- #1

- 14

- 0

## 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.