Astronomical Solutions & Codes

ZB23-N64
Download DEEP TIME ENSEMBLES (N=64): Earth's eccentricity, inclination, obliquity, precession (+ periods), past 3.5 Gyr
Caution: The interval before -50 Myr is unconstrained due to solar system chaos.
Caution: For the interval -300 to 0 Myr, ZB18a and ZB20x are recommended, not ZB23-N64.

For more information, see:
Zeebe, R. E. and Lantink, M. L. A secular solar system resonance that disrupts the dominant cycle in Earth's orbital eccentricity (g2-g5): Implications for astrochronology. The Astronomical Journal, 2024. PDF

Zeebe, R. E. and Lantink, M. L. Milankovic forcing in Deep Time. PDF

ZB23-N64




orbitN
A symplectic integrator for near near-Keplerian planetary systems

For more information, see:
Zeebe, R. E. orbitN: A symplectic integrator for planetary systems dominated by a central mass - Insight into long-term solar system chaos The Astronomical Journal, 2023. PDF


The C code is available on github: github.com/rezeebe/orbitN

Correspondence to:










ZB20
Download Earth's eccentricity and inclination, past 300 Myr
Caution: The interval -300 Myr to -66 Myr is unconstrained due to solar system chaos.

For more information, see:
Zeebe, R. E. and Lourens, L. J. Geologically constrained astronomical solutions for the Cenozoic era, Earth and Planetary Science Letters, 2022. PDF

ZB20x+18a-300Myr.tar.gz
ZB20a
ZB20b
ZB20c
ZB20d
ZB18a






PT-ZB18a
Download Earth's obliquity and precession, past 100 Myr (pre-computed). Plus C code package. Caution: Dynamical ellipticity and tidal dissipation are largely unconstrained in the past.

For more information, see:
Zeebe, R. E. and Lourens, L. J. A deep-time dating tool for paleo-applications utilizing obliquity and precession cycles: The role of dynamical ellipticity and tidal dissipation, Paleoceanography and Paleoclimatology, 2022. PDF

PT-ZB18a





ZB18
Download Earth's eccentricity and inclination, past 100 Myr
Caution: The interval -100 Myr to -58 Myr is unconstrained due to solar system chaos.

For more information, see:
Zeebe, R. E. and Lourens, L. J. Solar system chaos and the Paleocene-Eocene boundary age constrained by geology and astronomy. Science, 10.1126/science.aax0612, 2019. PDF Supplement

ZB18a





ZB17
Download Earth's eccentricity and inclination, past 100 Myr
Caution: The interval -100 Myr to -50 Myr is unconstrained due to solar system chaos.

For more information, see:
Zeebe, R. E. Numerical Solutions for the orbital motion of the Solar System over the Past 100 Myr: Limits and new results. The Astronomical Journal, 2017. PDF

ZB17-ALL.tar.gz
ZB17a
ZB17b
ZB17c
ZB17d
ZB17e
ZB17f
ZB17h
ZB17i
ZB17j
ZB17k
ZB17p


Varadi03
Download output from Varadi et al. (2003)

Thanks to Bruce Runnegar and Michael Ghil the files are made available here. For more information, see:
Varadi, F., Runnegar, B., and Ghil, M. Successive refinements in long-term integrations of planetary orbits. The Astrophysical Journal, 592(1), 620, 2003.

r5_earth.dat
r7_earth.dat
More output