MeepMeep 1.0.0

Fast Keplerian orbit computation using Taylor series expansions.

MeepMeep

Fast Keplerian orbits for exoplanet modelling.

MeepMeep computes Keplerian orbit quantities — transit geometry, projected separations, radial velocities, and phase curves — using 5th-order Taylor expansions around a set of expansion points distributed along the orbit. This makes it an order of magnitude faster than per-point Newton-Raphson while keeping the approximation error well below the photometric noise of current instruments. Optional analytic gradients with respect to the orbital parameters make it suitable for gradient-based inference (HMC, optimisers).

All hot paths are Numba-jitted and can be called directly from your own @njit kernels with no wrapper overhead.

The method is described in Parviainen & Korth (2020), MNRAS 499, 3356.

Installation

pip install meepmeep

For a development checkout:

git clone https://github.com/hpparvi/meepmeep.git
cd meepmeep
pip install -e ".[test]"

Quickstart

import numpy as np
from meepmeep import Orbit

o = Orbit(npt=15, ep_placement="ea")
o.set_pars(tc=0.0, p=3.4, a=8.0, i=1.55, e=0.1, w=0.4)   # times in days, angles in radians
o.set_data(np.linspace(-0.15, 0.15, 500))

x, y, z = o.xyz()                       # sky-frame position (R_star); z > 0 toward observer
sep = np.hypot(x, y)                    # sky-projected separation, the b(t) of transit models
rv  = o.radial_velocity(k=120.0)        # radial velocity in the units of k

Bind tp=... instead of tc=... to anchor the orbit at periastron passage.

Analytic gradients

o = Orbit(derivatives=True)
o.set_pars(tc=0.0, p=3.4, a=8.0, i=1.55, e=0.1, w=0.4)
o.set_data(times)
x, y, z, dx, dy, dz = o.xyz()           # gradients w.r.t. (tc, p, a, i, e, w, lan), shape (N, 7)

Conventions

• Units: times in days, angles in radians, lengths in stellar radii (a is the scaled semi-major axis a / R_star).
• Parameter order (solvers and gradients): (tc, p, a, i, e, w, lan) — transit-centre time, period, scaled semi-major axis, inclination, eccentricity, argument of periastron, longitude of the ascending node. lan is optional and defaults to 0.0.
• Coordinates: x, y span the sky plane; z is the line of sight, positive toward the observer. Transit occurs at z > 0, secondary eclipse at z < 0; i = pi/2 is edge-on.

Public API

Import	Purpose
meepmeep.Orbit	3D, multi-expansion-point orbit; any orbital phase
meepmeep.Expansion2D / Expansion3D	single-expansion-point, transit-window evaluators
meepmeep.numba2d / meepmeep.numba3d	low-level @njit Taylor primitives

Everything under meepmeep.backends/ is implementation detail and may be restructured without notice; import only from the entry points above. See docs/llms.md for a complete API cheatsheet.

Testing

pip install -e ".[test]"
pytest meepmeep/tests/                                   # full suite
NUMBA_DISABLE_JIT=1 pytest -m "not slow" --cov           # with coverage

Coverage must run with the JIT disabled — compiled kernels are invisible to the tracer otherwise.

Documentation

Full documentation is built with Sphinx from docs/source/:

cd docs && make html      # output in docs/build/html/

Citing

If MeepMeep contributes to work that leads to a publication, please cite Parviainen and Korth (2020):

@ARTICLE{2020MNRAS.499.3356P,
       author = {{Parviainen}, H. and {Korth}, J.},
        title = "{Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion}",
      journal = {Monthly Notices of the Royal Astronomical Society},
         year = 2020,
        month = dec,
       volume = {499},
       number = {3},
        pages = {3356-3361},
          doi = {10.1093/mnras/staa2953},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2020MNRAS.499.3356P},
}

License

MeepMeep is released under the GNU General Public License v3.0. See LICENSE for details.