Gravitational Force on 0.64 kg Sphere in Space Shuttle

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To calculate the gravitational force on a 0.64 kg sphere in a space shuttle orbiting 396.9 km above Earth, the formula F = (G*M*m)/r^2 is appropriate, where G is the gravitational constant, M is Earth's mass, m is the sphere's mass, and r is the distance from the center of Earth to the sphere. The radius r should be the sum of Earth's radius (6.37x10^6 m) and the altitude of the shuttle (396.9 km converted to meters). The calculated gravitational force of approximately 5.57 N suggests a potential miscalculation in the distance used. It's crucial to ensure that r represents the correct total distance from Earth's center to the sphere. Accurate application of the formula will yield the correct gravitational force.
nweis84
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I have this problem i have been trying to solve and can't seem to get it right. The question states:

The space shuttle is in orbit 396.9 km above the surface of the earth. What is the gravitational force on a 0.64 kg sphere inside the space shuttle?

mass Earth = 5.98x10^24 kg
radius of Earth = 6.37x10^6 m

I've tried using the equation F= (G*M*m)/r^2 and the answer i got was about 5.57 N

for the distance above Earth i converted the units and added them to the Earth's radius so I'm not sure what I could be doing wrong.

is it possible that i am using the wrong equation all together?
 
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r is defined as being the distance between the two point masses.

I might be wrong, but for this problem, would you not just use the distance from Earth as r?
 
F = GMm/r^2 , G is the universal gravity, M is mass of the object acting the force,
m is the mass of the object that the force is acted upon, r is the distance between the center of the Earth and the center of the object in space.
 
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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