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

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

Tardigrade Admin · Accepted Answer

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.

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