First slide

Gravitational force and laws

Question

If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been

Moderate

A

64.5
B

129
C

182.5
D

730

Solution

According to Kepler's third law, the ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distances from the sun i.e.
$\begin{array}{l} {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{r_{1}}{r_{2}})}^{3} = {[\frac{r_{1}}{\frac{1}{2} r_{1}}]}^{3} = 8 \Rightarrow \frac{T_{1}}{T_{2}} = 2 \sqrt{2} \\ ∴ T_{2} = \frac{T_{1}}{2 \sqrt{2}} = \frac{365 days}{2 \sqrt{2}} = 129 days \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App