Question

Use Kepler's third law to determine how many days it takes a spacecraft to travel in an elliptical orbit from a point 6 965 km from the Earth's center to the Moon, 385 000 km from the Earth's center.

Answer 1

Answer:

0.0665 days

Explanation:

We are given;

The mean distance from the Earth's center to the moon;a1 = 385000 km

The mean distance from the Earth's center to the space craft;a2 = 6965 km

Formula for kepplers third law is;

T² = 4π²a³/GM

However, the proportion of both distances would be;

(T1)²/(T2)² = (a1)³/(a2)³

Where;

T1 is the period of orbit of the moon around the earth. T1 has a standard value of 27.322 days

T2 is the period of the space craft orbit.

Making T2 the subject, we have;

T2 = √((T1)²×(a2)³)/(a1)³)

Thus, plugging in the relevant values;

T2 = √(27.322² × 6965³)/(385000)³

T2 = 0.0665 days