Question

It takes Venus 225 days to orbit the sun. If the Earth-sun distance is 1.5 × 1011 m, what is the mean distance between Venus and the Sun?

Answer 1

The mean distance between Venus and the Sun is $1.0864\times 10^{11}(m)$.

Explanation:

1. From Kepler's law, we know relation between time period of rotation and radius  is $T^{2}\propto R^{3}$

2.   Above relation can be written as

     $\frac{T_{2}^{2}}{T_{1}^{2}} = \frac{R_{2}^{3}}{R_{1}^{3}}$     ...a)

3. In equation a)

    $T_{1}$ is rotation period of earth about sun, which is 365 days.

    ${T_{2}$ is rotation period of venus about sun, which is 225 days.

   $R_{1}$ is mean radius between earth and sun, which is $1.5\times 10^{11} (m)$.

  ${R_{2}$ is mean radius between venus and sun.

4. Now from equation a)

 $\frac{R_{2}^{3}}{R_{1}^{3}} = \frac{T_{2}^{2}}{T_{1}^{2}}$

$\frac{R_{2}^{3}}{(1.5\times 10^{11})^{3}}= \frac{225^{2}}{365^{2}}$ ...b)

5. On solving equation b) , we get

  $R_{2}$ = $1.0864\times 10^{11}(m)$

  above value is distance between venus and sun.