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, Iuml 2) and (3, Iuml 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 Icirc cedil 0 Use them to show that 4 24 cos Icirc cedil 0 3 76 sin Icirc cedil 0 2 0 b Solve for 00 using Newton 's Method c How close does the comet get to the sun 1 cos(O a )

Question: 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

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, Ï€/2) and (3, Ï€/4) of the orbit. Here distances are measured in astronomical units (1 AU ‰ˆ. 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 Î¸0. Use them to show that 4.24 cos Î¸0 - 3.76 sin Î¸0 - 2 = 0.
b. Solve for 00 using Newton's Method.
c. How close does the comet get to the sun?

1 + cos(O-a.)

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