I I need help thank you

Question

The moon Titan orbits Saturn in an elliptical path with the center of Saturn at one focus. The major and minor axes of the orbit have lengths of 51,390 km and 49,255 km, respectively. Find the greatest distance, called the apogee, from Titan to Saturn.

Answer 1

The dimensions of an ellipse follow the pattern of a right triangle, except we have a² = b² + c².

Here, a represents 1/2 the length of the major axis (or, the distance from the center to a vertex), b represents 1/2 the length of the minor axis (or, the distance from the center to a covertex), and c represents the distance from the center to a focus. Drawing a quick diagram will demonstrate that, at its apogee, Titan will be at a distance = a + c from Saturn: Titan--------------a--------------ctr-----c-----Saturn

a = 25,695 km. b = 24,627.5 km (25,695)² = (24,627.5)² + c² c ~ 7,329 km

apogee distance from Titan to Saturn ~ 33,024 km