A planet moving around sun sweeps area `A_(1)` in 2 days, `A_(2)` in 3 days and `A_(3)` in 6 days, then find the relation between `A_(1),A_(2) and A_(3)`

Explanation

According to Kepler's second law, when a planet revolves around the sun, its areal velocity is constant
`:. (dA)/(dt)=` constant
`:. (A_(1))/(t_(1))=(A_(2))/(t_(2))=(A_(3))/(t_(3))`
Given, `t_(1) =2` days, `t_(2) =3` days and `t_(3) =6` days
`:. (A_(1))/(2)=(A_(2))/(3)=(A_(3))/(6)rArr 3A_(1)=2A_(2)=A_(3)`
This is the relation between `A_(1),A_(2) and A_(3)`.