Problem 1 Find the mass of the Moon On July 19 1969 the Apol

Problem 1 Find the mass of the Moon.

On July 19, 1969 the Apollo-11 Command Service Module and LEM entered orbit around the Moon. The orbital period was 2.0 hours and the space- craft was a distance of 1,737 km from the center of the Moon. These two pieces of information to determine the mass of the Moon. To do this balance gravitational force of the Moon on the spacecraft, Fg, with the centrifugal acceleration, Fc,

Fg = GMm/R^2

Fc = mV^2/R

To find V you will need the circumference of the orbit, divided by the period.

Solution

time period T = 2piR / v

(2 x 3600 sec) = (2 x pi x 1737 x 10^3 ) / v

v = 1515.82 m/s

centrifugal acc. a_c = v^2 / R = (1515.82^2) / (1737 x 10^3)

= 1.32 m/s^2