Question

A planet revolves around sun in elliptical orbit if v*p and v*a are the velocities of he planet at the perigee and apogee resp then eccentricity of the elliptical orbit is given by

Answer 1

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hope the pic helped... We know that areal velocity of planet is constant. The desired time is time taken to travel from A to B The time taken to cover complete area of ellipse =T ∴tAB=(AreaofSABAreaofellipse)∴tAB=(AreaofSABAreaofellipse)TT Area of ellipse =πab=πab Area of SAB =14=14πab−AreaofΔOSBπab−AreaofΔOSB =14=14πab−12πab−12b×aeb×ae ∴tAB=(πab4−12abe)Tπab∴tAB=(πab4−12abe)Tπab =T[14−e2π]