Calculating Earth's Mass Using Algebra

[surferbarney]

Trying to calculate the mass of earth. I am given the mass of the second object (2.00 kg) and the attraction between the Earth and the mass is 19.60 N.

I understand the concept and have successfully (I think) solved the problem using a Newton calculator online. I would just like to know how to solve this without a plug and play. Here is what I have

F= (6.67*10^-11) * [(M1*2.00)/(6.40*10^6)^2] = 19.60 N

I arrived at M1 = 6.016*10^24

How can i set this up to solve using algebra?

Thanks

 

[SteamKing]

How much algebra do you know? If you know any algebra, the setup should be straight forward.

 

[surferbarney]

Well i haven't done algebra since freshman year of college circa 2003

 

[Bandersnatch]

$6.67*10^{-11}*\frac{M_1*2}{(6.40*10^6)^2}=19.60$

Well, what do YOU think are the steps you need to take to isolate the M₁ on one side of the equation?
Start at the beginning. What's the first thing you could do?

 

[surferbarney]

mutltiply M1 by both sides...

6.67*10^-11 * (2/(6.40*10^6)^2)

= 3.2568*10^-24x = 19.60

I think i got it

 

[Bandersnatch]

Slow down, and think again. If you multiply the left side by M1, you should end up having M1*M1 somewhere in there, while on the right side there'd be 19.60*M1.

This is different from what you wrote, and doesn't help you much, as the goal is to have just one instance of isolated M1, not M1 squared or any higher order.
You already have M1 in the numerator in the original equation. You need to get rid of all the numbers on the same side where M1 is. If there's a value(on that side) in the numerator, divide both sides by it. If in the denominator, multiply both sides.

 

[surferbarney]

cant you just use the 3.2568*10^-24 x = 19.60 and then divide each side by 19.6

this gives you 6.0181*10^24 which the study guide says is correct

Did i just get lucky and stumble across the solution or is the solution wrong

Thanks for all our time

 

[Bandersnatch]

You keep saying one thing, and then doing another.
You'll get the answer if you divide both sides by 3.2568*10^-24, not by 19.6. You will get the right answer just from churning the numbers willy-nilly, as you know what you should get and there aren't that many options. But this is not algebra.

For example, you've somehow got rid of M1, and put an x in there completely arbitrarily. Why did you do that, if you're looking for M1?

The best approach to see the algebra at work would be to forget about the numerical values for a moment, and try to rearrange the equation $F=G\frac{M1*M2}{R^2}$ so that M1 is on one side, and all the rest of it is on the other. Then plug in the numbers.

 

[lendav_rott]

What distance is that 6.4 * 10⁶? Where did you get it?
Ah, it must be the distance between the surface and the Earth's core - in that case, are you certain you can calculate the Earth's mass like that? Do not presume without analysing.