Question

The radius of Martin orbit around the Sun is about 4 times the radius of the orbits of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

Options

• 88 Earth days

• 225 Earth days

• 172 Earth days

• 124 Earth days

Answer 1

88 Earth days

Explanation:

From Kepler’s law of periods,

T² ∝ r³ → T ∝ r^3/2

`T_"Mercury"/T_"Martin" = [(r_"Mercury")/(r_"Martin")]^(3//2)`

= `(1/4)^(3//2)`

= `1/8`

`T_"Mercury" = (T_"Martin")/8`

= `687/8`

= 85.87 ≈ 88 Earth days