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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

Let

a = 51,390km/2 = 25,695 km be the semi-major axis,

b = 49,255km/2 = 24,627.5 km be the semi-minor axis,

c = √(a²-b²) = 7329 km be the linear eccentricity.

Then the apogee is

a + c = 33024 km