The period of Jupiter's orbit around the Sun is approximately 12 years. What is the approximate distance from the Sun to Jupiter
A)144 AU
B)1728 AU
C)42 AU
D)5.2 AU
E)2.3 AU

Question

Quizplus · Accepted Answer

Jupiter's period of orbit around the Sun is approximately 12 years. We can use Kepler's third law to find the distance from the Sun to Jupiter.

Kepler's third law states that:

(T1/T2)^2 = (R1/R2)^3
where T is the period of orbit and R is the average distance from the center of mass.

If we let T1 be the period of Jupiter and T2 be the period of Earth (1 year), then:

(T1/1)^2 = (R1/1 AU)^3
T1^2 = R1^3
R1 = T1^(2/3)

Substituting in T1 = 12 years, we get:

R1 = (12)^ (2/3) = 5.2 AU

Therefore, the approximate distance from the Sun to Jupiter is 5.2 AU. The answer is D).

The Period of Jupiter's Orbit Around the Sun Is Approximately