MPIA Summer Internship 2023 - RV Code

Repository for RV code I created during my internship at MPIA, 2023. This code can be used for simple exoplanet and binary stars RV modeling.

Libraries:

Before using the code, please install kepler.py:

pip install kepler.py

Usage:

This code is better run in an interactive notebook *.ipynb file instead of running it in *.py.

Steps to use the code:

• Copy and run the code in RV.py to the first block of the Python notebook
• Define the input parameters: primary mass $M_1$ (kg), secondary mass $M_2$ (kg), semi-major axis $a$ (m), eccentricity $e$, inclination $i$ (rad), argument of periastron $\omega$ (rad), period $P$ (s), and the time of periastron passage $T_0$ (s).
  You can convert $a$ to $P$ or vice versa using ptoa or atop function from RV.py.
• Create an array of time $t$ you want to simulate, with $T_0$ as the first element of the array. Ensure that all the time unit in the array is in seconds (s).
• Steps on simulation:

1. Calculate the average angular speed of the (secondary) object in the orbit using avg_ang_speed function, using $P$ as the function's input.
2. Calculate the mean anomaly using mean_anomaly function, using $t$ and average angular speed as the input.
3. Calculate the eccentric anomaly and true anomaly using kepler_solve function, with mean anomaly and $e$ as the input.
4. Calculate the polar coordinate position of the object in orbit, $r$ and $\theta$ with pos function, using $a$, $e$, and true anomaly as the input.
5. Finally, calculate the radial velocity with radial_velocity function, using true anomaly $\omega$, $e$, systemic velocity, $a$, $i$, and $M_1$, $M_2$.

Finally, You can plot RV vs $t$.

An example ipynb file for any RV simulation (2-body and multiple bodies) is provided in this repository.

Note: beware of the notation of the system when doing the simulation.

This code is a very simple form of simulating the RV plot and needs a lot of improvisation. Feel free to contribute to this repository!