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 What is Physics? Mechanics Electricity and Magnetism Electric Field Gauss' Law about below subjects Electric Potential Capacity Direct Current Magnetic Field Magnetic Field Laws Magnetic Interactions Electromagnetic Induction Maxwell's Equations Oscillations and Waves Simple Harmonic Motion Damped Harmonic Motion Driven Harmonic Motion Electric Oscillation Alternating Current Wave Motion Elastic Waves Electromagnetic Waves Optics Light Waves Geometrical Optics Interference Polarization Diffraction Fraunhofer Diffraction Dispersion, Absorption, Diffusion Doppler Effect Thermodynamics Ideal Gas Molecular Statistics Transport Phenomena First Law of Thermodynamics Second and Third Laws of Thermodynamics Imperfect Gas Liquids Solids Quantum Physics Thermal Radiation Quantum Properties of Light Wave Properties of Particles Planetary Model of Atom X-Rays Particle in Potential Well Pauli Exclusion Principle Nuclear Physics Solid State Physics Appendices

# Gravitation

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

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