Angular Momentum: Constant Velocity, Elliptical Orbit

[vivinisaac]

if the angular momentum of planet is constant when its orbiting around the sun then
velocity X radius is a constant
vr=constant

but if we consider the velocity and distance from the sun of the planet in an elipticall orbit to be v and r
the centrepital force is provided by gravitational force then
GMm/r^2 =mv^2/r
GM=v^2r
ie. v^2r=constant
ie. angular momentum is not same in two different position in the elipticall orbit

is what i wrote correct or is there something wrong in the equation

 

[Meir Achuz]

L=m v r^2, not m r v^2.
Put the two equations together and you get Kepler III.

 

[vivinisaac]

L=m v r^2, not m r v^2.
Put the two equations together and you get Kepler III.

L=mvr

 

[Janus]

if the angular momentum of planet is constant when its orbiting around the sun then
velocity X radius is a constant
vr=constant

but if we consider the velocity and distance from the sun of the planet in an elipticall orbit to be v and r
the centrepital force is provided by gravitational force then
GMm/r^2 =mv^2/r
GM=v^2r
ie. v^2r=constant
ie. angular momentum is not same in two different position in the elipticall orbit

is what i wrote correct or is there something wrong in the equation

Your mistake is in assuming that $GM = v^2r$ holds for all parts of an elliptical orbit. It holds for all points of a circular orbit, but not elliptical ones.

What you have shown that two bodies of equal mass with different orbital radii don't have the same angular momentum. We don't expect them to.

For an eliptical orbit v at perhelion is larger than that needed to counter centripetal force and at aphelion it is less. If this were not true than a planet at perhelion would not climb out to aphelion and a planet at aphelion would not fall in towards perhelion.