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What is the mass of the Earth? 
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#1
Dec1312, 09:02 PM

P: 176

This isn't for homework or anything, I was just trying to figure this out for fun. So what I tried to do to find the mass of the Earth was this:
Fg=G(m1m2)/r^2 10kg(9.8)=6.67x10^11(10kg)(m2)/40,678,884 9.8=6.67x10^11(m2)/40,678,884 398,653,063=6.67x10^11(m2) 5.976x10^18=m2 I looked up the mass afterwards and it's apparently 5.97x10^24. So I was off by about a million kilograms... Where did I mess up? Or is my whole process just completely screwed up? Don't be too harsh on me, I just finished learning about forces in school, and had to look up the law of universal gravitation on wikipedia... PS. Sorry if I posted this in the wrong category (I tried the homework category, but when I saw the template I felt like I was definitely in the wrong place). 


#2
Dec1312, 09:10 PM

P: 841

You've mixed up your units. I recommend always keeping the units in your calculations; if you drop them and just write the numbers you're liable to mess up units.
Your value for G is in units of kg m^3 / s^2. Your value for m1 is in units of kg. Your value for g is in units of m/s^2. But your value for r is in units of km. The units don't cancel out the way you want them to, since you've switched from using meters to using kilometers. Convert r to meters and redo the calculation, and you'll get the right answer. 


#3
Dec1312, 09:10 PM

Mentor
P: 11,594

I suggest you check the units on your numbers.
[added] Ah, I didn't quack fast enough. 


#4
Dec1312, 09:31 PM

P: 176

What is the mass of the Earth?
Wow, you're right. Very stupid of me, sorry.



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