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

Hey Dear,

◆ Answer -

Orbital period of Jupiter = 4344 days

● Explaination -

Kepler’s Law of Periods states that the square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit.

i.e. T^2 ∝ R^3

For Mars & Jupiter,

(Tm/Tj)^2 = (Rm/Rj)^3

Substituting values,

(687/Tj)^2 = (1.52/5.2)^3

(Tj/687)^2 = 3.42^3

(Tj/687)^2 = 40

Tj = 687 × √40

Tj = 4344 days

Therefore, orbital period of jupiter will be approx 4344 days.

* Data has been manipulated as orbital period of the planet depends upon its mean distance from the sun (not from the earth).

Thanks dear.