Use Keplers third law to determine how many days it takes a

Use Kepler\'s third law to determine how many days it takes a spacecraft to travel in an elliptical orbit from a point 6.638 km from the Earth\'s center to the Moon. 385 000 km from the Earth\'s center.

Solution

the average radius or semi-major axis is the average of the distance from Earth\'s center to the nearest and farthest points on the elliptical orbit

Kepler\'s Third Law of Planetary Motion:
T² = (4²/g R²) r³

The average of the nearest and farthest distances from Earth\'s center on the elliptical orbit is (6638 + 385000) / 2 = 195819 km.

T² = (4²/9.81 (6,378,100²) (195819*1000)³
T = 861,966.9 s
861,966.9 seconds = 9.97646875 days
T = about 10 days.