Orbit of a satellite A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as shown in the figure. The height of the satellite above the earth varies between and . Assume that the earth is a sphere with radius Find an equation for the path of the satellite with the origin at the center of the earth.
The equation for the path of a satellite with the origin at the center of the earth.
Earth is in spherical shape with radius .
Centre of the earth is .
Height of the satellite above the earth lies between and and one of its foci is at the centre of the earth.
The general equation of an ellipse is
Here, is the centre of ellipse and , are the length of major or minor axis.
Suppose that major axis of elliptical orbit is -axis.
Then, from the given figure
Here, is the length of major axis and is the radius of the earth.
Again from the figure, the distance between focus and one end of major axis is
Here, is the eccentricity.
Now, is given by
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started