Deriving mass of Earth from definition of gravity

AI Thread Summary
To derive the mass of the Earth using the definition of gravity, the relevant equation is a = GM(earth)/r^2. The discussion suggests that while it may seem overly simplistic, utilizing known values for gravitational acceleration and radius can effectively yield the Earth's mass. Participants confirm that the problem can indeed be solved by substituting values directly into the equation. There is reassurance that no complex calculus is necessary for this calculation. Ultimately, the approach is straightforward, focusing on applying the formula with available data.
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Homework Statement


Using the definition of gravity, derive the mass of the Earth


Homework Equations


I am unsure if this is simply a plug n chug problem and I am over thinking it or there is some way to use calculus to derive the mass from the gravity equation.


The Attempt at a Solution



I am looking at the equation a=GM(earth)/r^2
I know I can simply find these values in my textbook, but I don't see why it would be that simple of a problem. So I just feel like there must be something I am missing.
 
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I don't think you're missing anything. Plug-n-chug away!
 
phyzguy said:
I don't think you're missing anything. Plug-n-chug away!

awesome thank you :D
 
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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