PyOrb

PyOrb is a lightweight package designed to convert back and forth between cartesian and kepler coordinates seamlessly and in a physically consistent manner, following defined rules. It provides a convenience class for handling orbits and is tested for special cases such as planar and circular orbits.

See full documentation here.

Feature list

Current features:

• Clear definition of an orbit, consistent throughout the code, including planar and circular orbits
• Kepler to Cartesian conversion
• Cartesian to Kepler conversion
• Can handle hyperbolic orbits
• All function handles all special cases (e.g. planar, circular and parabolic orbits)
• Convenient Orbit class or storing orbits and seamlessly convert between Kepler and Cartesian elements
• Access to all types of orbit anomalies
• Vectorized function for increased performance
• Access to alternative parameterizations such as Equinoctial elements

On the upcoming feature list:

• C-implementation of conversion function for performance
• Converting of orbits to a byte-stream
• Saving orbits to file (binary or HDFS 5)

To install

pip install pyorb

or to do the "nightly" build:

git clone https://github.com/danielk333/pyorb
cd pyorb
git checkout develop
pip install .

Alternatively, if you are following updates closely you can install using pip install -e . so that in the future a git pull will update the library.

Example

import pyorb

orb = pyorb.Orbit(M0 = pyorb.M_sol, degrees=True)
orb.update(a=1*pyorb.AU, e=0, i=0, omega=0, Omega=0, anom=0)

# Convert and get cartesian elements
print(orb.cartesian)

# Make eccentric and place at aphelion
orb.e = 0.2
orb.anom = 180

# print cartesian position in AU at aphelion after the above changes
print(orb.r/pyorb.AU)

To develop

First clone and branch off develop

git clone https://github.com/danielk333/pyorb
cd pyorb
git checkout develop
git checkout -b my-name/my-feature

then editable install with development extras and install the pre-commit hooks

pip install -e .[develop]
pre-commit install

and get to hacking!

Internal development

Please refer to the style and contribution guidelines documented in the IRF Software Contribution Guide.

External code-contributions

Generally external code-contributions are made trough a "Fork-and-pull" workflow towards the develop branch.

Ellipse and angle definitions

Variables:

• a: Semi-major axis
• e: Eccentricity
• i: Inclination
• omega: Argument of perihelion
• Omega: Longitude of the ascending node
• nu: True anomaly
• E: Elliptic, parabolic or hyperbolic eccentric anomaly
• M: Mean anomaly

Orientation of the ellipse in the coordinate system and angle definitions:

• For zero inclination: the ellipse is located in the x-y plane.
• The direction of motion as True anomaly increases for a zero inclination orbit is anti-coockwise, i.e. from +x towards +y.
• If the eccentricity is increased for an unrotated orbit, the periapsis will lie in +x direction.
• If the inclination is increased, the ellipse will rotate around the x-axis, so that +y is rotated toward +z.
• An increase in Longitude of the ascending node corresponds to a rotation around the z-axis so that +x is rotated toward +y.
• Changing argument of perihelion will not change the plane of the orbit, it will rotate the orbit in the plane.
• Changing argument of perihelion will rotate the periapsis in the direction of motion.
• True anomaly measures from the +x axis, i.e nu = 0 is located at periapsis and nu = pi at apoapsis.
• All anomalies and orientation angles reach between 0 and 2pi
• If the inclination is 0 or pi the longitude of the ascending node is always zero (the rotation is described by only argument of perihelion).
• If the eccentricity is zero, the argument of perihelion is always zero (the rotation is described by only the longitude of the ascending node).
• If both e=0 and i=0 or i=pi: the position on the circle is only described by the anomaly.
• The eccentric anomaly is used for elliptic, parabolic and hyperbolic cases but the kepler equation changes accordingly.

• For parabolic and hyperbolic orbits the true and eccentric anomaly wraps at pi to the same trajectory, not the mirror version.

  Shape definitions:

• The Semi-major axis is always positive.
• In the case of a parabolic orbit, as the Semi-major axis is undefined it is used as the periapsis distance instead.

Notes

Disabling direct conversion

There are two toggle flags in the pyorb.Orbit class for changing the conversion behavior: direct_update and auto_update that are True by default.

Disabling direct_update will stop automatic conversion between elements if any element is changed. This would allow for e.g.

orb.a = 1
orb.omega = 0

without any conversion to be done. However, as the kepler elements changed, the class has internally tracked this change and if auto_update=True once an access to a cartesian property is performed, e.g. print(orb.x), the conversion is performed so that the pair of cartesian-kepler elements are never contradictory.

If also auto_update is disabled, the update between kepler and cartesian needs to be manually by calling

orb.calculate_cartesian()

or

orb.calculate_kepler()

Using conversion functions directly

The pyorb.cart_to_kep or pyorb.kep_to_cart uses True anomaly and takes only numpy arrays ordered as per the function documentation.

Frames

Remember that an Keplerian orbit only makes sense in an inertial frame if gravitation dominated physics is your concern.

Array orbits

• Properties act on ALL orbits in the class
• Only way to update individual orbits of a set is to use self.update with the inds keyword
• Iterations are passive, the objects are copies from the array so the array itself is NOT modified

Rebound

The very excellent multi-purpose N-body integrator rebound has also implemented conversion from their particles to orbital elements. Important to note is that their conventions differ somewhat from ours by:

• Semi-major axis becomes negative when the orbit is hyperbolic
• Longitude of ascending node can become negative

otherwise the orbit routines should produce identical results.