What is the mass of the Earth?

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SUMMARY

The mass of the Earth is approximately 5.97 x 1024 kg, as derived from the law of universal gravitation. In the forum discussion, a user attempted to calculate this using the formula Fg = G(m1m2)/r2 but made an error by using inconsistent units, specifically mixing kilometers and meters. The correct approach requires converting the radius from kilometers to meters to ensure proper unit cancellation. Following this adjustment will yield the accurate mass of the Earth.

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  • Understanding of Newton's law of universal gravitation
  • Familiarity with gravitational constant (G = 6.67 x 10-11 m3 kg-1 s-2)
  • Basic knowledge of unit conversion (meters to kilometers)
  • Proficiency in algebra for solving equations
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  • Review the law of universal gravitation and its applications
  • Learn about unit conversion techniques, particularly for physics calculations
  • Explore gravitational force calculations using different celestial bodies
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Students learning physics, educators teaching gravitational concepts, and anyone interested in astrophysics and planetary science.

guitarphysics
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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).
 
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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.
 
I suggest you check the units on your numbers.

[added] Ah, I didn't quack fast enough.
 
Wow, you're right. Very stupid of me, sorry.
 

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