(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?

2.

Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = 11068 m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is at the surface of the moon!

3. The attempt at a solution

In our lecture concerning this topic we discussed distance= v(not) /2(μ)g, but there is no μ here clearly, so I tried not using the μ and that did not work and I dont know if I should use the formula for PE gravity close to earth or not close to earth, -G(m1m2/r)+U(not) or -G(m1m2/r^2)r. I dont understand how to get my distance without using μ.

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# A trip to the Moon!

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