3D PLOT OF AN ORBIT

Question

Suppose you have an orbit an and you know the 6 parameters $a,e,i,\Omega,\omega,\theta$ that characterize the orbit. In my case:

• $a=9661.07 \text{ km}$
• $e=0.0841816$
• $i=23.6047^\circ$
• $\Omega=29.7304^\circ$
• $\omega=48.3429^\circ$
• $\theta=81.269^\circ$

Now you want to have a 3D plot to visualize the orbit with a good render using MATLAB (or MATHEMATICA). My question is: is there such a way to do this? Could someone suggest me a good MATLAB code to have this rappresentation? Thank you vary much for the attention.

Answer 1

There's plenty of algorithms online that allow you to transform between orbital elements and $3$D orbits, this document is particularly useful

It takes as inputs

• Sem-major axis $a$
• Eccentricity $e$
• Argument of periapsis $\omega$
• Longitude of ascending node $\Omega$
• Inclination $i$
• Mean anomaly at epoch $t_0$ $M_0 = M(t_0)$

and produces the cartesian position ${\bf r}$ and velocity vectors $\dot{\bf r}$ at epoch $t$