Question

The moon is a sphere with radius of 408 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 781 km to 562 km.

Answer 1

Let us consider the moon is at the center and the satellite is revolving around it in an elliptical orbit.

The center of the moon is the center of the satellites orbit. Center is (0,0)

Now if you look at the drawing the vertices of the ellipse are at (1189 , 0) and (-1189,0) , X axis is the major axis. . This is your 'a'

The other two vertices are (0,970)and ( 0, -970) Y - axis is the minor axis. This is your 'b'.

Now the standard form of an equation for ellipse is \[\frac{ x ^{2} }{ a ^{2} } + \frac{ y ^{2} }{ b ^{2} } = 1\]

Now you know what a and b are. just substitute this in the standard equation and get your answer