Solving Kepler's Equation for Comet Orbit Time Around Sun

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SUMMARY

The discussion focuses on solving Kepler's Equation to determine the orbital period of a comet that is 10 times farther from the Sun than Earth. The relevant equation is T^2/R^3 = K, where K is given as 3.36 x 10^18. The solution concludes that the time T for the comet's orbit is 31.6 years. Participants clarify that Kepler's constant K is applicable to both the comet and Earth, allowing for the establishment of a ratio between their respective orbital periods and distances.

PREREQUISITES
  • Understanding of Kepler's Laws of Planetary Motion
  • Familiarity with the equation T^2/R^3 = K
  • Basic algebra for solving equations
  • Concept of orbital distance in astronomical units
NEXT STEPS
  • Study the derivation of Kepler's Laws of Planetary Motion
  • Explore the implications of Kepler's constant in different celestial bodies
  • Learn about the calculation of orbital periods for various celestial objects
  • Investigate the relationship between distance and time in orbital mechanics
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Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the mathematical principles governing planetary orbits.

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Homework Statement



A comet is 10 times farther from the sun than the Earth. Find the time it take to make its orbit around the sun.

Homework Equations


T^2/R^3 = K
K= 3.36X10^18


The Attempt at a Solution



I tried to create a ratio, but I honestly have no idea where to start. I'm not even sure I need to know kepler's constant for this problem. and the answer is T=31.6

I don't know what to put as R, and that leaves me with two variables, R and T.
I also don't know if Kepler's constant is the same for the comet and the earth.
 
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since k is equal for both objects, you can set each objects time^2/distance^3 ratio equal to each other. Then use that [tex]R_{comet}=10R_{earth}[/tex].
 

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