If the distance between earth and the sun becomes 1/4 its present  value, the number  of days in a year would been what and How ?

If the distance between earth and the sun becomes 1/4 its present value, the number of days in a year would been what and How ?

We know gravitational force acting between the sun and the earth responsible for providing the necessary centripetal force to earth and making it revolve around the sun, will increases with the decrease in the distance between them following inverse square law given by Newton. As a consequence speed of the earth's revolution will also increase and as time period of revolution which can be given by:

T = 2πR/Speed 

will further decrease!

If we assume the path traced by earth to be circular while revolving then using Kepler's Inverse square law we can get the new time period of the earth, since  

T² ∝ R³ where r be the mean distance between the sun and the earth

taking ratio:

(T₁/T₂)² = (R₁/R₂)³

^⇒ (T₁/T₂) =  (R₁/R₂)^3/2 

As T₁ is the time period of the earth in the present scenario.