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

AI Thread Summary
To calculate the mass of a star from a planet's orbital period, the formula P^2 = (4π^2a^3)/(G(m+M)) is relevant, but it can be simplified. The relationship M P^2/R^3 is a constant, allowing for easier calculations. Given a planet at 6 AU with an orbital period of 3 years, the mass of the star can be derived using this proportionality. The correct approach involves rearranging the formula to isolate the star's mass in solar masses. This method provides a straightforward way to determine the star's mass based on the planet's orbital characteristics.
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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

\frac {M P^2}{R^3}

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