So, anybody has the the instrument to measure mass of our earth? No one of course! So, why we know that the mass of our earth has the value 5.9736×10^24 kg? Is it fall from the sky? Or it is from epigraphy? Or it carved on legendary stone?
Nope! Of course no!
So, from where people know the mass of the third planet after the sun?
It was started by someone, he was sitting down below apple tree. He fall asleep and then suddenly waken up by a drop-apple to his head. I don’t know why he suddenly thinking about why apple fall to ground, not fall to sky.
Now, who was him? A man who was not unlucky because he was fallen by an apple?
(pict of Newton fallen by apple)
Yup! He was Sir Isaac Newton! Because of a naughty apple, Newton was able to find correlation between earth and things that around it. So do like moon and earth, sun and earth, sun and other planets and of course the mass of the earth..
Sir Isaac Newton derivate a complex formula to find earth and thing around it in mathematical expression. The result is Newton law. There are three.
The first is “sigma F = 0” which means when force that work on a thing is zero, then the thing will stay motionless or keep moving with constant velocity.
Next is “sigma F = m . a” which means an acceleration (a) on a thing is linier with force that work on it and oppose with mass of the earth. Acceleration direction same with acceleration direction.
The last one is “F act = – F react ” which means “If you push a wall with a certain force, then wall will push you with the same force just like you did it before”.
Hmmm…. So where are the formula to calculate mass of the earth? Now we come to main problem! Newton said that “every particle in the universe always attract other particle with the force which its value is linier with mass of that particles and oppose with quadrate of its distance.”
Mathematically, like this:
F = G (m1. m2 / r^2)
F = force between m1 and m2 (N)
m1, m2 = mass of the particle (kg)
G = Gravitational Constant = 6,673 * 10^-11 Nm^2/kg^2
r = Distance between particles
On this problem, we will determine that
F = G (m1. M / r^2)
M = (F/m1) (r^2/G)
F/m1 = 9.8 m/s^2
R earth = 6,4 * 10^6 m
G = 6,673 * 10^-11 Nm^2/kg^2
Input it… And then you will find the mass of the earth : 5.9736×10^24 kg.
Don’t you ask: Where can i find radius of the earth and Gravitational Constant?
Next post: How to find radius of the earth? Are we going to make the longest tape?
And from where we can get Gravitational Constant?
Also, what is your mass in other planet? You shouldn’t waster a billion dollars to go other planet like Mars, Jupiter or other planet if you just only to measure your own weight! We can do it by using this magic formula!