- #1
shifty89
- 1
- 0
Hello, I'm currently studying general relatively and am trying to plot orbits of planets around the sun using the schwarzchild metric. I've worked out the geodesic equations, working with c=1 to simplify things, and written a MATLAB script to plot trajectories, but I'm struggling to work out what magnitudes or units to use.
Basically i need a vector of initial conditions for (r, [tex]\phi[/tex], t, r',[tex]\phi[/tex]', t'), where r and [tex]\phi[/tex] are the polar coordinates, t is time, r' is the speed in the r direction, etc. Obviously i can set [tex]\phi[/tex] and t = 0 initially. I think t' = 1, i.e. initially time is traveling at the regular speed. This just leaves me with r, r', and [tex]\phi[/tex]' to deal with.
i know that for mercury:
mass of sun = 2x10^30 kg
distance from sun = 5.8x10^10 m
orbital velocity = 4.8x10^3 m/s (would this be phi' ? or would i need to break it up into r and phi components... somehow?!)
but what units should i be working with in the relativistic units where c=1?
apologies if this kind of thing has been asked before or if it seems a little silly, but I am a maths student, we don't generally worry about units!
Any help would be greatly appreciated!
Basically i need a vector of initial conditions for (r, [tex]\phi[/tex], t, r',[tex]\phi[/tex]', t'), where r and [tex]\phi[/tex] are the polar coordinates, t is time, r' is the speed in the r direction, etc. Obviously i can set [tex]\phi[/tex] and t = 0 initially. I think t' = 1, i.e. initially time is traveling at the regular speed. This just leaves me with r, r', and [tex]\phi[/tex]' to deal with.
i know that for mercury:
mass of sun = 2x10^30 kg
distance from sun = 5.8x10^10 m
orbital velocity = 4.8x10^3 m/s (would this be phi' ? or would i need to break it up into r and phi components... somehow?!)
but what units should i be working with in the relativistic units where c=1?
apologies if this kind of thing has been asked before or if it seems a little silly, but I am a maths student, we don't generally worry about units!
Any help would be greatly appreciated!