Question

If the radius of the orbit is half then the numbdr of days in 1 year will be?

Answer 1

`129` days `2.9` hours

Explanation:

The relation between radius `r` of the orbit (here considered to be Earth) and number of days `t` (`365` days `5` hours or `365 5/24=8765/24`) is given by

`r_1^3/r_2^3=T_1^2/T_2^2` i.e. `rpropT^(2/3)` or `Tpropr^(3/2)`

Hence if radius is halved, it will become

`8765/24xx(1/2)^(3/2)`

= `8765/24xx1/2.828427`

= `129.12065`

or `129` days `2.9` hours