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.

 

[PJC01]

Your approach to calculating the mass of the Earth is on the right track, but there are a few errors in your calculations. Let's break down where you may have gone wrong.

First, it's important to note that the equation you used, Fg=G(m1m2)/r^2, is used to calculate the force of gravity between two objects. In this case, you are trying to calculate the mass of the Earth, so we need to use a different equation.

The equation we need to use is Fg=ma, where Fg is the force of gravity, m is the mass of the object (in this case, the Earth), and a is the acceleration due to gravity. In this case, we can use the value of 9.8 m/s^2 for a.

Now, let's take a look at your calculations. In the first line, you have correctly set up the equation Fg=G(m1m2)/r^2, but you have used 10kg for both m1 and m2. This is incorrect because m1 and m2 represent the masses of two different objects. In this case, m1 represents the mass of the Earth, and m2 represents the mass of the object experiencing the force of gravity (in this case, a 10kg object). So, the equation should be written as Fg=G(m1)(10kg)/r^2.

Next, you have multiplied 10kg by 9.8, which is incorrect. This is because 9.8 is the acceleration due to gravity, not the mass of the object. So, the equation should be written as Fg=G(m1)(9.8)/r^2.

Now, let's look at the next line where you have substituted in the values for G, m1, and r. You have correctly used the value for G, but you have used the value of 10kg for m1, which is incorrect. As mentioned before, m1 represents the mass of the Earth, so the correct value to use is the unknown mass of the Earth, which we'll call M. So, the equation should be written as Fg=(6.67x10^-11)(M)(9.8)/r^2.

Finally, you have solved for M, but you have used the incorrect value for r. The value you have used, 40,678,884, is actually the radius