What is the Formula for Gravitational Force?

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The discussion revolves around the gravitational force formula and its application in calculating orbital periods and distances between planets. A user expresses confusion over discrepancies when substituting values into the gravitational equation, questioning why both sides do not equal. Participants emphasize the importance of deriving the relationship between a planet's orbital period and its radius using the formula T^2/R^3 = 4π^2/GM. The conversation highlights the need for clarity in applying the formula correctly to avoid errors in calculations. Understanding the relationship between gravitational force and orbital mechanics is crucial for accurate results.
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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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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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