When it orbited the Moon, the Apollo 11 spacecraft’s mass was 14800 kg, and its mean distance from the Moon’s center was 1.79877 × 106 m. Assume its orbit was circular and the Moon to be a uniform sphere of mass 7.36 × 1022 kg. Given the gravitational constant G is 6.67259 × 10−11 N m2 /kg2 , what is the minimum energy required for the craft to leave the orbit and escape the Moon’s gravitational field?

Explanation:

If M be mass of moon and m be mass of spacecraft

potential energy of moon -spacecraft system

= - G M m / R where R is radius of orbit of spacecraft

kinetic energy of spacecraft in the orbit

= 1/2 m v² = GMm / 2R

Total energy of spacecraft

=  GMm / 2R  - G M m / R

= - GMm / 2R

for spacecraft to leave the orbit,  energy required

= GMm / 2R

= 6.67259 x 10⁻¹¹ x  7.36 x 10²² x 14800 / (2 x 1.79877 x 10⁶)

= 202035.8 x 10⁵ J .

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered