What is the Formula for Gravitational Force?

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SUMMARY

The discussion focuses on the formula for gravitational force and its application in calculating the relationship between the orbital period (T) of a planet and the radius (R) of its orbit. The derived equation, 4π²/GM = T²/R³, is essential for understanding planetary motion. Participants emphasize the importance of substituting accurate values to ensure both sides of the equation yield equivalent results. The conversation highlights common pitfalls in applying gravitational formulas, particularly in the context of circular orbits.

PREREQUISITES
  • Understanding of Newton's Law of Universal Gravitation
  • Knowledge of circular motion principles
  • Familiarity with orbital mechanics
  • Basic algebra for equation manipulation
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  • Study the derivation of Kepler's Third Law of Planetary Motion
  • Learn about gravitational constant (G) and its significance in calculations
  • Explore the implications of orbital radius on gravitational force
  • Investigate the effects of mass on gravitational attraction
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Students of physics, astronomers, and anyone interested in understanding gravitational forces and planetary motion.

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But when i substitute the values into the equation they don't both equal the same amount on each sides. help me please!
That has to be. What is your problem? Post a specific problem where you want to apply this relationship. Mainly this relation is used to compare the distances of two planets when their periods of revolution is known.
 
2. Using your knowledge of circular motion and gravitation, derive an equation that shows the relationship between the orbital period (T) of a planet in a circular orbit and the radius of the planetary orbit (R).

4pi^2/GM = T^2/r^3

39.478/ 3.247E+14 = 1.08E+11/ 7.474E+21

1.215E-13 = 1.445E-11

I'm thought that the formula i had rearranged would have answered this question, except shouldn't both sides of the equations equal the same value when their values are substituted into the equation?
 
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