Gravitation
SI units & Physics constants
Gravitation investigates motion of objects under the force of gravity

Here (all units see here):
M and m are masses of objects
is gravitational force on m from M
- is gravitational force on M from m
is position vector of m with respect to M
is velocity vector of m
is total acceleration vector of m
h is height of m above M
General formulas
Gravitational force vector is defined by Newton's law of gravitation

where G is universal gravitational constant
Magnitude of gravitational force

Weight of object near the surface of the earth at height h
where:
m is mass of the object
Me is mass of the earth
Re is radius of the earth
Weight of object on the surface on the earth

Free-fall acceleration vector

Magnitude of free-fall acceleration near the surface of the earth

Magnitude of free-fall acceleration on the surface of the earth

Relation between weigh and mass

Gravitational potential energy with respect to infinitely far point

Gravitational potential energy of object in the vicinity of the surface at height h

Motion of object around the earth

The total linear acceleration of the object

Principle of conservation of energy for the object

Law of conservation of angular momentum of the object

Speed required for object to become artificial satellite near the surface

Speed required for object to escape earth's gravity from the surface

Kepler's laws for motion of planets around the sun

Where d is length of major axis of elliptical orbit
Kepler's first law: all planets are moving around the sun in elliptical orbits with the sun at one of the focuses
Kepler's second law: for any planet the line joining the planet to the sun sweeps out the same amount of area in a given moment of time no matter where the plane is on its orbit. Which is defined by vector product equation

Kepler's third law: the ratio of period of orbital motion of planet squared to length of major axis of its orbit cubed is the same for all planets

where T is period of orbital motion
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