Question

The Earth is an average distance of 1.50 x 10^11 m from the Sun and orbits it every 365.25 days. If Jupiter is an average distance of 7.79 x 10^11 m away, use Kepler's 3rd law to find its orbital period?

a) 12.5 years
b) 1.85 years
c) 3.65 years
d) 28.75 years

Answer 1

To find the orbital period of Jupiter using Kepler's third law, we can calculate the ratio of its average distance to that of Earth and raise it to the power of 1.5 (cubed root). By multiplying this ratio by Earth's orbital period, we find that Jupiter's orbital period is approximately 4,332.99 days.

Step-by-step explanation:

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun. We can use this law to find the orbital period of Jupiter.

Given that the Earth's average distance from the Sun is 1.50 x 1011 m and its orbital period is 365.25 days, we can find the ratio of the average distance of Jupiter (7.79 x 1011 m) to the average distance of the Earth and raise it to the power of 1.5 (cubed root).

This calculation gives us a value of approximately 11.86, which represents the ratio of the orbital periods of Jupiter to the Earth. Multiplying the Earth's orbital period by this ratio, we find that Jupiter's orbital period is approximately 11.86 x 365.25 days, which is equal to 4,332.99 days.