Answer to Question #87195 in Astronomy | Astrophysics for Amit

Question

The mean distance of Mars from the Earth is 0.5 A.U. and its orbital period is 687 days. Calculate the orbital period of Jupiter given that its mean distance from the Earth is 4 A.U.

Answer 1

According to the Third Kepler’s Law, the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In this case, we can write

$$\frac{T_M^2}{a_M^3} = \frac{T_J^2}{a_J^3} (1)$$

The axis of Mars a_M is 1.5 A. U. (0.5 A. U. form the Earth plus 1 A. U. between the Earth and the Sun) while the axis of Jupiter a_J is 5 A. U. (4 A. U. form the Earth plus 1 A. U. between the Earth and the Sun).

Using (1), we got:

$$T_J= \sqrt{\frac{T_M^2\times a_J^3}{a_M^3}} (2)$$

We calcuted using (2): T_J=4181 days

Answer:

4181 days