Could someone please explain orbital decay to me, with reference to the kinetic energy lost, and stuff like that. Also i would like to know how the equation for mechanical energy in orbits is derived, and how it is used.
Going on the assumption that you mean the decay of artificial satellite orbits, I believe that it's primarily a result of friction with the very tenuous bits of atmosphere that still exist at orbital altitudes, as Senior Frog mentioned. The same thing could happen, however, if the original orbital set-up was flawed. It could also result from collision with other orbital bodies. This is not an area that I'm particularly knowledgeable in, however, so you should wait for other opinions.
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