<p>Back in 1965, Peter Goldreich published a short and elegant <a href="https://ui.adsabs.harvard.edu/abs/1965AJ.....70....5G/abstract" rel="nofollow noreferrer">paper</a> addressing the orbital evolution of a satellite of a uniformly precessing oblate planet. Goldreich demonstrated that, assuming the initial inclination the orbit on the equator is small, the orbit follows the precessing equator, the inclination undergoing periodic variations.</p>
<p>As it turned out later, Goldreich's treatment was carried out in orbital elements which were nonosculating. An instantaneous orbit parameterised by such elements is <em>not</em> tangent to the actual physical trajectory. In 2005, <a href="https://ui.adsabs.harvard.edu/abs/2005CeMDA..91...75E/abstract" rel="nofollow noreferrer">accurate analysis</a> was carried out in osculating elements (by myself), and it confirmed Goldreich's conclusion.</p>

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2024-06-21T15:33:28.357Z
When you link to a paper that you have authored, please *always* mention it explicitly in your answer. That prevents   your post accidentally being treated as spam.
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2024-06-20T21:12:49.487Z
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Michael_1812
<p>Phobos and Deimos are very close to Mars' equatorial plane (the inclination of their orbits is roughly 1°). The axial tilt of Mars has changed a lot over time, and might have had a inclination of over 60° compared to the ecliptic at times.</p>
<p>Did the inclination of Phobos and Deimos also change over time, following the axial tilt of Mars (and if so, by what mechanism?)? Or have the equator of Mars and the orbits of Phobos and Deimos lined up at the present time by chance?</p>

<mars><orbital-elements><phobos><deimos>
Has the inclination of the orbital plane of Phobos and Deimos followed that of Mars' axial tilt?
usernumber
# Has the inclination of the orbital plane of Phobos and Deimos followed that of Mars' axial tilt?

(Asked by: username_0 on 2020-07-15)

Phobos and Deimos are very close to Mars' equatorial plane (the inclination of their orbits is roughly 1°). The axial tilt of Mars has changed a lot over time, and might have had a inclination of over 60° compared to the ecliptic at times.

Did the inclination of Phobos and Deimos also change over time, following the axial tilt of Mars (and if so, by what mechanism?)? Or have the equator of Mars and the orbits of Phobos and Deimos lined up at the present time by chance?

**Tags:** mars, orbital-elements, phobos, deimos


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## 1 answers

### Answer by username_1 on 2024-06-20. Score: 3

Back in 1965, Peter Goldreich published a short and elegant [paper](https://ui.adsabs.harvard.edu/abs/1965AJ.....70....5G/abstract) addressing the orbital evolution of a satellite of a uniformly precessing oblate planet. Goldreich demonstrated that, assuming the initial inclination the orbit on the equator is small, the orbit follows the precessing equator, the inclination undergoing periodic variations.

As it turned out later, Goldreich's treatment was carried out in orbital elements which were nonosculating. An instantaneous orbit parameterised by such elements is *not* tangent to the actual physical trajectory. In 2005, [accurate analysis](https://ui.adsabs.harvard.edu/abs/2005CeMDA..91...75E/abstract) was carried out in osculating elements (by myself), and it confirmed Goldreich's conclusion.

> **Comments:**
> **username_2**: When you link to a paper that you have authored, please *always* mention it explicitly in your answer. That prevents   your post accidentally being treated as spam.  

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