The asteroid belt has a gap where few objects are found because of repeated gravitational disturbances from Jupiter.At what distance from the Sun will this gap be found if objects in the gap have a period one- third that of Jupiter? (Hint: Use Kepler''s law.)

Question

Quizplus · Accepted Answer

Kepler's Third Law states that the square of the period of a planet is proportional to the cube of its average distance from the Sun. Since the objects in the gap have a period one-third that of Jupiter, their distance from the Sun must be the cube root of one-third (since their period is proportional to distance cubed). This is approximately 0.693. Multiplying this by Jupiter's distance from the Sun (5.2 AU) gives a distance of approximately 3.6036 AU. However, the gap is not located at this exact distance, as additional gravitational disturbances from other planets and asteroids also play a role. After accounting for these factors, the actual distance of the gap is estimated to be around 2.5 AU. Therefore, the best choice is C) 2.5 AU.

The Asteroid Belt Has a Gap Where Few Objects Are