Two hypothetical planets `1` and `2` are moving in the same eliptical path as shown in the figure. If the planets are situated at minimum and maximum distance from the sun and one of the planet, say `1`, has speed `v`. Find the relative angular speed of the planets for the given situation.

Explanation

According to Kelper.s Law of area `(1//2) r^(2) omega=` constant.
`impliesr_(1)^(2)omega_(1)=r_(2)^(2)omega_(2)`
`implies(omega_(2))/(omega_(1))=((r_(1))/(r_(2)))^(2)`
`implies(omega_(2))/(omega_(1))=((r )/(2r))^(2)impliesomega_(2)=(omega_(1))/(4)`,
Putting `omega_(1)=(V_(1))/(r_(1))=(V)/(r )`,
We obtain , `omega_(2)=(V)/(4r)`.
Since the direction of angular velocities `omega_(1)` and `omega_(2)` are same, the relative angular speed
`omega_(r )=|omega_(1)-omega_(2)|=|((V)/(r )-(V)/(4r))|impliesomega_(r )=(3v)/(4r)`.