Difference between F=GMm/r^2 and g=Gm/r^2

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The discussion clarifies the relationship between the equations F=GMm/r^2 and a=Gm/r^2 in the context of satellite motion. Both equations are equivalent, with the first representing gravitational force and the second representing acceleration due to gravity. Users are encouraged to use the equation that is most convenient for their calculations, typically the acceleration equation. The distinction between force and acceleration is explained as force being the product of mass and acceleration, while acceleration is the force divided by mass. Understanding these concepts is essential for solving problems related to gravitational motion.
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Homework Statement


I have been studying satellite motion and have come across 2 equations:
eq1. F=GMm/r^2
eq2. a=Gm/r^2

The Attempt at a Solution


By using Newton's second law, F=ma, we convert eq1. to eq2. Obviously one gives the Force and the other acceleration but what is the difference and when should I use each one?
 
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welcome to pf!

hi hmvince! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)

there's no difference … as you say, they're equivalent …

use whichever is most convenient (which however will almost always be the acceleration one)! :smile:
 
Clever, r2
Thanks for the reply:smile:, I'll keep that in mind!
 
Also, what is the difference between force and acceleration?
 
hmvince said:
Also, what is the difference between force and acceleration?

you know that …

force = mass times acceleratiom,

so acceleration = force per mass
 
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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