   Chapter 7, Problem 45P

Chapter
Section
Textbook Problem

A comet has a period of 76.3 years and moves in an elliptical orbit in which its perihelion (Closest approach to the Sun) is 0.610 AU. Find (a) the semimajor axis of the comet and (b) an estimate of the comet’s maximum distance from the Sun, both in astronomical units.

(a)

To determine
The semi major axis of the comet.

Explanation

Given info: The period of the comet is 76.3yr and the constant KS is 1yr2/AU3 .

Explanation: The semi major axis of the comet is determined from Kepler’s third law T2=KSa3 .

The formula for the semi major axis of the comet is,

a=(T2KS)1/3

• T is period of the comet.
• KS is Kepler’s constant.

Substitute 76

(b)

To determine
The maximum distance of the comet from the Sun.

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