How Can You Explore Black Hole Orbits with Interactive Animation?

[George Jones]

I'm new to PF, but in the shotr time ( a little more than 24 hours) since I registered, I've enjoyed myself. Some people hear might (or might not) be interested in the following.

In order to teach myself some Java, I have developed an interactive animation that shows orbits (timelike geodesics parametrized by proper time) about Schwarzschild black holes. The animation takes as input from the user the initial r coordinate, and the initial speed and angle with respect to an orthonormal frame of a platform hovering (and experiencing an incredibly large "g-force") at that r value.

The animation sits in a frame in a bunch of hyperlinked html files. These files contain a number of short explanations and write-ups for some suggested virtual experiments that can be performed with the package.

Experiment 1: Falling Into a Black Hole
Experiment 2: Escape Velocity
Experiment 3: Investigation of Stable Circular Orbits
Experiment 4: Investigation of Unstable Circular Orbits
Experiment 5: Investigation of Spiral Orbits
Experiment 6: Gravity Bends Light Rays!
Experiment 7: Boundaries Between Orbits of Various Kinds
Experiment 8: Orbital Precession and Closed Orbits

I've had a lot of fun (and some frustrations) developing and playing with the package. If anyone else out there in cyberspace thinks that they might enjoy fooling around with the animation, I have attached a zipped file that contains all the necessary files. To use the animation, unzip the zipped file, making sure that all files are extracted into the same folder. (A new folder should probably created before doing this.) Click on the file blackHoleOrbits.html to view and interact with the animation.

The animation is certainly not at a professional level, and it has glitches and warts. For example, on some machines, The Trail checkbox, which should be to the right of theAngle input field, does not appear.

Regards,
George

 

[gnnmartin]

Neat. A few comments though. Using Safari as a browser (on an Apple under OSX 10.3.9) I don't get an input area for the angle, and I don't get a 'trail' button. Using Internet Explorer those problems go away, but the buttons within the text are in almost the same colour as the background, and so completely unreadable for me. (Are you colour blind, perhaps? As well as being 'blind' to certain colour differences, colour blind people are actually more sensitive to other colour differences.)

I'm a bit surprised at the timings. I guess you are running it at 1:x model seconds to proper seconds, is that right? If so, you ought perhaps to point out that to a distant observer the orbits at low radius would look slower.
Nigel Martin

 

[pervect]

Would you be willing to make the human-readable source code available? It looks like a fun toy. The colors do seem to act "glitchy" on my machine, though.

 

[George Jones]

Would you be willing to make the human-readable source code available? It looks like a fun toy. The colors do seem to act "glitchy" on my machine, though.

I'd eventually like to have another at fixing up the code myself before I make it available for public scrutiny. I'm not sure when this is going to happen.

I would enjoy discussing some of the ideas behind the program. I've attached a pdf document about the some of the programming ideas. I wrote this document for a high school computer science teacher who wanted to know how the animation works. In the article, t is proper time.

This article starts with a simple system of ODE's without saying where they came from. I'll make another post that derives the equations from Schwarzschild, but the ideas are much same as you have used in the thread Acceleration At The Event Horizon on the Stellar Astrophysics Forum. I have just posted my take (very similar to yours) on velocities there (after a couple of botched attempts). I'll also post here a bit about the physics and numerical methods used for closed orbits (Experiment 8).

Regrads,
George