Finding the mass of the sun from T^2/R^3

Thread starter Sirsh
Start date Mar 16, 2010
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SUMMARY

The discussion centers on the equation T²/R³ = 4π²/(GM), which relates the orbital period (T), radius (R), and mass (M) of celestial bodies. Participants confirm that the slope derived from plotting T² against R³ corresponds to the value of 4π²/(GM). To find the mass of the sun, one must isolate M in this equation, leading to M = 4π²R³/G(T²). This mathematical relationship is crucial for understanding gravitational dynamics in astrophysics.

PREREQUISITES

Understanding of Kepler's laws of planetary motion
Familiarity with gravitational constant (G)
Basic knowledge of algebra and equations
Concept of celestial mechanics

NEXT STEPS

Study the derivation of Kepler's Third Law of Planetary Motion
Learn about the gravitational constant (G) and its significance
Explore the implications of T²/R³ in different celestial systems
Investigate how to apply this equation to other celestial bodies beyond the sun

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Astronomy students, astrophysicists, and educators looking to deepen their understanding of celestial mechanics and gravitational relationships.

Mar 16, 2010

Sirsh

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Last edited: Mar 16, 2010

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Mar 16, 2010

dacruick

Hi Sirsh, do you perhaps know the equation that links period, radius, and mass together?

Mar 16, 2010

Sirsh

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Last edited: Mar 16, 2010

Mar 16, 2010

dacruick

T² / R3 = 4p²/(GM) is the equation that I've got where hopefully p represents pi. so what you've done above to calculate the slope seems right. and the slope will represent 4p²/(GM). So you have to isolate the M in that equation.