Easily calculate precession and obliquity from an orbital solution (OS, defaults to ZB18a from Zeebe and Lourens (2019)) and assumed or reconstructed values for tidal dissipation (T_d) and dynamical ellipticity (E_d). This is a translation and adaptation of the C-code in the supplementary material to Zeebe and Lourens (2022), with further details on the methodology described in Zeebe (2022). The name of the C-routine is snvec, which refers to the key units of computation: spin vector s and orbit normal vector n.

Installation

You can install snvecR like so:

install.packages("snvecR")

To use the development version of the package, use:

remotes::install_github("japhir/snvecR")

Example

Here’s the main function that does the work in action:

library(snvecR)
solution <- snvec()
#> Integration parameters:
#> • `tend` = -1000 ka
#> • `ed` = 1
#> • `td` = 0
#> • `orbital_solution` = "ZB18a"
#> • `tres` = 0.4 kyr
#> • `atol` = 1e-05
#> • `rtol` = 0
#> • `solver` = "vode"
#> ℹ started at "2023-06-20 10:46:50.62214"
#> Final values:
#> • s[1][2][3]: 0.404184487124565 -0.0537555129057148 0.913036138471423
#> • s-error = |s|-1: 0.353152142725588
#> Final values:
#> • obliquity: 0.413060472710089 rad
#> • precession: -0.562357122261027 rad
#> ℹ stopped at "2023-06-20 10:46:51.950145"
#> ℹ total duration: 1.33s

see ?snvec for further documentation.

Here we create a quick plot of the calculated climatic precession with the eccentricity envelope:

library(ggplot2)
solution |>
  ggplot(aes(x = age, y = cp)) +
  labs(x = "Age (ka)", y = "(-)", colour = "Orbital Element") +
  # the age scale goes from old to young
  scale_x_reverse() +
  # plot climatic precession
  geom_line(aes(colour = "Climatic Precession")) +
  # add the (interpolated) eccentricity envelope
  geom_line(aes(y = eei, colour = "Eccentricity")) +
  scale_color_discrete(type = c("skyblue", "black")) +
  theme(legend.pos = c(.9, .95))

References

Zeebe, R. E., & Lourens, L. J. (2019). Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy. Science, 365(6456), 926–929. doi:10.1126/science.aax0612.

Zeebe, R. E., & Lourens, L. J. (2022). A deep-time dating tool for paleo-applications utilizing obliquity and precession cycles: The role of dynamical ellipticity and tidal dissipation. Paleoceanography and Paleoclimatology, e2021PA004349. doi:10.1029/2021PA004349.

Zeebe, R. E. (2022). Reduced Variations in Earth’s and Mars’ Orbital Inclination and Earth’s Obliquity from 58 to 48 Myr ago due to Solar System Chaos. The Astronomical Journal, 164(3), doi:10.3847/1538-3881/ac80f8.

Wikipedia page on Orbital Elements: https://en.wikipedia.org/wiki/Orbital_elements