Kepler's third law for orbits around the Sun is a³ = P² where the semimajor axis is in au, and the period P is in years. For objects in orbit around Jupiter, one must use a³ = 0.001 P² because the mass of Jupiter in solar masses is approximately 0.001. The period for Comet Shoemaker-Levy 9 in its orbit around Jupiter was about 2 years. What was its maximum distance from Jupiter in this orbit (in u)? A) 0.05 B) 0.16 C) 0.32 D) 0.48

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Quizplus · Accepted Answer

Using Kepler's third law for orbits around Jupiter, $a^3 = 0.001P^2$, where $P = 2$ years for Comet Shoemaker-Levy 9. Substituting $P = 2$ into the equation gives $a^3 = 0.001(2)^2 = 0.004$. Taking the cube root of both sides, $a = \sqrt[3]{0.004} \approx 0.16$, which is the semimajor axis in astronomical units (au). However, the question asks for the maximum distance from Jupiter, which for an elliptical orbit is the same as the semimajor axis in this context, making 0.16 the correct answer.

Kepler's Third Law for Orbits Around the Sun Is A3

Kepler's Third Law for Orbits Around the Sun Is A³