Particle Celestial Mechanics


Particle celestial mechanics deals with Newton's law of gravitation and its consequences. The important case of systems with two particles can be examined, and includes orbital mechanics and Kepler's laws. It also includes studies of three and more bodies, which resists exact solution in the general case.	Sapience Home Site Map About Sapience Science Physics Mechanics Gravitation

Particle celestial mechanics deals with Newton's law of gravitation and its consequences. The important case of systems with two particles can be examined, and includes orbital mechanics and Kepler's laws. It also includes studies of three and more bodies, which resists exact solution in the general case.

Newton's Law

Newton's universal law of gravitation is:

F :: Force between two bodies. (in Newtons)

M :: Mass of larger body

m :: Mass of smaller body

r :: Distance beween centers of mass of two bodies

G :: 6.674 e-11 N*m²*kg ^-2

F =	GMm

	r²

Two body systems

Kepler's three laws of planetary motion can be derived from Newton's law of gravitation and his laws of motion.

Kepler's third law gives:

T :: Period (in sec)

r :: Distance (between centers)

C :: (Kepler's constant; G * mass of body being orbited)

T² = C*r³.

Kepler's laws are among the exact solutions for the elementary case of two point masses.

Many body systems

The problem of using these Newton's to find exact equations of motion when there are three or more interacting bodies has not been solved in the gneral case. Although solutions have been found for a few restricted cases, usually numeric and computational methods for finding approximate solutions must be used.


This subject is closely connected to other areas of physics, including other areas of mechanics. Particle mechanics, rigid body mechanics, nonrigid mechanics, and other aspects of gravitation are connected. It is also connected to thermodynamics, electromagnetism, relativity theory, quantum physics, and structure of matter. It has applications in chemistry, astronomy, earth science, and biology. Personal studies including the human body, pyschology, and biography are less directly connected. Anthropology including social foundations, demography, physical anthropology, human ecology, human geography, and physical anthropology is somewhat applicable. Culture including material culture, conceptual culture, and behavioral culture is highly important. Institutions including families, education, economics, government, and religion may be significant. Sociology including social structure and change, communities, and peoples of the world can be connected. Connections to history will be developed as the site expands.	Sapience Home

This subject is closely connected to other areas of physics, including other areas of mechanics. Particle mechanics, rigid body mechanics, nonrigid mechanics, and other aspects of gravitation are connected. It is also connected to thermodynamics, electromagnetism, relativity theory, quantum physics, and structure of matter. It has applications in chemistry, astronomy, earth science, and biology. Personal studies including the human body, pyschology, and biography are less directly connected. Anthropology including social foundations, demography, physical anthropology, human ecology, human geography, and physical anthropology is somewhat applicable. Culture including material culture, conceptual culture, and behavioral culture is highly important. Institutions including families, education, economics, government, and religion may be significant. Sociology including social structure and change, communities, and peoples of the world can be connected. Connections to history will be developed as the site expands.

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