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

Options

A. 730
B. 182.5
C. 129
D. 64.5

Answer

C

Explanation

By Kepler's law, `T^(2)prop R^(3)`
`therefore ((T_(1))/(T_(2)))^(2)=((R_(1))/(R_(2)))^(3)=((2R_(2))/(R_(2)))^(3)=8`
`therefore (T_(1))/(T_(2))=2sqrt(2)`
or `T_(2)=(T_(1))/(2sqrt(2))=(365)/(2sqrt(2))=(365)/(2xx1.414)=129` days