# Change in velocity of a circular orbit?

For a body in a circular orbit will any (i.e. however small) decrease in velocity mean it falls to earth or will it go into an elliptical orbit? I originally thought that it was the first (i.e. falls to earth) but this the answer by User58220 in this question What may be effect of air friction to the velocity of satellite? seems to take the latter point of view. Here are my reasoning,

1. The force is central and therefore never does work on the tangential component of velocity.
2. This means that it will never gain the tangential velocity it has lost and therefore never be able to return to a stable orbit and will continually gain a radial velocity towards the earth until it crash.

So which is it? Could you also give the relevant equations, thanks

• @LDC3 Would this orbit not need a negative eccentricity, given by $$\sqrt{1+\frac{2EL^2}{m\alpha^2}}$$ since in the case for a circular orbit it is already 0 and E is decreasing more? – user43487 Nov 8 '14 at 17:01