Gravitation and Newton's Synthesis Problem

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SUMMARY

The discussion focuses on calculating the orbital period of the Sun as it rotates around the center of the galaxy. The relevant equation involves gravitational force and centripetal motion, specifically g(m1)(Ms)/(r1^2) = m1(4π^2r1/t1^2). Here, m1 represents the mass of the Sun (4×10^41 kg), r1 is the distance from the Sun to the galactic center (3×10^4 light years), and Ms is the mass of the galaxy. The participants clarify that in this context, the mass of the Sun cancels out, leaving the calculation dependent solely on the mass of the galaxy.

PREREQUISITES
  • Understanding of gravitational force equations
  • Familiarity with centripetal motion concepts
  • Knowledge of astronomical units and conversions (e.g., light years to meters)
  • Basic algebra and manipulation of equations
NEXT STEPS
  • Research the mass of the Milky Way galaxy (Ms) for accurate calculations
  • Learn about the dynamics of galactic orbits and their implications
  • Study gravitational force equations in astrophysics
  • Explore the concept of orbital mechanics in celestial bodies
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Astronomy students, astrophysicists, and anyone interested in understanding the dynamics of galactic motion and gravitational interactions.

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Homework Statement


Our sun rotates about the cneter of the galaxy (m = 4*10^41kg) at a distance of about 3*10^4 light years ( 1ly=(3*10^8m/s)*(3.16*10^7 s/y) what is the period of our orbital motion about the center of the galaxy?


Homework Equations


Okay so I believe you would use g(m1)(Ms)/(r1^2)= m1(4pie^2r1/t1^2) but i don't understand
what do i put in for ms and m1 and r1 i assume r1 is the (3*10^4) and m1 is the (m = 4*10^41kg) but then what is Ms any help would be great thanks
 
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I think you have m1 and Ms reversed. In calculating solar orbits, Ms would be the mass of the sun in the center and m1 the mass of the planet- with the result that the mass of the planet cancels and the answer depends only on the mass of the sun.


But the sun is orbiting the center of galaxy so "m1" is now the mass of the sum, which cancels out and "Ms" is the mass of the galaxy.
 

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