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Homework Statement
You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the Earth with enough speed to make it to the moon. Some information that will help during this problem:
mass of Earth = 5.9742 x 10^24 kg
radius of Earth = 6.3781 x 10^6 m
mass of moon = 7.36 x 10^22 kg
radius of moon = 1.7374 x 10^6 m
distance from Earth to moon = 3.844 x 10^8 m (center to center)
G = 6.67428 x 10^-11 N-m2/kg2
1) On your first attempt you leave the surface of the Earth at v = 5534.0 m/s. How far from the center of the Earth will you get?
Homework Equations
Wnet = ΔKE
(G * M * m)((1/rf) - (1/ro)) = (m * v^2)/2, M = mass of Earth & m = mass of satellite
(G * M)((1/rf) - (1/ro)) = (v^2)/2
The Attempt at a Solution
ro = radius of Earth (?)
(rf^-1 - ro^-1) = (.5v^2)/(G * M)
rf^-1 = ((v^2)/(2G*M)) - (ro^-1)
rf = (((v^2)/(2GM)) - (ro^-1))^-1
I plugged in the corresponding values, but they seem to be wrong. I got 26022994.95 m.