Semi major axis - planetary Science

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SUMMARY

The discussion centers on calculating the semi-major axis of a comet's orbit, given its perihelion distance of 1.242 AU and its current distance of 4.499 AU from the Sun. The user attempted to apply Kepler's third law, represented by the equation P² = a³, but struggled with determining the orbital period, P. The conversation emphasizes the need to utilize additional formulas and reasoning based on the provided data to identify the comet's orbital characteristics.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with orbital mechanics and conic sections
  • Knowledge of astronomical units (AU) and their significance
  • Ability to manipulate algebraic equations
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  • Study Kepler's laws in detail, focusing on Kepler's third law
  • Learn about the properties of conic sections in orbital mechanics
  • Research methods to calculate the orbital period of celestial bodies
  • Explore the significance of perihelion and aphelion distances in orbit calculations
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Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the dynamics of cometary orbits will benefit from this discussion.

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Homework Statement


A comet with a perihelion distance of d = 1.242 is currently 211(degrees) from pericenter, and 4.499 AU from the Sun. Compute the semi-major axis a of this comet’s orbit.

Homework Equations


P(^2) = a^3

The Attempt at a Solution


I tried to use Kepler's third law but I don't know how to find the period, P.
I think that is not the right way to approach this problem...
IMAG0230.jpg


Any help would be appreciated, thank you [/B]
 

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You'll need to search your notes and textbook for other formulas that include the given variables.

You should be able to use a bit of reasoning from the given data to determine what type of conic section the comet orbit must have.
 

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