(Solution Download) The position of a comet with a highly eccentric elliptical

The position of a comet with a highly eccentric elliptical orbit (e very near 1) is measured with respect to a fixed polar axis (sun is at a focus but the polar axis is not an axis of the ellipse) at two times, giving the two points (4, ?/2) and (3, ?/4) of the orbit. Here distances are measured in astronomical units (1 AU ?. 93 million miles). For the part of the orbit near the sun, assume that e = 1, so the orbit is given by

a. The two points give two conditions for d and ?0. Use them to show that 4.24 cos ?0 - 3.76 sin ?0 - 2 = 0.
b. Solve for 00 using Newton's Method.
c. How close does the comet get to the sun?

 

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