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Newton's Law of universal gravitation
Every particle in the universe attracts every other with a force which is directly proportional
to the product of their masses, and inversely proportional to the square of their separation.
The law is usually summarized using this diagram:
The law gives this equation:
F = GMm
Where M and m are the two masses, r is the separation, F is the force and G is a constant of
proportionality, known as the universal constant of gravitation.
The force is always attractive and the range is infinite
Strictly, the equation applies only to point masses.
r is the distance between the centres of the bodies
G is very small hence gravitational forces are very small, unless one of the masses is huge,
as with a planet.
Inverse square laws
Newton's law of universal gravitation is an example of an inverse square law. This simply means that
the size of the force is inversel proportional to the square of the separation of the objects:
If the separation is doubled, the force is quatered
If the separation is made 10 times bigger, the force is made 10² times smaller
Inverse-square laws generate graphs which have a characteristic shape
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Motion of planets and satellites
For an object in orbit, the centripetal force required to keep it moving in a ircle is provided by the
gravitational force, given by the equation:
F = GMm
r² = m²r
Where M is the mass of the object being orbited, m is the mass, v is the velocity and is the angular
velocity of the orbiting object, r is the radius of the orbit.…read more