How far will Comet Halley be from the Sun when it reaches its farthest point from the Sun,or aphelion,if its sidereal period is 76 years? (Caution: This calculation needs Kepler''s law and a little care.Assume that the comet''s perihelion distance from the Sun is negligible.)

Question

Quizplus · Accepted Answer

According to Kepler's laws, the square of a planet's sidereal period is proportional to the cube of its average distance from the Sun. The same holds true for comets orbiting the Sun. Therefore, if Comet Halley's sidereal period is 76 years, then its average distance from the Sun cubed is proportional to 76 squared.

We know that at its perihelion, Comet Halley gets as close as 0.586 AU to the Sun. Since this distance is negligible compared to the distance at aphelion, we can assume that the average distance from the Sun is the same as the aphelion distance. Therefore, we can solve for this distance by setting up the following proportion:

(aphelion distance)^3 = (76 years)^2
(aphelion distance)^3 = 5776
aphelion distance = 36 AU

Therefore, the correct answer is D: about 36 AU, between the orbits of Neptune and Pluto.

How Far Will Comet Halley Be from the Sun When