Question regarding artificial satellites

[Declan McKeown]

Hey guys,

I just had a question regarding artificial satellites:

From what I understand, satellites are able to enter into a lower orbit by reducing their velocity, which makes sense because of V=2*pi*r/T

However, decreasing radius should also increase Fg and thus acceleration and thus velocity because of Fg=GMm/r^2 and also directly if you make Fc=Fg, then v^2=GM/r

I am quite confused with this because It seems that the velocity and radius of a satellite are both inversely and also directly proportionate at the same time. Could someone please explain to me how this works?

Thanks a tonne :)

 

[nasu]

The period is not a constant, it depends on radius. So you first equation does not mean what you think.
Actually, for circular orbits, the speed is highest in low orbit and decreases for higher orbits. As shown in your last equation.

But circular orbits are not the only possible ones. If the satellite is in circular orbit and you decrease the speed the orbit will became elliptic. The ellipse will be tangent with the original orbit in the point where you change speed so on this elliptical orbit the satellite will move closer to Earth.
To go back to a circular orbit but closer to Earth you will need to fire the engines one more time.