Calculating the Mass of a Star from a Planet's Orbital Period

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SUMMARY

The discussion focuses on calculating the mass of a star based on a planet's orbital period and distance from the star. The formula used, P² = (4π²a³)/(G(m+M)), was initially attempted but proved ineffective. A key insight shared is that the ratio M P²/R³ remains constant, allowing for a simplified approach to determine the star's mass in solar masses. This method emphasizes the importance of recognizing proportional relationships in celestial mechanics.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with gravitational constant (G)
  • Knowledge of basic algebra and proportional relationships
  • Concept of solar masses as a unit of measurement
NEXT STEPS
  • Study Kepler's Third Law of Planetary Motion in detail
  • Learn about the gravitational constant (G) and its applications
  • Explore celestial mechanics and orbital dynamics
  • Investigate methods for calculating stellar masses using different astronomical observations
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Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the calculation of stellar masses.

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Suppose there is a planetary system in which a planet with an average distance of 6 AU from the star has an orbital period of 3 years. What is the mass of the star?

The answer should be in SOLAR MASSES.


I tried to use the formula: P^2 = (4pi^2*a^3)/G(m+M)
but it didnt work:(

any hint?
thanks
 
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This is a simple variation problem and you should recognize that

[tex]\frac {M P^2}{R^3}[/tex]

is a constant so you can easily setup the appropriate proportion.
 

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