# Sample Problem

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**Sample Problem**

Comet Halley orbits about the Sun with a period of 76 years and. in 1986. had a distance of closest approach to the Sun. its perihelion distance . shows that this is between the orbits of Mercury and Venus.

(a) What is the comet’s farthest distance from the Sun. its aphelion distance Ru?

SOLUTION:The Key idea comes from F. in which we see that RQ + R,. = la. where a is the semi major axis of the orbit of comet.

(b) What is the eccentricity e of the .orbit of comet Halley?

SOLUTION: The Key Idea here is that we can relate e, a, and Rp via Fig. 14-13. We see there that ea = a – Rp.

This cometary orbit, with an eccentricity approaching unity, is a long thin ellipse.