satellites need help?

Question

A satellite is placed in orbit 7.50 105 m above the surface of the planet Jupiter. Jupiter has a mass of 1.90 1027 kg and a radius of 7.14 107 m. Find the orbital speed of the satellite.

Answer 1

First a few equations:

Universal gravitation: F = Gm1m2/r^2
Newton's 2nd: F = ma

Set these equal to each other:

ma = Gm1m2/r^2

One mass (the satellite) cancels out leaving

a = G m/r^2 (the mass in this case is Jupiter)

An object moving in a circle has centripetal acceleration.

a = v^2/r

Set the two acceleration equations equal to each other.

v^2/r = Gm/r^2

Rearrange for v

v = sqroot(Gm/r)

Now, G = 6.67 x 10^-11 (Universal Grav. Constant)
m = 1.9 x 10^27 kg
and r = 7.14 x 10^7 m + 7.5 x 10 ^5 m = 72150000 m

Solving for v gives:

v = 41910 m/s

Answer 2

assuming orbit is circular... if not impossible to do
F=m(v^2/r)
F=(Gmm)/r^2
(mv^2)/r=(Gmm)/r^2
rv^2=Gm
v=sqrt((Gm)/r)
v=sqrt(((6.67x10^-11)(1.90x10^27))/(7.14x10^7+7.5x10^5))
v=41910m/s