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What is the mass of the Earth?

  1. Dec 13, 2012 #1
    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. jcsd
  3. Dec 13, 2012 #2
    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.
     
  4. Dec 13, 2012 #3

    jtbell

    User Avatar

    Staff: Mentor

    I suggest you check the units on your numbers.

    [added] Ah, I didn't quack fast enough.
     
  5. Dec 13, 2012 #4
    Wow, you're right. Very stupid of me, sorry.
     
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