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Newton and gravity

 

We all live with the effects of gravity here on Earth. It is everywhere - you just can't get away from it. But what is it and what does it do exactly?

 

Gravity creates a force between every two objects in the Universe that have mass: no exceptions. Strange as it may seem, the most distant star in the furthest galaxy is pulling you towards it right now, and you are pulling it back.

 

It took the genius of Sir Isaac Newton to realise this and to describe the effect of gravity in a scientific way. He was the first person to say that the force that made objects 'fall' to the Earth's surface was the same force that kept the Moon in orbit around the Earth and all the planets in orbit around the Sun.

 

Being a mathematician Sir Isaac created an equation to describe the action of gravity...here it is.

 

Image of Newton's law of gravity

 

What this equation says is that the force due to gravity is equal to a number, G, (called the gravitational constant) times the mass of both objects divided by the square of the distance between the objects.

 

Scientists have been able

to measure the gravitational

constant to be
G = 6.67 x 10-11 m3 kg -1 s-2


which is a very small number...

G = 0.0000000000667 m3 kg -1 s-2

 

Let's see if these numbers make sense. Can we calculate what the force of gravity felt by an object with a mass of 1 kg is when it is near the Earth's surface?

 

In this case:

Force = G x (mass of Earth) x (mass of object)

          -------------------------------------------------

(distance between them)2

 

Now there is one really big catch here. The fact that the object is on the Earth's surface does not mean that the distance between them is zero (or even just a few centimetres). When calculating the force of gravity for roughly spherical objects like the Earth we need to work as if all the mass was concentrated at the centre. This is not just a convenient 'fiddle'. There is a very good reason for this, but it's a bit too complicated to explain here. Anyway this means that in our example the distance between the objects is actually the radius of the Earth! So now we can plug in some numbers to Newton's equation.

 

Force =( 6.67 x 10-11) x( 5.976 x 1024) x 1

             --------------------------------------------

(6.374 x 106)2

 

Where the masses are in kilograms and the distance in metres. Working out the numbers gives the answer 9.81 - and what is force measured in? Newtons! So it all works out correctly, a mass of 1 kg on the Earth's surface feels a gravitational force of 9.81 newtons. For convenience we often round-off the value and say the weight of a one kilogramme mass is 10 newtons.

 

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