I was just watching some video and reading some articles to learn the basics of orbital mechanics. I find it to be an interesting subject. The basics seem to be that to catch up to another craft in your same orbit it's necessary to go into a lower orbit (and go into a higher orbit if you need to slow down). The slower speed of a higher orbit is due to the reduced effect of gravity. A burn in an orbit changes the shape of that orbit except for the spot where the burn is executed. To move from one circular orbit to another circular orbit requires two burns as the first will create an elliptical orbit and a second at the opposite side of the orbit will be required to change that elliptical orbit to a circular orbit. A burn with the nose of the craft facing the direction of travel is a prograde burn and when the nose is opposite the direction of travel it's a retrograde burn. A retrograde burn is frequently used to slow down and to change the elliptical orbit to one that allows for reentry. A craft in orbit (around the Earth for example) is actually continuously falling and that is why its occupants experience weightlessness (just as a skydiver does before the chute opens). It's not because one is weightless in space due to the absence of gravity. Earth's gravity is still there. The particular orbit is just big enough for the craft to miss the Earth as it's continuously falling. Anyone with more knowledge (than me) on this subject (not hard to do) please correct anything I've said and add anything else that you finding interesting regarding this subject.
Seems OK Seattle, but I can only offer certainty in accuracy with the last two paragraphs concerning retrograde and prograde burns and of course the factual detail of orbital free fall.
This results in the very non-intuitive conclusion that you have to thrust away from an object in orbit in order to move closer to it. From a very old NASA article about these problems: ============ Meanwhile, on Gemini-IV, a naive and poorly-prepared plan for stationkeeping with the Titan-ll booster's second stage fell afoul of orbital mechanics when the pilot, relying on airplane instincts, attempted to overtake the booster from behind and above by thrusting towards it, thus actually building up his orbital energy and flying past into a higher orbit which rapidly pulled him away from the target . The behind/above region of the relative motion plot was later privately dubbed "the McDivitt Quadrant" by rendezvous planners; many years later, during a briefing for the Solar Max mission, MS "T.J." Hart expressed his sincere intention to succeed so that there never would be any such thing as a "Hart Quadrant". Themission report plus Hacker's narrative, plus Aldrin's pointed criticisms, show what happened and why, and how the embarrassment had a major positive role in demonstrating that orbital rendezvous had to be taken seriously by astronauts, it couldn't be done with existing instincts and reflexes. ==============
