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The Dependence of Earth Milankovitch Cycles on Martian Mass

Stephen R. Kane, Pam Vervoort, Jonathan Horner

TL;DR

This study quantifies how Earth’s Milankovitch climate forcing responds to changes in Mars’ mass by performing long, high-fidelity $N$-body simulations of the eight-planet system with Mars mass varied from 0% to 1000% of its present value. Using the Mercury integrator with post-Newtonian corrections and a Laskar-based spin dynamics model for Earth, the authors track the evolution of $k=e\cos\varpi$, $e$, $q=\sin(i/2)\cos\Omega$, and the obliquity $\varepsilon$ over $10^8$ year runs and analyze their spectra in terms of the secular $g_i$ and $s_i$ modes. They find that while the $\sim405$ kyr metronome driven by $g_2-g_5$ persists across masses, the inner-planet $g$-modes strengthen and re-distribute power as Mars becomes more massive, shortening the $\sim$70 kyr apsidal bands and eventually damping the $\sim$171 kyr component. Obliquity cycles lengthen from $\sim$41 kyr toward $45$–$55$ kyr with higher Mars mass, and very long envelopes emerge at extreme masses, indicating strong coupling and near-commensurabilities. These results yield a calibrated exo-Milankovitch template: planetary architecture, via perturber mass, imprints predictable shifts in the periods and amplitudes of eccentricity and obliquity forcing, with direct implications for climate stability and habitability assessments of Earth-like exoplanets.

Abstract

The Milankovitch cycles of Earth result from gravitational interactions with other bodies in the Solar System. These interactions lead to slow changes in the orbit and angular momentum vector of Earth, and correspondingly influence Earth's climate evolution. Several studies have shown that Mars may play a significant role in these Milankovitch cycles, such as the 2.4 Myr eccentricity cycle related to perihelion precession dynamics. Here we provide the results of a detailed dynamical analysis that explores the Earth Milankovitch cycles as a function of the Martian mass to quantify the extent that Mars influences variations in Earth's orbital eccentricity, the longitude of perihelion, the longitude of the ascending node, and obliquity (axial tilt). Our results show that, although the 405 kyr long-eccentricity metronome driven by $g_2$ (Venus) and $g_5$ (Jupiter) persists at all Mars masses, the $\sim$100 kyr short-eccentricity bands driven by $g_4$ (Mars) lengthen and gain power as Mars becomes more massive, consistent with enhanced coupling among inner-planet $g$-modes. The 2.4 Myr grand cycle is absent when Mars approaches zero mass, reflecting the movement of $g_4$ with the Martian mass. Meanwhile, Earth's obliquity cycles driven by $s_3$ (Earth) and $s_4$ (Mars) lengthen from the canonical $\sim$41 kyr with increasing Mars mass, relocating to a dominant 45--55 kyr band when the mass of Mars is an order of magnitude larger than its present value. These results establish how Mars' mass controls the architecture of Earth's climate-forcing spectrum and that the Milankovitch spectrum of an Earth-like planet is a sensitive, interpretable probe of its planetary neighborhood.

The Dependence of Earth Milankovitch Cycles on Martian Mass

TL;DR

This study quantifies how Earth’s Milankovitch climate forcing responds to changes in Mars’ mass by performing long, high-fidelity -body simulations of the eight-planet system with Mars mass varied from 0% to 1000% of its present value. Using the Mercury integrator with post-Newtonian corrections and a Laskar-based spin dynamics model for Earth, the authors track the evolution of , , , and the obliquity over year runs and analyze their spectra in terms of the secular and modes. They find that while the kyr metronome driven by persists across masses, the inner-planet -modes strengthen and re-distribute power as Mars becomes more massive, shortening the 70 kyr apsidal bands and eventually damping the 171 kyr component. Obliquity cycles lengthen from 41 kyr toward – kyr with higher Mars mass, and very long envelopes emerge at extreme masses, indicating strong coupling and near-commensurabilities. These results yield a calibrated exo-Milankovitch template: planetary architecture, via perturber mass, imprints predictable shifts in the periods and amplitudes of eccentricity and obliquity forcing, with direct implications for climate stability and habitability assessments of Earth-like exoplanets.

Abstract

The Milankovitch cycles of Earth result from gravitational interactions with other bodies in the Solar System. These interactions lead to slow changes in the orbit and angular momentum vector of Earth, and correspondingly influence Earth's climate evolution. Several studies have shown that Mars may play a significant role in these Milankovitch cycles, such as the 2.4 Myr eccentricity cycle related to perihelion precession dynamics. Here we provide the results of a detailed dynamical analysis that explores the Earth Milankovitch cycles as a function of the Martian mass to quantify the extent that Mars influences variations in Earth's orbital eccentricity, the longitude of perihelion, the longitude of the ascending node, and obliquity (axial tilt). Our results show that, although the 405 kyr long-eccentricity metronome driven by (Venus) and (Jupiter) persists at all Mars masses, the 100 kyr short-eccentricity bands driven by (Mars) lengthen and gain power as Mars becomes more massive, consistent with enhanced coupling among inner-planet -modes. The 2.4 Myr grand cycle is absent when Mars approaches zero mass, reflecting the movement of with the Martian mass. Meanwhile, Earth's obliquity cycles driven by (Earth) and (Mars) lengthen from the canonical 41 kyr with increasing Mars mass, relocating to a dominant 45--55 kyr band when the mass of Mars is an order of magnitude larger than its present value. These results establish how Mars' mass controls the architecture of Earth's climate-forcing spectrum and that the Milankovitch spectrum of an Earth-like planet is a sensitive, interpretable probe of its planetary neighborhood.

Paper Structure

This paper contains 12 sections, 6 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Dynamical Simulations
  4. Obliquity Calculations
  5. Results
  6. Baseline Dynamics
  7. Longitude of Perihelion
  8. Eccentricity
  9. Longitude of the Ascending Node
  10. Obliquity
  11. Discussion
  12. Conclusions

Figures (6)

  • Figure 1: Earth orbital evolution results, where the mass of Mars is set to 100% of its present value. The panels show, from top to bottom, the longitude of perihelion in terms of the $k$ parameter, the orbital eccentricity, the longitude of the ascending node in terms of the $q$ parameter, and the obliquity of the axial tilt. The panels on the right shown the normalized Fourier power, with major peaks identified in terms of the $g_i$ and $s_i$ nodes.
  • Figure 2: Periodograms resulting from a Fourier analysis of the $10^8$ yr longitude of perihelion data for Earth, shown for the cases of a 0%, 100%, 200%, and 1000% Mars mass, from top to bottom, respectively. The panels on the right shown the normalized Fourier power, with major peaks identified in terms of the $g_i$ nodes.
  • Figure 3: Periodograms resulting from a Fourier analysis of the $10^8$ yr eccentricity data for Earth, shown for the cases of a 0%, 100%, 200%, and 1000% Mars mass, from top to bottom, respectively. The panels on the right show the normalized Fourier power, with major peaks identified in terms of the $g_i$ nodes.
  • Figure 4: Periodograms resulting from a Fourier analysis of the $10^8$ yr longitude of the ascending node data for Earth, shown for the cases of a 0%, 100%, 200%, and 1000% Mars mass, from top to bottom, respectively. The panels on the right shown the normalized Fourier power, with major peaks identified in terms of the $s_i$ nodes.
  • Figure 5: Periodograms resulting from a Fourier analysis of the $10^8$ yr obliquity data for Earth, shown for the cases of a 0%, 100%, 200%, and 1000% Mars mass, from top to bottom, respectively. The panels on the right shown the normalized Fourier power, with major peaks identified in terms of the $s_i$ nodes.
  • ...and 1 more figures