If the earth be one-half of its present distance from the sun, how many days will be in one year ?

Explanation

If orbit of earth's radius is R, in previous example we've discussed that time period is given as
`T = 2pi r sqrt((r )/(Gm)) = (2pi)/(sqrt(GM))r^(3//2)`
If radius changes or r' `= (r )/(2)`, new time period becomes
`T' = (2pi)/(sqrt(GM))r^(3//2)`
or `T' = T((r')/(r ))^(3//2)`
`= 365((1)/(2))^(3//2) = (365)/(2sqrt(2))` days