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Circular motion and gravity

Working anything out about orbits involves two basic ideas: circular motion and gravity. For something to go in a circle it needs a centripetal force. This could be the tension in the string tied to a bucket of water as you swing it around your head, or it could be the friction on the tyres of a car as it corners.

For a satellite the centripetal force is provided by the Earth's gravitational attraction. So the starting point for any calculation is:


R = total distance between the Earth and satellite
G = gravitational constant
M = mass of the Earth
m = mass of satellite
v = speed of satellite

Another useful starting point is to look at the acceleration due to gravity (or the force per unit mass - otherwise known as gravitational field strength) where you are. Even when they are in orbit, the satellites are accelerated by gravity:

where g' is the gravitational field strength at that orbital height - which is much less as you move further away.

For example, for a geostationary satellite:

The acceleration due to gravity decreases as the satellite's orbit gets bigger. This is why they can afford to go more slowly without risking being pulled back down to Earth.

Important point…
Wherever a satellite is orbiting, the centre of its orbit has to be the centre of the Earth; this defines the direction of the force exerted by the Earth.

Lose weight - go to the equator…..
You weigh less when standing on the equator than you do when standing on the poles. Firstly the radius of the Earth north-south is less than east-west (the Earth is an oblate spheroid), so you are nearer to the centre of the earth. Secondly you are slightly 'thrown out' from the Earth by its spin. In your frame of reference you experience a centrifugal force which is away from the centre of your circular motion. This is the same as the feeling of being thrown outwards on spinning fairground rides.

Astronauts on the orbiting space station are weightless. This is not because there is no pull of gravity on them. It is because the floor of the space station does not push back upon them - they experience no reaction force. They are in free fall as the space station is in free fall. In fact they train for weightlessness by going up in a large training jet which then free falls. The astronauts and the jet fall at the same rate (accelerating at 9.8m/s2 as they are near to the Earth). The astronauts never catch up with the jet so it never exerts a reaction force on them - this is how they feel weightless.

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NASA video An astronaut demonstrates the effect of weightlessness

NASA video Eating a banana in space!

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