General equation of motion with gravitational field

AI Thread Summary
The discussion centers on the general equations of motion for objects in a gravitational field, highlighting that free fall and launch equations are specific cases of this broader concept. It is noted that the central force problem, specifically the Kepler problem in Newtonian mechanics, provides a framework for understanding these motions. To fully describe an object's trajectory through a gravitational field, twelve initial values are required, including two positions and two velocities, each with three components. The conversation emphasizes the complexity of motion in gravitational fields and the necessity of comprehensive initial data. Understanding these principles is crucial for accurately modeling trajectories influenced by gravity.
Jhenrique
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I was studying the equations of free fall and of launch when I realize that those equations are spetial case of a object in motion through of a gravitational field. So exist some general equation that describe the motion (the trajetory*) of the object through of the field (using initial values like moment, velocity, position, direction, mass, gravity, distance, etc)?

* Illustration:
attachment.php?attachmentid=70234&stc=1&d=1401666592.png
 

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There certainly are...this is just the central force problem (actually it's the Kepler problem) in Newtonian mechanics. You need 12 initial value data, 2 initial positions, and 2 initial velocities (each of which have 3 components).

See here: http://en.wikipedia.org/wiki/Kepler_problem
 

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