You plan to take a trip to the moon. Since you do not have a traditional spacesh

Question

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:
mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 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?

Explanation / Answer

initial energy:

Einitial = Ue +Um + K

Ei = 6.673e-11*((5.9742e24/6.3781e6)+(7.36e22/(3.844e8-6.3781e6))) + 0.5*5534.0*5534.0

Ei = 77829821.60 J

Ef = 6.673e-11*((5.9742e24/x)+(7.36e22/(3.844e8-x)))

77829821.60 = 6.673e-11*((5.9742e24/x)+(7.36e22/(3.844e8-x)))

x = 194729539 m

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