Calculating the Year Length of Planet Y Around Alpha

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SUMMARY

To calculate the year length of Planet Y orbiting the star Alpha, Kepler's Third Law is applied, specifically the formula T^2 = (4π^2/GM)r^3. Given that Planet X has a year of 200 Earth days and orbits at a distance of r, Planet Y orbits at nine times that distance (9r). By substituting the values into the proportional relationship T12/r13 = T22/r23, the year length for Planet Y can be determined as 600 Earth days.

PREREQUISITES
  • Understanding of Kepler's Laws of planetary motion
  • Familiarity with the formula T^2 = (4π^2/GM)r^3
  • Basic algebra for solving equations
  • Knowledge of orbital mechanics
NEXT STEPS
  • Study Kepler's Laws in detail, focusing on the Third Law
  • Learn how to apply gravitational formulas in astrophysics
  • Explore the concept of orbital radius and its impact on orbital period
  • Investigate the relationship between distance from a star and year length for various celestial bodies
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in orbital mechanics and the calculations of planetary year lengths.

jnimagine
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Planet X orbits the star Alpha with a 'year' that is 200 Earth days long. Planet Y circles Alpha at nine times the distance of planet X. How long is a year on planet Y?

I know that I have to use the kepler's law : T^2 = (4pi^2/GM)r^3
but I'm not too sure how to do solve this...
Please help!
Thanks.
 
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jnimagine said:
Planet X orbits the star Alpha with a 'year' that is 200 Earth days long. Planet Y circles Alpha at nine times the distance of planet X. How long is a year on planet Y?

I know that I have to use the kepler's law : T^2 = (4pi^2/GM)r^3
but I'm not too sure how to do solve this...
Please help!
Thanks.
Wikipedia said:
The third law : "The squares of the orbital periods of planets are directly proportional to the cubes of the axes of the orbits."

So T12/r13 = T22/r23
 

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