- #1
Heimdall
- 42
- 0
Hi !
first, excuse my english, I'm just a poor french student... and we are so bad in languages here... anyway..
I'm trying to make a little program which could calculate the motion (and some other little things) of n bodies linked with gravitationnal interaction.
(my final aim will be to simulate planets orbits arount binary stellar systems)..
In fact I have already wrote the code, but I don't understand some things... that I hope you'll be able to explain to me ;)
I use the 4th order runge-kutta method to solve the equations of the motion, with a fixed step for the moment (I'll write a method with an adaptable step later).
I have tested my code with the three bodies system : Earth moon and sun. using the JPL orbital parameters for my starting conditions.
I suppose that at time t=0, the orbits are elliptic so I can calculate positions and velocities with the semi-major axis 'a', the excentricity 'e' and the inclinaision angle 'i'.
At time t=0 I put the planets at their apogee with the formula Rmax = a*(1+e).
so for example the cartesian coordonnates for Earth at t=0 are :
x_t = a*(1+e)
y_t=0
z_t=0
for the moon, the inclinaison i is 5.16 deg, so :
x_m = x_t + a_m*(1+e_m)*cos(i)
y_m = 0
z_m = a_m*(1+e_m)*sin(i)
(a_m and e_m are respectively semi major axis and excentricity of the moon).
for the velocities, they're purely according to Oy with the module :
v = 2*pi*a*sqrt(1-e²)/(T*(1+e))
(with T the period)
of course, I have added the Earth velocity for the moon..
but my result, seems to be incorrect, since I find a minimal distance earth-sun of only 149.5 millions of km, whereas it should be around 147...
You can see my results and the graphics here : http://nicolas.aunai.free.fr/cours/magistere/3c/tl2a2s/tl2a.htm
(please do not pay attention to the x and y labels, I made some mistakes with my plotting program)
thanks if you can help me to solve this mystery :)
first, excuse my english, I'm just a poor french student... and we are so bad in languages here... anyway..
I'm trying to make a little program which could calculate the motion (and some other little things) of n bodies linked with gravitationnal interaction.
(my final aim will be to simulate planets orbits arount binary stellar systems)..
In fact I have already wrote the code, but I don't understand some things... that I hope you'll be able to explain to me ;)
I use the 4th order runge-kutta method to solve the equations of the motion, with a fixed step for the moment (I'll write a method with an adaptable step later).
I have tested my code with the three bodies system : Earth moon and sun. using the JPL orbital parameters for my starting conditions.
I suppose that at time t=0, the orbits are elliptic so I can calculate positions and velocities with the semi-major axis 'a', the excentricity 'e' and the inclinaision angle 'i'.
At time t=0 I put the planets at their apogee with the formula Rmax = a*(1+e).
so for example the cartesian coordonnates for Earth at t=0 are :
x_t = a*(1+e)
y_t=0
z_t=0
for the moon, the inclinaison i is 5.16 deg, so :
x_m = x_t + a_m*(1+e_m)*cos(i)
y_m = 0
z_m = a_m*(1+e_m)*sin(i)
(a_m and e_m are respectively semi major axis and excentricity of the moon).
for the velocities, they're purely according to Oy with the module :
v = 2*pi*a*sqrt(1-e²)/(T*(1+e))
(with T the period)
of course, I have added the Earth velocity for the moon..
but my result, seems to be incorrect, since I find a minimal distance earth-sun of only 149.5 millions of km, whereas it should be around 147...
You can see my results and the graphics here : http://nicolas.aunai.free.fr/cours/magistere/3c/tl2a2s/tl2a.htm
(please do not pay attention to the x and y labels, I made some mistakes with my plotting program)
thanks if you can help me to solve this mystery :)
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