Off topic but I have never understood this quote. can anyone please explain. "In order to go fast, slow down, anybody who has learnt orbital mechanics know this"
My understanding is as follows:
Lower orbits are faster because you need more radial ("forward" or outward) velocity to keep the orbit in equilibrium with the stronger pull of gravity as you get closer to the orbited body. In to reach a lower orbit from a higher one, though, and thus go faster, you essentially must slow down (remove energy) to fall toward the body which results in a faster speed when you reach the other side of the orbit
Very distant objects need very little speed to orbit, take for instance a geosynchronous orbit that orbits every 24 hours, which enables it to hover over the same part of the equator indefinitely.
With a braking burn from geosync orbit your orbital period would keep decreasing from 24 hours as your orbital velocity keeps increasing. The ISS and similar low earth orbits have a period of 90 minutes.
Keep in mind if trying to speed up/catch another object you can just use more thrust and keep adjusting your angle. But it's fuel intensive and when you stop thrusting you might well be in a crazy orbit, very different than the target you are trying to catch.
There's a game called Osmos on most platforms that turns this kind of thing into a game, I recommend it. As mentioned elsewhere there's kerbel space program, however there's much more than orbital mechanics involved.
