An asteroid has a perihelion (the orbit's closest approach to the sun)of 1.5 AU and a period of revolution of 8.0 y.What is its greatest distance from the sun (its aphelion)?
A) 8.0 AU
B) 6.5 AU
C) 4.0 AU
D) 2.5 AU

Question

Quizplus · Accepted Answer

We can use Kepler's laws of planetary motion to solve this problem. The third law states that the ratio of the square of a planet's period of revolution to the cube of its average distance from the sun is a constant for all planets in the solar system. Mathematically, it can be expressed as:

(T1/T2)^2 = (a1/a2)^3

where T is the period of revolution and a is the average distance from the sun. We can rearrange this equation to solve for a2, the aphelion distance:

a2 = a1(T2/T1)^(2/3)

In this case, a1 = 1.5 AU (the perihelion distance), T1 = 8.0 years, and we want to find a2. The period T2 is the same as T1, since the asteroid's orbit is fixed, so we can plug in the values:

a2 = 1.5 AU (8.0 years / 8.0 years)^(2/3) = 6.5 AU

Therefore, the asteroid's greatest distance from the sun (its aphelion) is 6.5 AU.

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