Canceling Effects of Conjunctions Render Higher Order Mean Motion Resonances Weak
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910018380496896 |
|---|---|
| author | Jones, Elizabeth K Hadden, Samuel Teekamongkol, Supakrai Tamayo, Daniel |
| author_facet | Jones, Elizabeth K Hadden, Samuel Teekamongkol, Supakrai Tamayo, Daniel |
| contents | Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling as $e^q$, where $q$ is the order of the resonance. This explains why first-order MMRs (e.g., 3:2 and 4:3) are important, while the infinite number of higher order integer ratios are not. However, this relationship derived from a technical perturbation series expansion provides little physical intuition. In this paper, we provide a simple physical explanation of this result for closely spaced orbits. In this limit, interplanetary interactions are negligible except during close encounters at conjunction, where the planets impart a gravitational "kick" to each other's mean motion. We show that while first-order MMRs involve a single conjunction before the configuration repeats, higher order MMRs involve multiple conjunctions per cycle, whose effects cancel out more precisely the higher the order of the resonance. Starting from the effects of a single conjunction, we provide an alternate, physically motivated derivation of MMRs' $e^q$ strength scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Canceling Effects of Conjunctions Render Higher Order Mean Motion Resonances Weak Jones, Elizabeth K Hadden, Samuel Teekamongkol, Supakrai Tamayo, Daniel Earth and Planetary Astrophysics Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling as $e^q$, where $q$ is the order of the resonance. This explains why first-order MMRs (e.g., 3:2 and 4:3) are important, while the infinite number of higher order integer ratios are not. However, this relationship derived from a technical perturbation series expansion provides little physical intuition. In this paper, we provide a simple physical explanation of this result for closely spaced orbits. In this limit, interplanetary interactions are negligible except during close encounters at conjunction, where the planets impart a gravitational "kick" to each other's mean motion. We show that while first-order MMRs involve a single conjunction before the configuration repeats, higher order MMRs involve multiple conjunctions per cycle, whose effects cancel out more precisely the higher the order of the resonance. Starting from the effects of a single conjunction, we provide an alternate, physically motivated derivation of MMRs' $e^q$ strength scaling. |
| title | Canceling Effects of Conjunctions Render Higher Order Mean Motion Resonances Weak |
| topic | Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2601.10585 |