An asteroid has a perihelion (the orbit's closest approach to the Sun) of 2.5 AU and a period of revolution of 8.0 y. What is its greatest distance from the Sun (its aphelion)? (Hint: For an elliptical orbit, the effective radius of the orbit is half the sum of the nearest distance to the Sun and the greatest distance from the Sun.)
A) 8.0 AU
B) 6.5 AU
C) 5.5 AU
D) 2.5 AU

Question

Quizplus · Accepted Answer

The semi-major axis (a) of the orbit can be found using Kepler's third law: a^3 = T^2, where T is the period in years. Here, a^3 = 8^2 = 64, so a = 4 AU. The semi-major axis is the average of the perihelion (2.5 AU) and aphelion (A). Thus, (2.5 + A)/2 = 4, solving gives A = 5.5 AU.

An Asteroid Has a Perihelion (The Orbit's Closest Approach to the Sun)