Fundamentals of Astrodynamics

Roger R. Bate, Donald D. Mueller, Jerry E. White

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Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.

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I'm interested in doing a "Solar System" simulator that will allow me to simulate the rotational and gravitational forces of planets and stars.

I'd like to be able to say, simulate our solar system, and simulate it across varying speeds (ie, watch Earth and other planets rotate around the sun across days, years, etc). I'd like to be able to add planets and change planets mass, etc, to see how it would effect the system.

Does anyone have any resources that would point me in the right direction for writing this sort of simulator?

Are there any existing physics engines which are designed for this purpose?

Fundamentals of Astrodynamics by Bate, Muller, and White is still required reading at my alma mater for undergrad Aerospace engineers. This tends to cover the orbital mechanics of bodies in Earth orbit...but that is likely the level of physics and math you will need to start your understanding.

+1 for @Stefano Borini's suggestion for "everything that Jean Meeus has written."