Does Reducing a Satellite's Speed Guarantee Its Descent to Earth?

[goh]

Suppose we have a satellite orbiting in circular motion around the Earth (steady velocity) in a radius R.Everything is ok now.
If suddenly we reduce the speed of the satellite is it bound to fall to the Earth ? Or it can continue moving in circular orbit with smaller R ? If i want it to fall , how can i calculate where on Earth does it fall ? And what should be the reduced speed so it will fall there ?
Ok I am not expecting from you to tell me all the exact equations to solve this but some general eplain would be useful. Thanks

 

[jtbell]

If suddenly we reduce the speed of the satellite is it bound to fall to the Earth ? Or it can continue moving in circular orbit with smaller R ?

It will start to move in an elliptical orbit whose apogee (point of maximum R) is at the point where the speed was suddenly reduced. If the perigee (point of minimum R) of the new orbit lies below the Earth's surface (or better for practical purposes, within the Earth's atmosphere), then the satellite will hit the earth.