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 yr.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

Using Kepler's laws of planetary motion, we know that the square of the period of revolution (T) is proportional to the cube of the semi-major axis (a) of the orbit.

T^2 ∝ a^3

Rearranging the equation, we get:

a = (T^2)^(1/3)

a = (8.0)^{2/3}

a ≈ 3.07

The asteroid's semi-major axis is approximately 3.07 AU.

The distance between the aphelion (farthest distance from the Sun) and the perihelion (closest distance to the Sun) is twice the semi-major axis.

2a ≈ 6.14 AU

Rounding off to the nearest decimal, the greatest distance from the Sun (aphelion) is 6.5 AU.

Therefore, the best choice is B) 6.5 AU.

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