Astronomy - aphelion/perihelion from conservation

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SUMMARY

The discussion focuses on deriving the velocities at perihelion and aphelion using two methods: conservation of specific angular momentum and conservation of energy. The user expresses confidence in the energy method but seeks assistance with the angular momentum approach. Key concepts include the formula for angular momentum, which is defined as the product of the radius (r), mass (m), and velocity (v) when the velocity is perpendicular to the radius vector.

PREREQUISITES
  • Understanding of conservation of angular momentum
  • Familiarity with conservation of energy principles
  • Basic knowledge of orbital mechanics
  • Ability to manipulate algebraic equations
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  • Study the derivation of velocity at perihelion using conservation of specific angular momentum
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Astronomy students, physics enthusiasts, and anyone studying celestial mechanics who seeks to understand the dynamics of orbits and the calculations involved in determining velocities at key points in an orbit.

Odyssey
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Hi all,

I'm stuck on this question for my assginment...i need to derive the velocity at perhelion and aphelion using two separate methods: the conservation of specific angular momentum and energy.

I think I'm OK with the energy part but I'm stuck on getting the velocities at aphelion and perihelion using the conservation of specific angular momentum. If you guys can help me out it'd be great! Thanks.
 
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Odyssey said:
Hi all,

I'm stuck on this question for my assginment...i need to derive the velocity at perhelion and aphelion using two separate methods: the conservation of specific angular momentum and energy.

I think I'm OK with the energy part but I'm stuck on getting the velocities at aphelion and perihelion using the conservation of specific angular momentum. If you guys can help me out it'd be great! Thanks.
Angular momentum magnitude is just rmv when the velocity is perpendicular to the vector r.
 

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