The distance between Sun and Earth is R . The duration of year if the distance between Sun and Earth becomes…

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :
  1. 3 yr 
  2. 33 yr
  3. 3 yr 
  4. 9 yr

Solution

According to Kepler's Third Law – The Law of Periods,

         T2∝R3

where T is time taken by the planet to go once around the sun and R is the semi-major axis (distance) of the elliptical orbit.

∴ T2=k R3   …(i)

Where k is a constant of proportionality.

When R becomes 3 times, let the time period be T'.

∴                    T'2=k(3R)3             …(ii)

∴                    T2T'2=127

So, time period will be 33 yr.

Asked in: JEE Main 2022 (24 Jun Shift 2)

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