Computing trajectories in Schwarzschild spacetime

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Discussion Overview

The discussion revolves around computing the trajectories of test particles in Schwarzschild spacetime, focusing on the numerical methods for integrating equations of motion. Participants explore various approaches to generate plots of these trajectories, particularly for massive particles in orbits that may cross the event horizon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes an initial strategy using the equation of motion in terms of (r, phi) but encounters difficulties with numerical integration, particularly with sign determination at turning points.
  • Another participant suggests using elliptic functions as an exact solution, noting the need for a suitable programming implementation.
  • Some participants propose using (t, x, y) coordinates and the geodesic equation as potentially more numerically stable than the (r, phi) approach.
  • Several participants discuss the challenges of handling turning points in both timelike and null geodesics, emphasizing the need for robust algorithms to manage these transitions.
  • One participant shares a method involving a coupled set of first-order equations derived from the geodesic equation, which may simplify the numerical integration process.
  • Another participant mentions using Kostic's analysis to plot ellipsoidal bound orbits, highlighting the chaotic nature of the parameter space and associated computational difficulties.
  • A participant references a side-by-side comparison of Newtonian and General Relativity orbits using Stormer-Verlet integration, noting its advantages for long-term accuracy.

Areas of Agreement / Disagreement

Participants express a range of views on the best numerical methods to use, with no consensus on a single approach. The discussion remains unresolved regarding the optimal strategy for computing trajectories in Schwarzschild spacetime.

Contextual Notes

Participants highlight limitations related to numerical errors, the handling of turning points, and the complexity of the parameter space in their calculations. These factors contribute to the challenges faced in achieving accurate trajectory plots.

  • #31
I saw that but wasn't sure if that was for the orbit model code or just required boilerplate for distributing anything running Java.
 
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  • #32
Jimster41 said:
I saw that but wasn't sure if that was for the orbit model code or just required boilerplate for distributing anything running Java.

It's an open-source license. There is no such license required for java code in general.
 
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  • #33
Jimster41 said:
Question about copyright.
I downloaded the source for this simulator from github. Is this code I can play with? I assumed some copyright, yours, by default. But then I've never heard of github, and got the idea it was considered open source. I'm pretty good with C#, and I code with it often (in application/algorithm contexts, not as a pure developer), but I'm pretty new(100%noob) to java. I made some changes and was having no luck saving them. I assumed because I am a doof with java. But then I thought I better check to be sure that I wasn't misunderstanding the copyright context (and my saves weren't working because it was locked).

Actually it is JavaScript, not Java. JavaScript can have objects see here for instance https://developer.mozilla.org/en-US/docs/Web/JavaScript/Introduction_to_Object-Oriented_JavaScript
I downloaded the zip file from github and the code is working locally in FireFox. I'm still impressed.
 
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  • #34
Mentz114 said:
Actually it is JavaScript, not Java. JavaScript can have objects see here for instance https://developer.mozilla.org/en-US/docs/Web/JavaScript/Introduction_to_Object-Oriented_JavaScript
I downloaded the zip file from github abd the code is working locally in FireFox. I'm still impressed.

I was able to run it no problem after the download. Just trying to figure out how to monkey around with the pieces. Thank s for the ref. I've got a good book and I'm pretty familiar with OO architecture, just not HTML, or CSS, or .JS. I've been working in a proprietary environment for... Too long. Its all drag and drop, with bits of custom C#. Lost my skillz.
 
  • #35
Jimster41 said:
I was able to run it no problem after the download. Just trying to figure out how to monkey around with the pieces. Thank s for the ref. I've got a good book and I'm pretty familiar with OO architecture, just not HTML, or CSS, or .JS. I've been working in a proprietary environment for... Too long. Its all drag and drop, with bits of custom C#. Lost my skillz.

OK, you'll soon get familiar with Javascript. It's easy and pretty 'fiendly'.

I've changed some colours and I'm going to lay out the screen differently and add a trace list to log (say) the differences between succesive ##\phi_{min}## values to get the precession of the major axis.

All good fun ...
 
  • #36
I was away yesterday, but glad to see you have all got it working. BTW I consider the program finished in terms of what I set out to do, so feel free to fork/fix/improve as you wish, it's GPL after all ;).
 
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