If Earth be at one half its present distance from the sun, how many days will there be in a 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)` ….(i)
If radius changes to `r' = (r )/(2)`, new time period become
`T' = (2pi)/(sqrt(GM))r'^(3//2)` ....(ii)
From equation (i) and (ii) we have
`(T)/(T')=((r )/(r'))^(3//2)`
or `T' = T((r')/(r ))^(3//2)`
`= 365 ((1)/(2))^(3//2) = ((365)/(2sqrt(2)))` days