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 themoon. 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 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 atthis 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 thesurface 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 themoon!
3)Which of the following would change the minimum velocity needed to make it to the moon?
the mass of the earth
the radius of the earth
the mass of the spaceship

Answer 1

M = mass of earth, kg
m = mass of satellite, kg
G = value given in the question, N∙m²/kg²
Re = radius of earth, m
R = radius of orbit = Re + H, meters
H = altitude of orbit , meters

1) GPE = G*M*m*[1/Re - 1/R]

GPE = 361.32*103 * 10 ^8
2) KE = G*M*m/(2R)

K.E = 222.17*10 13

3) Divide (1) by (2) and find the answer

167.36 * 10 - 5

4, 5) Substitute new value for H into the above eqs and calculate new ratio.

GPE = 12935.941

KE= 1239.10 * 10 8