Final answer:
The eccentricity of the satellite's elliptical orbit around Earth is calculated using the apogee and perigee distances from the center of Earth and is found to be 0.59.
"The correct option is approximately option C"
Step-by-step explanation:
The question asks for the eccentricity of an Earth satellite's elliptical orbit given its perigee altitude, apogee altitude, and the length of the semi-major axis. To find the eccentricity of the orbit, we can use the formula e = (ap - pe) / (ap + pe), where ap is the apogee distance from the center of the Earth and pe is the perigee distance from the center of the Earth.
To calculate these distances, we need to add Earth's radius (6371 km taken as an average value) to the altitude of the orbit at the respective points. Thus, the apogee distance is 20,000 km + 6371 km = 26,371 km, and the perigee distance is 400 km + 6371 km = 6,771 km.
Plugging these values into the formula gives us:
e = (26371 - 6771) / (26371 + 6771) = 19600 / 33142 ≈ 0.59
Therefore, the eccentricity of the satellite's orbit is 0.59, which corresponds to option c.