At what speed must a satellite of a mass M be launched horizontally at the surface of the earth if it's orbit is to be a circle just grazing the highest mountains?( assume no air resistance). How much time would elapse between successive passes of this imaginary satillite?

Answer 1

Having been a member of the Southwestern Rocket Society in its infant days, we learned that launching rockets horizontally was dangerous.

At the altidude of the highest mountains, say 10^4 meters, then

the gravitational field strength g, is given by
9.8Nt/kg * (re/(re+10^4))^2
look up the radius of the earth re, in meters, and you have that part.
Then that gravational field strength mus be equal to centripetal acceleration, which is

acceleartion= V^2/(re+10^4) where
v is 2PI(re+10^4)/Period

set them equal, solve for Period.