What is the mass of the Earth?

guitarphysics

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).

The_Duck

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.

jtbell

I suggest you check the units on your numbers.

[added] Ah, I didn't quack fast enough.

guitarphysics

Wow, you're right. Very stupid of me, sorry.