Lunar Orbit For an object in an elliptical orbit around the moon, the points in the orbit that are closest to and farthest from the center of the moon are called perilune and apolune, respectively. These are the vertices of the orbit. The Apollo 11 spacecraft was placed in a lunar orbit with perilune at mi and apolune at mi above the surface of the moon. Assuming that the moon is a sphere of radius mi, find an equation for the orbit of Apollo 11. (Place the coordinate axes so that the origin is at the center of the orbit and the foci are located on the x-axis).
The equation of orbit of Apollo .
From the figure, radius of moon is , the distance between spacecraft and moon at perilune is and distance between spacecraft and moon at apolune is .
Let the coordinates of spacecraft be at perilune and at apolune and let the moon be at one of the foci .
Equation of ellipse with foci at and , major axis and minor axis is:
Eccentricity for this ellipse is given by,
The value of can be calculated as,
The distance between spacecraft and moon at perilune is which is equal to
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