Solving for Mercury's Perihelion Distance

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SUMMARY

This discussion focuses on calculating Mercury's perihelion distance using gravitational principles and Kepler's Laws. The problem states that Mercury's orbital speed ranges from 38.8 km/s at aphelion to 59.0 km/s at perihelion, with a known aphelion distance of 6.99x1010 m from the Sun. Utilizing the conservation of energy equation (Pe + Ke = constant) and the gravitational potential energy formula (Pe = -Gm1m2/r2), participants aim to derive the perihelion distance based on the provided parameters, including the masses of Mercury and the Sun.

PREREQUISITES
  • Understanding of gravitational potential energy and kinetic energy equations
  • Familiarity with Kepler's Laws of planetary motion
  • Knowledge of the gravitational constant (G) and its application
  • Basic algebra and calculus for solving equations
NEXT STEPS
  • Study the derivation of Kepler's Laws and their implications for planetary motion
  • Learn about the conservation of mechanical energy in orbital mechanics
  • Explore the calculation of areal velocity in celestial mechanics
  • Investigate the gravitational potential energy formula and its applications in astrophysics
USEFUL FOR

Astronomy students, physics enthusiasts, and anyone interested in celestial mechanics and the dynamics of planetary orbits will benefit from this discussion.

Kinash
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I have been struggling with this particular problem related to gravity.

Homework Statement


Mercury's orbital speed varies from 38.8 km/s at aphelion to 59.0 km/s at perihelion. If the planet is 6.99x10^10m from the sun's center at aphelion, how far is it at perihelion.


Homework Equations



Pe+Ke=constant

Pe= (-Gm1m2)/r2


Sun mass = 1.99x1030kg
Sun Mean Radius= 696x10m
Sun surface gravity=274m/s2
Sun Mean distance from central body=2.6x1017km

Mercury mass = .330x1024kg
Mercury mean Radius = 2.44x106m
Mercury Surface Gravity = 3.7m/s2
Mercury Mean dist. from central body = 57.6x106km
 
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