Question

What should be the duration of year if the distance between the sun and the earth gets doubled the present fistance

Answer 1

We can use Kepler’s 3rd law to find the duration of the year if dist between earth and sun is tripled. This law shows relationship between the distance of planets from the Sun, and their orbital periods.

According to this law the expression P^2/A^3 = k

has the same value for all the planets in the solar system. Here P is the time taken for a planet to complete an orbit round the sun, and A is the mean value between the maximum and minimum distances between the planet and sun.

The distance between earth and sun (A) is approx 150 million km.

if it is tripled.......

Now, lets assume ‘p’ is the new orbital period and ‘a’ is the new dist between earth and sun.

P^2/A^3=k=p^2/a^3

Also, a = 3A

We get p = √27 P = 5.19 P

So, the duration of new year will be 5.19 times the current earth year. That would be about 1894 days.