Planetary motion the mass of the sun

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SUMMARY

The discussion focuses on deriving the equation for orbital velocity using Newton's Law of Gravitation and circular motion principles. The key equation presented is V = √(GM/r), where G represents the universal gravitational constant, M is the mass of the central body (the Sun), and r is the radius of the orbit. Participants emphasize the importance of rearranging the force equations, specifically F = GMpMs/r² and Fc = MpV²/r, to isolate V. The solution involves recognizing that certain variables can be canceled during the rearrangement process.

PREREQUISITES
  • Understanding of Newton's Law of Gravitation
  • Familiarity with circular motion equations
  • Knowledge of basic algebraic manipulation
  • Concept of orbital mechanics
NEXT STEPS
  • Study the derivation of orbital velocity in detail using Newton's Law of Gravitation
  • Explore the implications of varying mass (M) on orbital velocity (V)
  • Investigate the effects of different radii (r) on the motion of celestial bodies
  • Learn about Kepler's laws of planetary motion for a broader context
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and celestial dynamics, as well as educators looking to enhance their teaching of gravitational concepts.

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Homework Statement



Derive the equation using Newton's Law of gravitation and the equation for circular motion.


Homework Equations




V = [tex]\sqrt{\stackrel{GM}{r}}[/tex]

Where G is the universal gravitational constant, M is the mass of the central body and r is the radius of the orbit

The Attempt at a Solution




F= GM1*m2/r2


F= GMp*Ms/r2

Fc= MpV2/r

F=FC

GMpMS/r2 = mpV2/r

I'm not sure how to derive this equation ?
 
Physics news on Phys.org
Your heading in the right direction, now all you do is re-arrange the last equation until you've solved for V. (hint: some of the variables at least partially cancel out.)
 

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