Change in speed around elliptical orbit

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SUMMARY

The discussion focuses on calculating the speed of a comet in an elliptical orbit around the Sun, specifically at a distance of 6e12 m. The comet's closest approach to the Sun is 5e10 m with a speed of 9e4 m/s. To find the speed at a different point in the orbit, participants suggest using the principles of gravitational and centrifugal forces, as well as the conservation of energy, which involves kinetic and potential energy equations. The challenge lies in determining the effective radius at various points along the elliptical path.

PREREQUISITES
  • Understanding of elliptical orbits in celestial mechanics
  • Familiarity with gravitational force and centrifugal force concepts
  • Knowledge of kinetic and potential energy equations
  • Basic skills in algebra for solving equations
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  • Study the equations governing elliptical orbits in celestial mechanics
  • Learn about the conservation of mechanical energy in orbital dynamics
  • Explore the relationship between speed and distance in gravitational fields
  • Investigate the mathematical derivation of orbital speed at various points in an ellipse
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Astronomy students, astrophysicists, and anyone interested in orbital mechanics and the dynamics of celestial bodies.

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A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 5e10 m (inside the orbit of Mercury), at which point its speed is 9e4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6e12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)

how do I find the speed? (equations needed)
 
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Two options
At any point in the orbit the centrifugal force (depends on speed) must balance the gravitational force (depends on radius)

The energy is constant during the orbit, kinetic energy (depends on speed) + potential energy (depends on radius) must be the same
 
i have a question, because its an ellipse how do you determine the radius, or do you mean the distance from the sun to the two points on the ellipse?
 

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