game.github.io

Precession orbit in General Relativity

Analytic Derivation

The exact form of the equation motion near a spheical symmetry black hole with no charge and angular momentum is derived in our Project paper

~/GRorbit/Simulation_of_the_Orbit_near_Compact_star.pdf

The classical dynamics (C.D.) and general relativity (G.R.) provided that the effective force are

eq:effective force

pluggin the intial value $r_0$ and $v_0$, we have the ODE

eq:effective force

Python code

If you don’t already have packages vpython, you need to go to Windows PowerShell or Mac Terminal. Then type

pip install vpython

or

pip3 install vpython

You may

  1. excute the python code directly.
  2. cd ~/GRorbit then python3 npyMain.py or python3 vpyMain.py

python: https://www.python.org vpython: https://www.glowscript.org/docs/VPythonDocs/index.html

Interface

interface

graph place

  1. The orange sphere represent the solar in this system.
  2. The sphere with trail represent the planet in this system.
  3. background
    • If your computer system is Mac OS, the blackground would be Milky Way.
    • If your computer system is Windows, the blackground would be black.

      Buttons

      We have many buttons to control the scene

  4. pause/run icon: is to run the iteration.
  5. cycle icon: is to initalize all the iteration and trail.
  6. center:
    1. None: You may control the camera as in the spaceship.
    2. Solar: The center of view will lock on solar.
    3. Planet: The center of view will lock on planet.
  7. Scroll: is to toogle the scroll option of user.
  8. Axis: is to toogle showing the axis arow.
  9. Stop icon: is to stop the entire iteration, but still may rotate the scene.
  10. view: is to move camera to upper of system, same plane of system or none to control.

    Slider

    The sliders are use to control the intial value, so it would stop updating to reset the intial radius, velocity or mass. ###

    Scene coordinate

    The scene coordinate are also given in vpython API

scene_milkyway