Find the acceleration due to gravity at an altitude of 8.00 X 10^2 km above the earth's surface.?

Question

Find the orbital velocity of a satellite at this altitude....

any help is appreciated....

Answer 1

Hi chrisco_1010

The gravitational force F on an object m a distance r from the centre of a mass M is given by:

F = GMm/r^2

The object m will feel an acceleration g (wrt the mass M) given by:

F = mg

Equate these:

mg = F = GMm/r^2

g = GM/r^2

Plug in your numbers and you get:

g = 6.673*10^-11m^3kg^-1s^-2 * 5.974*10^24kg / (7178000m)^2

g = 7.737m/s^2


For your second question you want to balance the reation to the centripetal acceleration of the satellite with the gravitational acceleration:

v^2/r = g

solve for v:

v = sqrt(gr)

Plug in your numbers:

v = sqrt(7.737m/s^2 * 7178000m)

v = 7452m/s, or 7.45km/s


Hope this helps!
The Chicken