No theoretical basis for orbit–spin coupling as a forcing of Martian global dust storms

Introduction:
The interannual variability of Martian global dust storms remains one of the major questions in Mars atmospheric science. While regional dust storms occur every year during southern spring and summer, only some Martian years exhibit planet-encircling dust storms. Several studies have proposed that this variability may be statistically correlated to Mars orbital angular momentum relative to the solar system barycenter. In particular, Shirley (2015, 2017) proposed that an inertial acceleration, referred to as the Coupling Term Acceleration (CTA), could couple the orbital motion of Mars to its proper rotation and act as a dynamical forcing on the atmosphere. Consequently, this term was used in both numerical and observational studies to investigate whether orbit-spin coupling could contribute to the timing and occurrence of Martian global dust storms (Shirley and Mischna, 2017; Mischna and Shirley, 2017; Newman et al., 2019; Shirley et al., 2020). Here, following Pierron and Forget (2026), we reassess the theoretical framework of this orbit-spin coupling hypothesis by rederiving the inertial forces acting on a parcel of air in a rotating and orbiting planetary frame.

The orbit-spin coupling hypothesis:
In Shirley (2017), the CTA was obtained from the derivation of the velocity of an atmospheric parcel expressed in an inertial frame and then transformed into rotating reference frames associated with the orbital and spin motions of the planet. The resulting acceleration was argued to contain a term proportional to (Ω × ω) × r, where Ω is the orbital angular velocity, ω is the planetary spin angular velocity, and r is the position of the air parcel relative to the planet center. Such a term would represent a direct inertial coupling between orbit and spin. Since it is proportional to the orbital angular velocity, and expressed in terms of the time variation of the orbital angular momentum, it has been hypothesized to provide a dynamical forcing depending on time, that could contribute to the initiation of Martian global dust storms.

As shown in Pierron and Forget (2026),  this term results from an inconsistent use of the transport theorem between rotating frames and should not appear in the correctly derived momentum equation.

Inertial forces and gravitational tides:
We start from the velocity of a parcel of air in the inertial frame,

V = dR/dtR0 + ω × r + v,

where R is the position of the planet center, ω is the planetary spin angular velocity, r is the parcel position relative to the planet center, and v is the parcel velocity in the planet-fixed frame. The standard transport theorem gives

dV/dtR0 = dv/dtR2 + ω × (ω × r) + 2ω × v + dω/dtR2 × r + d²R/dt²R0.

This expression contains only the classical inertial accelerations (centrifugal, Coriolis, and Euler terms). The last term is the translational acceleration of the planet along its orbit. It can be expressed as a function of the orbital angular momentum and its time derivative, but it does not involve the planetary spin and therefore is not an orbit-spin coupling term.

Moreover, this orbital inertial acceleration is not an atmospheric forcing. Applying Newton's second law to the whole planet-atmosphere system gives, to first order,

d²R/dt²R0 = g_ext(R),

therefore, for an atmospheric parcel we have

m g_ext(R + r) - m d²R/dt²R0 = m ∇g_ext(R) · r.

Thus, the orbital inertial acceleration is almost entirely compensated by the external gravitational field. The remaining term is the well known gravitational tide and not a direct orbit-spin coupling acceleration.

Implications for Martian global dust storms:
Our calculations show that the CTA should not be included in the atmospheric momentum budget of Mars general circulation models. Although true orbit-spin coupling exists through gravitational tidal torques, it acts slowly by modifying the spin rate of a planet over long timescales. It does not provide an instantaneous atmospheric forcing capable of explaining the interannual variability of Martian global dust storms. The occurrence of such storms is therefore more likely controlled by atmospheric dynamics, radiative-dust feedbacks, and the spatial and temporal variability of surface dust reservoirs (Mulholland et al., 2013; Newman and Richardson, 2015).

Figure 1: Schematic representation of the reference frames and vectors used in this study. R0 is the inertial barycentric frame, R1 rotates with the orbital angular velocity Ω, and R2 is the planet-fixed frame rotating with spin angular velocity ω. The vectors R, r, and v denote the planet position, the parcel position relative to the planet center, and the parcel velocity in R2, respectively.

References:
Shirley, J. H. (2015). Icarus, 251, 128-144.
Shirley, J. H. (2017). Planetary and Space Science, 141, 1-16.
Shirley, J. H., and Mischna, M. A. (2017). Planetary and Space Science, 139, 37-50.
Mischna, M. A., and Shirley, J. H. (2017). Planetary and Space Science, 141, 45-72.
Newman, C. E., Lee, C., Mischna, M. A., Richardson, M. I., and Shirley, J. H. (2019). Icarus, 317, 649-668.
Shirley, J. H., McKim, R. J., Battalio, J. M., and Kass, D. M. (2020). Journal of Geophysical Research: Planets, 125, e2019JE006077.
Mulholland, D. P., Read, P. L., and Lewis, S. R. (2013). Icarus, 223, 344-358.
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Pierron, T., and Forget, F. (2026). Icarus, 450, 116984.