What is the mass of the Earth?

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    Earth Mass
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Discussion Overview

The discussion revolves around the calculation of the Earth's mass using the law of universal gravitation. Participants explore the methodology and potential errors in the calculations, focusing on unit consistency and conversion.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant presents a calculation attempt to find the mass of the Earth using gravitational force equations, noting a discrepancy between their result and the known mass of the Earth.
  • Another participant points out a potential error related to unit conversion, specifically the use of kilometers instead of meters in the calculations.
  • A third participant echoes the suggestion to check units, emphasizing the importance of maintaining unit consistency throughout the calculations.
  • A later reply acknowledges the mistake and expresses regret over the oversight.

Areas of Agreement / Disagreement

Participants generally agree that unit conversion is a critical aspect of the calculation, but the discussion does not resolve whether other errors may exist in the original approach.

Contextual Notes

The discussion highlights the importance of unit consistency in physics calculations, but does not delve into specific assumptions or limitations of the gravitational model used.

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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