Find angular momentum of a body moving around other in elliptical path?

AI Thread Summary
To find the angular momentum of a planet in an elliptical orbit around the sun, the maximum and minimum distances from the sun, r1 and r2, are essential. Angular momentum can be expressed as m(R*v), where R is the distance and v is the velocity at those points. The discussion highlights the need for the velocity at perihelion (closest point) and aphelion (farthest point) to calculate angular momentum accurately. Additionally, the relationship between gravitational and centrifugal forces is noted as relevant for understanding the motion. Ultimately, the user successfully derived the answer after considering these factors.
vkash
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planet of mass m is moving in an elliptical orbit around the sun of mass M. maximum and minimum distance of the planet from the sun is r1 and r2. Find the angular momentum of planet about the sun.(Consider M to be fixed in it's position.)

Angular momentum= m(R*v)
At farthest point from sun angular momentum is mr2v2
and at the closest point it is mr1v1
I am thinking to make third equation with the forces of interaction between the two bodies bodies. that might be something like centrifugal force = gravitational force of interaction, but i don't know that value of instantaneous radius of curvature of the m at the two points.

So this is my problem. what should i do?
 
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What information about the orbital parameters can you extrapolate from the perihelion and aphelion distances?

To find the angular momentum it seems that it'd be handy to know the velocity at either perihelion or aphelion. Sounds like kinetic and potential energy will play a role...
 
gneill said:
What information about the orbital parameters can you extrapolate from the perihelion and aphelion distances?

To find the angular momentum it seems that it'd be handy to know the velocity at either perihelion or aphelion. Sounds like kinetic and potential energy will play a role...[/color]
thanks! . these words are enough to hint me. (why didn't it strike in my mind)

r1 is the closest point on the major axis of elliptical path of planet(idk is it perihelion or aphelion). and the farthest distance that also lies on major axis is r2

OK!. thanks for replying. I have got the answer...
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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