Question

The mean distance of mars from sun is $1.5$ times that of earth from sun. What is approximately the number of years required by mars to make one revolution about sun?

• A. $2.35$ years
• B. $1.85$ years
• C. $3.65$ years
• D. $2.75$ years

Answer 1

The correct option is B $1.85$ years

Kepler's law tells us that the square of the Time period $\left(T\right)$ of a satellite is proportional to the cube of its distance $\left(R\right)$ from the orbitting planet.

$\therefore T^2\propto R^3$

The time period of earth's orbit around the sun is 1 year, and assuming the mean distance between earth and sun as $R$,

we can write the mean distance between mars and sun as $1.5R$.

Let, $T$ be the time period of mars' orbit around the sun.

Thus from the above proportionality,

$\frac{T^2}{R^3}$ is a constant.

$\therefore \frac{(1\text{year}{)}^2}{R^3}=\frac{T^2}{(1.5R{)}^3}$

$\therefore T^2=(1.5{)}^3$

$\therefore T=(1.5{)}^{3/2}\approx 1.85$ years

Therefore, mars takes approximately 1.85 years to make one revolution around the sun.