Sciences
What is gravity?
What Newton came up with.
Over
three centuries ago,
Isaac Newton invented a new kind of mathematics called
calculus
so that
he could model motion in the natural world using mathematics.
Calculus
is
about
measuring change and so calculus became a
vital tool in describing
the motions of simple objects.
Newton was able to make a
mathematical model that encompassed both
objects falling
because of gravity
on Earth, and the
motion of heavenly bodies in the skies.
Newton decided that the
force of gravity on Earth was the same force that organized the motions
of the
moon around the Earth and the Earth and all the planets around the sun.
He
invented a formalism and developed mathematical formulas for
calculating the
size of the gravitational force both on Earth and in outer space.
One of the important
formulas in Newton's model is his law for calculating the force of
gravity
between two objects
1 and
2
with mass
m_{1} and
m_{2},
which are separated by a distance
R:
F_{12} = F_{21}
= G m_{1} m_{2} / R^{2}
The constant
G
is a
number that occurs in Nature, like the speed of light
c.
The constant
G
is called
Newton's gravitational constant.
Newton's law of gravity
winds up describing the observed motions of the planets extremely well.
Another
thing it models quite well is the way the gravitational force felt on
the
surface of a planet depends on the size and mass of the planet. For
example,
comparing the gravitational force at the surface of the Earth vs. the
moon, we
get
F_{moon}/F_{earth}
= (M_{moon}/M_{earth}) (R_{earth}^{2}/R_{moon}^{2})
which is about 1/6, and the astronauts who walked on the moon felt it,
too. You
can see how much lighter lunar gravity is if you watch films of
astronauts
moonwalking.
This was an enormous thing
Newton did  to invent a new kind of math to build a model that
described in the
same formula the observed motion of both falling objects on Earth and
the
planets in the heavens.
BUT unfortunately,
Newtonian
gravity falls apart when we try to combine it with what we've
just learned
about
Special Relativity.
What was wrong with that?

When electromagnets were studied, our picture
of space and time changed, too. 
Newton's model for gravity
looked pretty good until scientists started learning more about the
force of
electromagnetism.
They learned that
light
was made of electromagnetic waves, and they could model the
observed
behavior of light very well by looking at solutions of the
wave
equation for
the electromagnetic field.
When they looked at those
wave equations, they could see that causality and Special Relativity
were both
already there. The mathematical equations that modeled electromagnetism
were
consistent
with causality and Special Relativity.
But
Newton's law
of
gravitation depends only on the distance between two massive
objects at a
given moment in time. Newton's law doesn't model what happens when the
gravitational field changes in time. There was
no wave
equation to be had
from Newton's model of gravity, and
there wasn't a way to
make it consistent
with causality and Special Relativity. (Plus, Newton had
spent a lot of time
convincing himself that light was not wavelike in nature, so his
theories really
needed updating by the time electromagnetism came around.)
This was where Einstein
came in. Not only did Einstein give us the Special Theory of
Relativity, but in
his quest to make gravity consistent with Special Relativity, he
invented the
General Theory of Relativity.
And what a
can of
worms
that opened up, as we shall see later.