Physics- Amount Of Work Required To Knock A Satellite Out Of Orbit

A satellite is in orbit around the earth. It fires rockets to increase its speed. What happens to the average radius of its orbit?

You have to be very careful with your terminology because orbital dynamics is anything but intuitive.For example- lets take your question. If you fire a rocket to increase it’s speed you will reduce the average radius of it’s orbit. This has led to the analogy that in order to speed up- hit the brakes and in order to slow down hit the accelerator.What your rocket will do will depend on which direction you fire. If your rocket is firing backward along your spacecraft you are adding energy to your orbit and you will move to a higher orbit. However your speed will decrease.If you fire the rocket along your path- you will reduce the energy of your orbit and lower it. But your speed will increase.Incidentally the most efficient way to raise or lower the low point of the orbit is to fire the engine at the high point. The most efficient way to raise or lower the high point is to fire the engine at the low point.Firing laterally does not change your speed but it does change the plane of the orbit and is the best way to waste large amounts of fuel. Gemini 10 in the 1960s nearly had to cancel some planned activities because they got slightly out of plane wth the Agenda spacecraft with which they were rendezvousing and ended up doing an out of plane whifferdill- i.e a series of decreasing spirals around their target. The biggest fuel waster in the book.btw- for any point in your orbit the equation is v*v=G(M+m)(2/r-1/a)v is your velocityG is the Gravitational Constant of the universeM is the mass of the body you are orbiting.m is the your spacecraft. Normally this is so small relative to M that you can ignore it.r is the radius vector of your orbit.a is the semi-major axis of the orbit (one half the long axis )