Question

If distance between earth and sun become four times then time period becomes

• A. 4 times
• B. 8 times
• C. 1/4 times
• D. 1/8 times

Answer 1

Answer: (B)

8 times

Answer 2

According to Kepler's third law (law of periods),
$T^{2} \propto R^{3}$
where $T$ is time taken by the planet to go once around the sun $R$ is semimajor axis (distance) of the elliptical orbit.
$=T^{2} \propto k R^{3}$
(where $k$ is constant of proportionality)
When $R$ becomes $4$ times let time period be $T$'.
$=T^{2}=k(4 R)^{3}$
$=\frac{T^{2}}{T^{2}}=\frac{1}{64}$
or $\frac{T}{T'}=\frac{1}{8}$
or $T'=8 T$
So, time period becomes $8$ times of previous value.