Ellipse Word Problem. Explanation/(answer)

Question

The Moon orbits the Earth in an elliptical path with the center of Earth at one focus. The major and minor axes of the orbit have lengths of 768,800 kilometers and 767,640 kilometers, respectively. a) Find the greatest distance, called the apogee, and the lest distance, called the perigee, from Earth's center to the moon's center.

Answer 1

2a = 768800; a = 384400 km; 2b = 767640; b = 383820 km; c = (a² - b²)^1/2 = (384400² - 383820²)^1/2 =

21108.47

Apogee = a + c = 405508.47 km

Perigee = a - c = 363291.53 km