Question

A satellite orbits the Earth with an elliptical orbit modeled by x squared over 43 million eight hundred twenty four thousand four hundred plus y squared over forty seven million one hundred ninety six thousand nine hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?

250 km
500 km
6,620 km
6,870 km

Answer 1

The maximum distance between the satellite and the Earth is 6620 km.

Step-by-step explanation:

To find the maximum distance between the satellite and the Earth, we need to determine the semi-major axis of the elliptical orbit. In this case, the semi-major axis is represented by the square root of the denominator in the equation that models the orbit: x^2/43,824,400 + y^2/47,196,900 = 1. The semi-major axis is equal to the square root of 43,824,400, which is approximately 6620 km.

Therefore, the maximum distance between the satellite and the Earth is 6620 km.