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Asked by to Clara, Simon, Thomas on 20 Mar 2014. This question was also asked by .
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Clara Nellist answered on 20 Mar 2014:
Hi @13rayan. To work out how much gravity something has, we’re going to use a bit of maths. Don’t worry, I’ll explain what I’m doing as I go! 🙂
Gravity is how much pull two things have on each other, so it’s not just the Earth pulling you, you also pull back. This is also the case with you and your friend. You will both gravitationally pull towards each other. However, gravity is actually a very weak force and we only notice it on Earth, because it is so much bigger.
We can work out how much force (F) two things will have on each other with the following equation by Isaac Newton:
F = Gm1m2 / r^2
where m1 is how much mass the first object has, m2 is how much mass the second object has, r^2 is the distance between them squared and G is something called the “gravitational constant”. This last one, G, is just a number we always use and is roughly 6.674×10^−11 N m^2 kg^−2.
But we want to know what the acceleration would be due to the gravity on earth. We use another of Newton’s equations: F = ma. I’m going to be a little confusing and change the ‘a’ here to a ‘g’, because it’s the acceleration due to gravity. When we put that in, we get:
m1g = Gm1m2 / r^2
We can cancel the two m1’s on either side to get:
g = Gm2 / r^2
Now m2 is the mass of the Earth in kilograms (5.98 × 10^24) and r is the radius of the Earth, the distance from the centre to the surface in meters (6.38 × 10^6). Plug this all in and we get:
g = (6.674×10^−11 N m^2 kg^−2) x (5.98 × 10^24 kg) / (6.38 × 10^6 m)^2
If you don’t have a scientific calculator, you can google one and it comes up.
From this we get:
g = 9.8 N kg^-1
This tells us the acceleration (the increase in speed) something falling towards the Earth near the surface will have. The interesting thing is now, if we know the mass and size of other planets, we can work out the gravity on them too!
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Thomas Elias Cocolios answered on 20 Mar 2014:
Gravity is a form of acceleration. In order to estimate how much gravity Earth has, the best way is to study motion kinematics, e.g. dropping a flower pot from the second floor window! By measuring the time behaviour of that object and, if possible, its impact velocity, you may then determine the Earth gravity from the famous F = m x a, where gravity is given by F = m x g, and therefore g (gravity) = a (acceleration).
I recommend marking off the area where you expect the flower pot to fall to minimise hazard to your colleagues.
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Simon Albright answered on 20 Mar 2014:
Since Clara’s answer requires us to know the mass of the earth I’ll answer assuming that we DON’T know the mass of the earth. I’m afraid mine needs some maths to, but slightly less making it superior.
We know from Newton’s 2nd law that you can work out the force needed for a given acceleration of an object by:
f= ma
Or that to accelerate a mass m at an acceleration a you need force f
1Newton will accelerate 1kg at 1m/s/s for example.We also know that the force of attraction between an object and another object is given by:
f=mg
again f is the force and m the mass but this time g is what we want to calculate, it’s the gravity of the object.knowing this we can do something clever. We have f twice so we can combine f=mg with f=ma and get:
ma=mg
and of course the m is the same on both sides so:
a = g
And that’s a really important answer because it means that if you want to know how much gravity something has all you need to measure is how quickly something accelerates towards it. It also tells you that the acceleration is the same no matter how heavy something is.
In theory a feather, a person, a cannon ball and a battleship dropped off the Eiffel Tower will all hit the ground at the same time. The reason they won’t is air resistance, but that’s a discussion for another time 🙂
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