You plan to take a trip to the moon. Since you do not have atraditional spaceship with rockets, you will need to leave theearth with enough speed to make it to the moon. Some informationthat 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 m/s. How far from the center of the earth will you get?
2) Since that is not far enough, you consult a friend whocalculates (correctly) the minimum speed needed as vmin = 11068m/s. If you leave the surface of the earth at this speed, how fastwill you be moving at the surface of the moon? Hint carefully writeout an expression for the potential and kinetic energy of the shipon the surface of earth, and on the surface of moon. Be sure toinclude the gravitational potential energy of the earth even whenthe ship is at the surface of the moon!
(Please inlude step-by-step solution or even an online video linkthat can teach me this as well)
