Figure shows elliptical path ‘abcd’ of a planet around the sun S such that the area of triangle ‘csa’ is 1/4 the area of the ellipse. (See figure) With ‘db’ as the major axis, and ‘ca’ as the minor axis. If `t_1` is the time taken for planet to go over path ‘abc’ and `t_2` for path taken over ‘cda’ then:

Options

A. `t_(1)=3t_(2)`
B. `t_(1)=t_(2)`
C. `t_(1)=2t_(2)`
D. `t_(1)=4t_(2)`

Answer

A

Explanation

Total area `=A`
Area of `sabc=(3A)/A`
Area of `sadc=A/4`
`(3A)/(4t_(1))=A/(4t_(2))impliest_(1)=3t_(2)`