Question

The moon orbits Earth every 27.3 days and has an average distance of3.8✕10^8from the center of the Earth. Find the period if a satellite orbits 1500 km above Earth.

a. 0.92 days
b. 1.08 days
c. 1.22 days
d. 1.37 days

Answer 1

The period of the satellite is approximately 1.08 days.

Step-by-step explanation:

According to Kepler's third law of planetary motion, the period of an orbiting satellite is related to its distance from the center of the Earth. The period (T) and radius of orbit (r) are related by the equation T^2 = 4π^2r^3/GM, where G is the gravitational constant and M is the mass of the Earth. In this case, the satellite orbits at an average altitude of 1500 km above Earth's surface. To find the period, we need to calculate the radius by adding the height of the satellite to the radius of the Earth, then substituting the values into the equation.

The radius of Earth is 6380 km. Adding 1500 km to this gives a radius (r) of 7880 km.

Substituting the values into the equation, we get T^2 = 4π^2(7880)^3/GM. Solving for T, we find T ≈ 1.08 days.