How Do You Calculate the Sun's Mass Using Mars' Orbital Data?

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SUMMARY

The mass of the Sun can be calculated using Mars' orbital data by equating gravitational force (Fg) to centripetal force (Fc). The formula derived is G * Ms = 4π²r³/T², where G is the gravitational constant (6.67 x 10^-11 N(m/kg)²), r is the radius of Mars' orbit (2.18 x 10^11 m), and T is the orbital period of Mars (1.68 Earth years or 5.298048 x 10^7 seconds). Substituting these values allows for the calculation of the Sun's mass (Ms), resulting in a definitive numerical value.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with centripetal force concepts
  • Knowledge of orbital mechanics
  • Basic proficiency in algebraic manipulation
NEXT STEPS
  • Study the gravitational constant and its applications in astrophysics
  • Learn about the derivation of Kepler's laws of planetary motion
  • Explore the concept of orbital period and its calculations
  • Investigate the methods for calculating mass in celestial mechanics
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Astronomy students, astrophysicists, and anyone interested in celestial mechanics and gravitational calculations.

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Mars travels around the Sun in 1.68 Earth years in an approximately circular orbit with a radius of 2.18 x 10^8 km. Determine the mass of the Sun.

Fairly easy, I know most of how to do it but I keep getting wrong answers. Help me out a bit? Thanks!
 
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Ok well you can you can set Fg equal to Fc.

Fg = Fc

G msmm/r2 = mm2r/T2

Simplifies to

G Ms = 4π2r3/T2

So

(6.67x10-11) Ms = 4(3.14)2(2.18x1011)3/(52980480)2

Ms = UDOIT kg
 
Last edited:

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