Calculate Perihelion Distance of Mars Using Solar System Parameters

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SUMMARY

The perihelion distance of Mars, calculated using the semi-major axis of 1.5237 AU and eccentricity of 0.0934, is definitively 1.38 AU. The formula used for this calculation is r = a(1 - e^2) / (1 + e cos θ), where θ is 0°. Initial miscalculations led to an incorrect result of 16.17 AU, but upon reevaluation, the correct perihelion distance was confirmed.

PREREQUISITES
  • Understanding of orbital mechanics and Kepler's laws
  • Familiarity with the formula for calculating perihelion distance
  • Basic knowledge of astronomical units (AU)
  • Proficiency in using scientific calculators for trigonometric functions
NEXT STEPS
  • Study the derivation of the perihelion distance formula in celestial mechanics
  • Explore the implications of eccentricity on planetary orbits
  • Learn about the orbital parameters of other planets in the solar system
  • Investigate the effects of gravitational perturbations on perihelion distances
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in celestial mechanics and planetary motion will benefit from this discussion.

ZedCar
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Homework Statement


Assuming that the sun lies at the principal focus of the solar system, and given that the semi-major axis and eccentricity of Mars is 1.5237 AU and 0.0934 respectively, calculate:

The distance (in AU) when Mars is closest to the Sun (known as perihelion). The angle θ=0°


Homework Equations



r = a(1 - e^2) / (1 +e cos θ)



The Attempt at a Solution



The correct solution is 1.38 AU

Though if I use the above eqn putting a=1.5237 and e=0.0934 I get an answer of 16.17.

Thanks for any help!
 
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Must be finger problems with the calculator :smile:

What values do you calculate for the numerator and denominator of the expression?
 
Sorry about that! I'm getting the correct answer now...!
 

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