Question

Earth's gravitational parameter is μ=398600 km³/s². Earth's radius is RE​=6378 km. An unmanned satellite orbits the earth with a perigee radius of 20,000 km and an apogee radius 150,000 km.

Calculate: the eccentricity of the orbit

Answer 1

The eccentricity of the satellite's orbit, given a perigee radius of 20,000 km and an apogee radius of 150,000 km, is approximately 0.7059.

Step-by-step explanation:

To calculate the eccentricity of an orbit for a satellite, you need to know the perigee and apogee distances. The perigee distance (closest point to Earth) is given to be 20,000 km. The apogee distance (farthest point from Earth) is 150,000 km. The equation for eccentricity (e) is e = (apogee - perigee) / (apogee + perigee). First convert these distances to the distances from the center of the Earth by adding the radius of the Earth (RE) to both the perigee and apogee distances.

Perigee radius = 20,000 km + RE = 20,000 km + 6378 km = 26378 km
Apogee radius = 150,000 km + RE = 150,000 km + 6378 km = 156378 km

Now, plug the values into the eccentricity formula:

e = (156378 km - 26378 km) / (156378 km + 26378 km)
e = 129,000 km / 182,756 km
e = 0.7059

The eccentricity of the satellite's orbit is approximately 0.7059.