force the period and shape of the satellite’s orbit won’t change
  • a satellite in a low orbit moves faster than one further out
  • if thrust is applied at only one pointin the satellite’s orbit it will return to that same point on each subsequent orbit, though the rest of it path will change
  • from a circular orbit, a thrust applied in a direction opposite to the satellite’s motion changes the orbit to an ellipse
    • it will then reach its lowest orbital point at 180 degrees away from the firing point
    • if thrust is applied towards the direction of motion, highest point is 180 degrees away

Nifty pictures may be edited in on a later date. No promises.


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