If the distance between the earth and the sun were half its present value, the number of days in a year would have been

Explanation

Here, `T_(1)` is `(= 1 year)` the present time period of revolution of earth around the sun and `R` is the present radius of orbital path of earth around sun.
When the distance between the earth and sun is `R' = R + 2R = 3R`, let `T_(2)` be the time period of revolution of earth the sun. Then
`(T_(2)^(2))/(T_(1)^(2)) = ((3R)^(3))/(R^(3)) = 27`
or `T_(2) = T_(1) sqrt(27) = 1 sqrt(27) = 3 sqrt(3) = 3 xx 1.732`
`= 5.196 years`