Question

Assume that the Earth rotates in a circular orbit round the Sun in 365 days. If the mass of the sun gets doubled but the radius of the orbit remains unchanged, the length of the year would be approximately

• A. 183 days
• B. 258 days
• C. 516 days
• D. 730 days

Answer 1

Answer: (B)

$T=2\pi \sqrt{\frac{R^3}{GM}}$
$T\propto \frac{1}{\sqrt{M}}\left(forgivenorbitalradius\right)$
$\frac{T_1}{T_2}=\frac{\sqrt{2M}}{\sqrt{M}}$
$T_2=\frac{T_1}{\sqrt{2}}=\frac{365}{\sqrt{2}}\approx 258days$