Orbits

A library for working with orbits in 2D and 3D space.

Includes optional API calls to NASA's HORIZONS system for initial vector data of our solar system bodies.

Provides a variety of options to evolve the orbits, including:

• 4th order symplectic (Forest/Ruth) integrator
• 2nd order symplectic (Verlet) integrator
• 1st order symplectic (Modified Euler) integrator
• Runge-Kutta 4th order (not recommended)

Adaptive time step sizing is also included by default.

Allows for online (i.e. while the simulation is running) and offline (i.e. after the simulation is complete) plotting of the orbits.

Installation

Only numpy is used for calculations, so it is the only major dependency.

matplotlib is used for plotting, tqdm for progress bars, and requests for API calls to NASA's HORIZONS system.

pip install -e .

Example Usage

from orbits import StarSystem

solar_system = StarSystem.our_solar_system(
    t0='1945-01-01',
    step_size=1E-3)

## Evolve the solar system for a number of days
t = 0
duration =  3 # years
t_end = t + duration * 365.25 # days

## Animate the orbits of the inner solar system
solar_system.plot_orbits(
    t, 
    t_end, 
    indices=[0,1,2,3,4], 
    keep_points="all", 
    resample_every_dt=1,
    animated=False,
    mark_every_dt=1*365.25, 
    real_time=False,
    save=False, 
    adaptive=True, 
    relative_error=1E-5)

On the upper plot, the scales of the x and y axes are the equal and the units are AU. Each black dot corresponds to January 1st of a year.

The lower plot displays the evolution of the fractional energy change $\Delta E/ E(t=0)$, as a function of time (in days). Since this remains substantially lower than 1, this is an indication that the evolution of the system has not gone horribly wrong.

On the left, the orbits of the inner solar system are shown for a duration of three years. On the right, the motion of the Sun with respect to the Solar System Barycenter is shown over 50 years (see more information here and here).

Or you can use the StarSystem class to create your own star system, and evolve it for a number of days.

from orbits import StarSystem

while True:
    solar_system = StarSystem.random_solar_system(
        n_objects=3,
        step_size=1E-6,
    )
    if solar_system.get_total_energy() < 0:
        break

## Evolve the solar system for a number of days
t = 0
duration =  0.25 # years
t_end = t + duration * 365.25 # days

## Animate the orbits of the inner solar system
solar_system.plot_orbits(
    t, 
    t_end, 
    indices=None, 
    keep_points="all", 
    resample_every_dt=1,
    animated=True,
    mark_every_dt=1*365.25, 
    real_time=False,
    save=False, 
    adaptive=True, 
    relative_error=1E-10)

Here is example output for n=3 and n=5. Note the much smaller relative error that the adaptive integrator is able to achieve.