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 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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