Solving Kepler Problem for 2-Body System: Velocity & Position

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Discussion Overview

The discussion revolves around solving the Kepler Problem for a two-body system, specifically focusing on how to determine the new velocity and position vectors given an initial state over a certain time interval. The scope includes theoretical approaches and references to existing literature.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant inquires about methods to solve the Kepler Problem for a two-body system with a significant mass difference.
  • Another participant references Landau and Lifshitz Mechanics as a source for the solution.
  • A different participant asks for online resources where the problem is solved.
  • Another participant suggests that the solution may also be found in Fowles and Cassiday, specifically in Chapters 5 or 6.
  • It is noted that there are numerous methods to solve Kepler's equation, with many celestial mechanics texts providing various approaches.
  • A participant recommends the works of Jean Meeus for those engaged in celestial computing.
  • A link to a Wikipedia page on the Kepler problem is provided as a potential resource.

Areas of Agreement / Disagreement

Participants express differing views on where to find solutions and methods for the Kepler Problem, indicating that multiple resources and approaches exist without a consensus on a single solution.

Contextual Notes

Some responses reference specific chapters in textbooks, suggesting that the solutions may depend on the definitions and contexts presented in those texts. The discussion does not resolve which source is the most appropriate or comprehensive.

Who May Find This Useful

Individuals interested in celestial mechanics, students working on related homework problems, or those seeking to understand the dynamics of two-body systems may find this discussion relevant.

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How do you solve the Kepler Problem for a 2-body system where m1<<m2 with a given velocity and position vector resulting in a new velocity and position for a certain time interval?
 
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The solution is in Landau and Lifshitz Mechanics. Chapter 3.
 
Is there anywhere on the web that it is solved?
 
I think it is also in Chapter 5 or 6 in Fowles and Cassiday.
 
There are many ways of solving Kepler's equation - hundreds of them. Any decent celestial mechanics text should present several. Have you searched around on the web?
In general, if you're going to do much celestial computing, I recommend the works of Jean Meeus.
 

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