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Gravity

Gravity is the weakest of the four
fundamental forces, yet it is the dominant force in the universe for
shaping the large scale structure of galaxies, stars, etc. The
gravitational force between two masses m1 and m2 is given by the
relationship:

This is often called the "universal law of gravitation" and G the
universal gravitation constant. It is an example of an inverse
square law force. The force is always attractive and acts along the
line joining the centers of mass of the two masses. The forces on the two
masses are equal in size but opposite in direction, obeying Newton's
third law. Viewed as an exchange
force, the massless exchange particle is called the graviton.

The gravity force has the same form as Coulomb's
law for the forces between electric charges, i.e., it is an inverse
square law force which depends upon the product of the two interacting
sources. This led Einstein to start with the electromagnetic
force and gravity as the first
attempt to demonstrate the unification
of the fundamental forces. It turns out that this was the wrong place to
start, and that gravity will be the last of the forces to unify with the
other three forces. Electroweak
unification (unification of the electromagnetic and weak forces) was
demonstrated in 1983, a result which could not be anticipated in the time
of Einstein's search. It now appears that the common form of the gravity
and electromagnetic forces arises from the fact that each of them involves
an exchange particle of zero mass, not because of an inherent symmetry
which would make them easy to unify.

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Gravity
Concepts

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Examples of Trajectories

Common misconceptions about guns:

A dropped bullet will hit the ground before one which is
fired from a gun.
As shown in the illustration of a horizontal
launch, gravity acts the same way on both bullets, giving them the
same downward acceleration and making them strike the ground at the same
time if the bullet is fired horizontally over level ground.

Bullets fired from high-powered rifles drop only a few
inches in hundreds of yards.
Fired at twice the speed of sound, a
bullet will drop over 3 inches in 100 yards, and at 300 yards downrange
will have dropped about 30 inches. Plug in numbers into the bullet
drop calculation to see for yourself. Ammunition manufacturers
contribute to this misconception by stating the drop of their projectiles
as just the extra drop caused by frictional drag compared to an ideal
frictionless projectile.

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Trajectory
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Drop of a Bullet

If air friction is neglected, then the drop of a bullet fired
horizontally can be treated as an ordinary horizontal
trajectory. The air friction is significant, so this is an
idealization.

If the muzzle velocity is
v = m/s = ft/s = mi/hr = km/hr

and the distance downrange is
R = m = ft = yards,

Then the amount of drop of the bullet below the
horizontal would be
d = m = cm = inches

If the gun is fired on level ground at a height of
m = ft, then the bullet will hit the ground in
seconds, having traveled a distance of meters =
feet.

To hold the drop to cm = inches at the downrange distance R above would require a muzzle
velocity of m/s = ft/s.

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Trajectory
concepts

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