How does the gravitational force between two objects change with distance?

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The discussion centers on understanding how gravitational force changes with distance using the formula for gravitational attraction. Participants clarify that "r" represents the distance between the centers of two objects, which is sometimes denoted as "d" in diagrams. It's noted that for the problem at hand, the masses of the objects and the gravitational constant (G) can be simplified or canceled out, making the calculations easier. The main challenge expressed is the confusion around the formula and the variables involved, particularly for someone new to physics. Overall, the focus is on applying the gravitational formula correctly to analyze the effects of distance on gravitational force.
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You know what r is in both cases so just use the formula to express F and F' for both cases and compare the two results.
 
I still don't understand...where does R come into the formula?? :rolleyes:
 
r is the distance between the center of the Earth and the object in question. That is the symbol people usually use but I just noticed the picture you showed uses "d" to represent that distance so r is the same as your d.
 
Ok please bear with me if I sound dumb...never taken physics before so I'm finding it realli difficult :cry:
So do I have to find m1 and m2? And for G I've been given an approximation for it, and I don't know if I'm suppose to use it :confused:
 
Assuming that neither the mass of the plane nor of the Earth change then they both cancel out - along with G! They made it really convenient for you. :)
 
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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