Physics orbiting satellite?

Question

When in orbit, a communication satellite attracts the earth with a force of F and the earth-satellite gravitational potential energy (relative to zero at infinite separation) is - U

a) What is the satellite's altitude above the earth's surface?
b) What is the mass of the satellite?

Answer 1

The force of attraction (F) is related to altitude of satellite (mas m) [R + h] where h is altitude above earth surface and R- radius of earth (mass -M, grav. acceleration g = GM/R^2) as follows

F = G M m / (R+h)^2 ----------(1)

PE of satellite = - U = - G M m / (R+h) ------(2)

h >>> infinity 1 / (R+h) >>> 0 PE = 0 (maximum for this attractive force field)

(a) eliminating G M m from (1) & (2)

we get altitude of satellite above earth surface
h = (U / F) - R [ al least R has to be known]

(b) mass of satellite = G M m / F

(R+h)^2 = G M m / F (from -1)
(R+h)^2 = G^2 M^2 m^2 / U^2 (from -2) equate

G M m / F = G^2 M^2 m^2 / U^2

U^2 / F = G M m

m = U^2 / G M F [ but GM = g * R^2 ] where g 9.8 m/s^2

m = U^2 / g R^2 F
answer

Answer 2

ry0534 has the 1st 3 questions suited yet I disagree on the spectacular 2. 4) the mass of the satellite tv for pc is beside the point in calculating speed because of the fact it gets canceled out. F= (G*M*m)/r^2 v= sqrt(F*r/m) subsequently v= sqrt(G*M/r) 5) the ratio of the era (T) of the orbit to the radius of the orbit is: T(preliminary)^2/ r(preliminary)^3 = T(very final)^2/ r(very final)^3

Answer 3

see the link