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
M_{e} is mass of the earth
R_{e} is radius of the earth
Weight of object on the surface on the earth
Freefall acceleration vector
Magnitude of freefall acceleration near the surface of the earth
Magnitude of freefall 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
