A planet revolves about the sun in an elliptical orbit of semi-major axis `2xx10^(12) m`. The areal velocity of the planet when it is nearest to the sun is `4.4xx10^(16) m//s`. The least distance between the planet and the sun is `1.8xx10^(12) m//s`. The minimum speed of the planet in `km//s` is `10 K`. determine the value of `K`.

Explanation

Area covered by line joining planet and sun in time dt is
`dS=(1)/(2)x^(2)dtheta` area velocity `=dS//dt=(1)/(2)x^(2)dtheta//dt=(1)/(2)x^(2)omega`
where `x=` distance between planet and sun
and `omega=` angular speed of planet about sum
From keplers second law areal velocity of planet is constant
At farthest position
`A=dS//dt=(1)/(2)(2R-r^(3))omega=(1)/(2)(2R-r)[(2R-r)omega]=(1)/(2)(2R-r)V_(B)`
`V_(B)=40km//s`