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Introduction to universal gravitation

by Steve Bain

Created on: February 16, 2009   Last Updated: March 26, 2009

Gravity is the force that holds our solar system together. Without it, planets would simply float off into space, remaining un-deviated until they collide with another body. The detailed study of gravity began with Galileo, who was the first to notice that all objects, regardless of their mass, are accelerated at the same rate. Isaac Newton published a theory of universal gravitation which correctly describes the motion of the planets, the moon and the tides. Newton's methods are sufficiently accurate, and will be used in this article. However, his work has been superseded by Einstein's general relativity which is even more accurate, but more difficult to use.

A commonly held misconception is that only very large bodies, such as planets and stars, exert gravity. In reality all objects, regardless of their size, exert gravity. However, for most everyday objects, that gravity is extremely small and can be deemed insignificant. The gravitational field strength of an object is proportional to its mass, i.e. the larger the object, the larger the gravitational force it exerts. Large ships, such as aircraft carriers, have enough mass to exert a significant amount of force. If two ships, each weighing 35,000 tonnes, separated by 100 metres of water, will exert a force on each other of over 8.2 Newton's. This force, though relatively small, shows that even a small (when compared to planets) object can exert a significant amount of gravity.

The gravity exerted by object falls in proportion to an "inverse square" law when the distance from the object increases, i.e. if you move twice as far away, the force quarters. This means that a force produced by gravity falls rapidly at a distance. One consequence of this is the gravitational field strength at the north and south poles being higher than the field strength at the equator. The reason for this is that the earth is not a perfects sphere. The poles are closer to the centre of the earth than the equator; hence the force of gravity at the equator is less.

Although the force of gravity falls rapidly at a distance, the sun is large enough to have a significant effect on the earth. It is the sun's gravity which keeps the earth (and the other planets) in orbit around it. The sun's gravity is also strong enough to have an effect on the tides. The sun causes two tides per day, while the moon cause two tides per 25 hours. If these tides are in phase (together) then a spring tide is produced. If these tides are out of phase then

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