If the distance of the earth from the sun suddenly decreases to half its present value, then how many days will make a year ?

Explanation

Let the present distance of the earth from the sun =r, time period (T) =365 d.
If distance decreases to `r/2` , the corresponding time period is `T_1` (say).
Following Kepler.s law,
`(T^2)/(r^3)=(T_1^2)/(r_1^3) or, T_1^2=T^2*(r_1^3)/(r^3)`
or, `T_1=Tsqrt(r_1^3/r^3) =365 sqrt((r/2)^3/(r^3))=365 sqrt(1/8)=(365)/(2sqrt(2))=129 d.`