How Do You Calculate the Mass of the Sun from Mars' Orbital Motion?

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SUMMARY

The discussion focuses on calculating the mass of the Sun using Mars' orbital motion. Mars orbits the Sun in approximately 1.88 Earth years with a radius of 2.28 x 108 kilometers. The orbital speed of Mars was calculated to be 24145.7 m/s using the formula v = 2πr/T. To find the mass of the Sun, participants suggested equating gravitational force (F = Gm1m2/r2) with centripetal force (F = mv2/r), allowing for the calculation of the Sun's mass (m1).

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  • Understanding of gravitational force and Newton's law of universal gravitation
  • Familiarity with centripetal force concepts
  • Basic knowledge of orbital mechanics
  • Proficiency in using mathematical formulas for circular motion
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  • Investigate the methods for calculating masses of other celestial bodies using similar techniques
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Mars travels around the sun in 1.88 (earth) years, in an approximately circular orbit with radius 2.28 x 10^8 kilometers determine

a)orbital speed of Mars relative to sun
b)mass of the sun..

for part a) i did

v= 2(pi)(r)/ T

which i got 2(3.14)(2.28x10^11 meters)/ 5.93 x10^7 seconds

v= 24145.7 m/s

if that's correct, how do i calculate the mass of the sun
 
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Have you done gravitational force?

So you know that the force between them is

F = Gm1m2/r^2

And force also = mv^2/r where m is the mass of mars.

If you equate them, I think you can solve for m1, the mass of the sun.
 

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