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Earth’s Gravity and Orbit

What keeps the Moon going round the Earth? Why doesn’t it just carry on in a straight line? What keeps any smaller object in orbit around a much larger object? It was Newton who first realised that it was the force of gravity that kept objects in orbit. The same force that pulls a falling apple to the ground.

Newton’s laws of motion

Imagine firing a cannonball horizontally from the top of a mountain. As it falls towards the Earth it follows a curved path. If you fire it fast enough it could actually follow the curvature of the Earth and go into “orbit”. Air resistance would slow it down of course, unless you were high enough to be above the Earth’s atmosphere, i.e. in space.

 

Newtons Third Law
Image via: NASA

Isaac Newton (1643-1727) is famous for many things including his work on optics and his laws of motion. In the field of astronomy his greatest achievement was his universal law of gravitation.

All bodies in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of their separation.

So the gravitational force due to the Sun which acts on a planet is proportional to the mass of the planet. Also, the gravitational field strength of a planet is proportional to its mass. As you move away from a planet its gravity becomes weaker. As it varies with 1/r2 when the distance doubles the field strength will decrease by a factor of 4.

This graph below shows how the Earth’s gravity gets less as you move away from the Earth.

 

Earth's gravity
Image via: NASA

At the Earth’s surface gravity is about 10 N/kg. At twice this distance, a distance of 2r, the field is 2.5 N/kg, a quarter of what it is at the surface. At 3r it is a ninth etc..

G (big “G”) is Newton’s Universal Gravitational Constant. Its value is 6.67 x 10-11 Nm2/kg2.

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