Question #5ba10

1 Answer
Apr 9, 2016

Answer:

please see below

Explanation:

If we apply Newton's law, the force due to gravity will be
#F=(GMm)/r^2#

The satellite moves in a circular orbit, and the centripetal force must be provided by the gravitational force. So for a stable orbit
#F=(mv^2)/r=(GMm)/r^2#

So if the velocity is too high, then

#(mv^2)/r>(GMm)/r^2#

The force of gravity is insufficient to maintain the satellite in a circular orbit and the satellite will "fly off into space" unless it can be directed into an orbit of lower radius.

Or seen another way, rearranging the above equations gives:
#GM=r*v^2#
Since #GM# is constant, if #v# is too high, #r# must be reduced (or the satellite will not maintain its orbit).

If velocity is too low:
#(mv^2)/r<(GMm)/r^2#
The force gravity exceeds the centripetal force required. Unless the orbit can be moved to a larger radius (reducing the force of gravity until the above are in equilibrium), the satellite will spiral in towards the earth.