Studies of lunar timing report mixed, population-specific findings. Small laboratory and field studies have reported sleep associations; a 2,125-person population study found no significant overall effect. Marine mechanisms, human observations and cultural practice require different kinds of evidence.

The sleep comparison distinguishes participants from repeated recordings and preserves contradictory results. A personal check-in is exploratory and does not validate an individual lunar rhythm. This collection draws from 10 seed papers published in journals including Science Advances, Nature Communications, Molecular Psychiatry, and EMBO Reports. Below, our evidence matrix describes study design, reported findings and limitations. Its labels are editorial descriptions, not a validated grading system.

The Skeptical Chronobiology & Evidence Matrix

Selected studies and reviews, including null findings. Labels describe study design or review status, not a validated quality score. Reviewed 10 October 2026.

Sources and limits
Sleep Architecture · 2013Laboratory analysis

A retrospective laboratory analysis reported sleep differences around the full moon.

Cajochen, C., Altanay-Ekici, S., Münch, M., Frey, S., Knoblauch, V., & Wirz-Justice, A. (2013). Evidence that the lunar cycle influences human sleep. Current Biology, 23(15), 1485–1488. https://doi.org/10.1016/j.cub.2013.06.029

Reported sample:33
Study Design:Retrospective analysis of controlled laboratory observations
Measured Effect:Reported 20-minute shorter sleep and 30% lower NREM delta activity around full moon

The authors reported sleep differences in a small laboratory sample. Lunar phase was analyzed after the original experiment; this was not a preregistered test of a lunar hypothesis.

33 participants; retrospective lunar-phase analysis

Limits: Cordi and colleagues’ larger retrospective EEG datasets did not replicate the reported sleep effects. Haba-Rubio and colleagues also found no significant overall association in a population cohort. These are differing designs, not one pooled experiment.

Proposed mechanism: An endogenous lunar rhythm was proposed. This study did not establish a human cryptochrome pathway or show that gravity caused the findings.
Source-specific summaryDOI: 10.1016/j.cub.2013.06.029
Sleep Architecture · 2014Null finding

Retrospective EEG analyses did not replicate the reported lunar sleep effects.

Cordi, M., Ackermann, S., Bes, F. W., Hartmann, F., Konrad, B. N., Genzel, L., Pawlowski, M., Steiger, A., Schulz, H., Rasch, B., & Dresler, M. (2014). Lunar cycle effects on sleep and the file drawer problem. Current Biology, 24(12), R549–R550. https://doi.org/10.1016/j.cub.2014.05.017

Reported sample:See sample description
Study Design:Retrospective comparison across three EEG datasets
Measured Effect:Reported Cajochen sleep effects were not replicated; no pooled effect estimate

The authors found no significant replication of the sleep effects reported in 2013 across these datasets. They also raised possible publication bias from unpublished null results.

Three separate datasets: 470 EEG recordings from 366 participants; 757 recordings from 29 volunteers; home EEG recordings from 870 volunteers. Recordings and people must not be added as equivalent units.

Limits: A published contradictory analysis with repeated recordings in one dataset. It does not prove that every possible lunar association is absent.

Proposed mechanism: These analyses establish no human lunar pathway. Differences between study designs and selective publication require consideration.
Source-specific summaryDOI: 10.1016/j.cub.2014.05.017
Sleep Architecture · 2021Observational

Field observations reported later, shorter sleep before the full moon.

Casiraghi, L., Spiousas, I., Dunster, G. P., McGlothlen, K., Fernández-Duque, E., Valeggia, C., & de la Iglesia, H. O. (2021). Moonstruck sleep: Synchronization of human sleep with the moon cycle under field conditions. Science Advances, 7(5), Article eabe0465. https://doi.org/10.1126/sciadv.abe0465

Reported sample:See sample description
Study Design:Wrist-actimetry field observations; separately collected student data
Measured Effect:Reported timing and duration patterns before full moon; estimates vary by cohort

Sleep timing and duration varied with lunar phase in the reported communities and student analyses. The paper uses different recording periods and fitted subsets; it does not predict any individual’s sleep.

98 Toba/Qom participants recorded; 69 had enough data for individual fitting and 51 entered a fit-quality subset. Separately, 464 Seattle students were recorded and one inconsistent wearer was excluded. These are distinct analysis populations.

Limits: Toba/Qom recordings lasted one to two months, while student recordings lasted one to three weeks. Cohorts and fitted subsets are not one pooled sample or independent preregistered replications.

Proposed mechanism: Evening moonlight was proposed as a contributor. The observational design does not isolate a universal causal mechanism.
Source-specific summaryDOI: 10.1126/sciadv.abe0465
Sleep Architecture · 2015Null finding

A population study found no significant overall association between lunar phase and sleep.

Haba-Rubio, J., Marques-Vidal, P., Tobback, N., Andries, D., Preisig, M., Kuehner, C., Vollenweider, P., Waeber, G., Luca, G., Tafti, M., & Heinzer, R. (2015). Bad sleep? Don’t blame the moon! A population-based study. Sleep Medicine, 16(11), 1321–1326. https://doi.org/10.1016/j.sleep.2015.08.002

Reported sample:2,125
Study Design:Population cohort with home polysomnography
Measured Effect:Overall sleep-duration comparison: p = 0.31

The study found no significant overall differences in subjective sleep quality, sleep duration or other assessed sleep parameters between lunar phases.

2,125 participants; EEG spectral analysis in a 759-person subset

Limits: Overall findings were null. Exploratory subgroup trends reported in the abstract are separate from the overall duration comparison; neither proves zero effect in every setting.

Proposed mechanism: No lunar mechanism was established by these null findings.
Source-specific summaryDOI: 10.1016/j.sleep.2015.08.002
Mood & Bipolar Cycling · 2018Observational

A small retrospective clinical series proposed an association between mood cycles and lunar tidal periods.

Wehr, T. A. (2018). Bipolar mood cycles and lunar tidal cycles. Molecular Psychiatry, 23(4), 923–931. https://doi.org/10.1038/mp.2016.263

Reported sample:17
Study Design:Retrospective clinical time-series analysis
Measured Effect:Reported alignment in selected mood time series; no general population effect estimate

The paper’s selected clinical observations are hypothesis-generating. They do not establish a lunar effect on mental health in the general population.

17 patients in the reported clinical series

Limits: Small selected sample and retrospective analysis limit generalization. This archive does not document an independent preregistered replication.

Proposed mechanism: A biological pathway remains a hypothesis; gravity, geomagnetism and electrolyte effects are not established here.
Source-specific summaryDOI: 10.1038/mp.2016.263
Marine Reproduction · 1986Observational

Field observations documented synchronous spawning across reef-building coral species.

Babcock, R. C., Bull, G. D., Harrison, P. L., Heyward, A. J., Oliver, J. K., Wallace, C. C., & Willis, B. L. (1986). Synchronous spawnings of 105 scleractinian coral species on the Great Barrier Reef. Marine Biology, 90(3), 379–394. https://doi.org/10.1007/bf00428562

Reported sample:See sample description
Study Design:Marine field observations
Measured Effect:Spawning documented on a few annual nights between full and last-quarter moon

The study documents coral reproduction in a particular marine setting, with seasonal, lunar and daily timing. It does not establish a comparable effect in humans.

105 species at five reefs; species count is not a count of independent individuals

Limits: Species, location and season constrain interpretation. Universal verification across all reefs is not claimed.

Proposed mechanism: The authors discuss possible timing cues. This 1986 field study does not demonstrate a cryptochrome receptor or a hormonal pathway.
Source-specific summaryDOI: 10.1007/BF00428562
Emergency Medicine (Myth) · 1985Literature review

A historical review examined claims of a “lunar-lunacy” association.

Rotton, J., & Kelly, I. W. (1985). Much ado about the full moon: A meta-analysis of lunar-lunacy research. Psychological Bulletin, 97(2), 286–306. https://doi.org/10.1037/0033-2909.97.2.286

Reported sample:See sample description
Study Design:Literature meta-analysis
Measured Effect:Former hardcoded correlation removed pending verification against the full paper

This review is retained as a source for inspecting lunar-lunacy claims. Its presence in the library does not certify every modern emergency-care claim.

Meta-analysis; the former pooled individual count was unverified and is withdrawn

Limits: The former list of conclusive replications was not supported by complete reference records and has been withdrawn.

Proposed mechanism: No biological mechanism is established by this reference record.
Source-specific summaryDOI: 10.1037/0033-2909.97.2.286
Financial Volatility · 2006Release hold

Historical lunar-market research is bibliographic context; Lunologium’s market results remain withheld.

Yuan, K., Zheng, L., & Zhu, Q. (2006). Are investors moonstruck? Lunar phases and stock returns. Journal of Empirical Finance, 13(1), 1–23. https://doi.org/10.1016/j.jempfin.2005.06.001

Reported sample:See sample description
Study Design:Historical econometric paper; separate from the current release-controlled observatory
Measured Effect:Current derived market results are withheld

The reference identifies a published paper. This card does not publish a local analysis, establish predictive validity or reinstate retired market statistics.

Not presented as a current Lunologium dataset

Limits: The current market source-rights gate remains in force. No local results, price history or derived event windows are released through this research summary.

Proposed mechanism: Investor mood is a hypothesis, not an established lunar causal pathway.
Source-specific summaryDOI: 10.1016/j.jempfin.2005.06.001

Checked seed bibliography

Source identities checked 11 October 2026. Complete references remain available without search or scripts. Summaries distinguish observations, mechanisms and reviews.

  1. Helfrich-Förster, C., Monecke, S., Spiousas, I., Hovestadt, T., Mitesser, O., & Wehr, T. A. (2021). Women temporarily synchronize their menstrual cycles with the luminance and gravimetric cycles of the Moon. Science Advances, 7(5), eabe1358. https://doi.org/10.1126/sciadv.abe1358

    Selected long-term records from 22 women showed intermittent timing associations. The analysis does not establish universal synchronization, a gravity receptor, clinical benefit or an individual prediction.

    Open source: Women temporarily synchronize their menstrual cycles with the luminance and gravimetric cycles of the Moon

  2. Helfrich-Förster, C., Domenie, E. D., Mitesser, O., Hovestadt, T., Ferlin, A., Wehr, T. A., Costa, R., & Montagnese, S. (2025). Synchronization of women’s menstruation with the Moon has decreased but remains detectable when gravitational pull is strong. Science Advances, 11(39), eadw4096. https://doi.org/10.1126/sciadv.adw4096

    The authors compare selected long-term menstrual records across historical periods. They propose light exposure and gravitational timing as explanations for changed associations; this observational comparison does not isolate those causes or validate a cycle prediction.

    Open source: Synchronization of women’s menstruation with the Moon has decreased but remains detectable when gravitational pull is strong

  3. Ecochard, R., Stanford, J. B., Fehring, R. J., Schneider, M., Najmabadi, S., & Gronfier, C. (2024). Evidence that the woman’s ovarian cycle is driven by an internal circamonthly timing system. Science Advances, 10(15), eadg9646. https://doi.org/10.1126/sciadv.adg9646

    Ecochard and colleagues analyze 26,912 cycles from 2,303 European women and 4,786 cycles from 721 North American women. Time-series characteristics support an internal timing hypothesis. The reported lunar alignment differs between populations; these records do not demonstrate a molecular lunar sensor or an effective fertility intervention.

    Open source: Evidence that the woman’s ovarian cycle is driven by an internal circamonthly timing system

  4. Poehn, B., Krishnan, S., Zurl, M., Coric, A., Rokvic, D., Häfker, N. S., Jaenicke, E., Arboleda, E., Orel, L., Raible, F., Wolf, E., & Tessmar-Raible, K. (2022). A Cryptochrome adopts distinct moon- and sunlight states and functions as sun- versus moonlight interpreter in monthly oscillator entrainment. Nature Communications, 13(1), 5220. https://doi.org/10.1038/s41467-022-32562-z

    Experiments on Platynereis dumerilii and its L-Cryptochrome examine species-specific light responses relevant to reproductive timing. The marine bristle-worm findings do not establish a corresponding sensor in humans.

    Open source: A Cryptochrome adopts distinct moon- and sunlight states and functions as sun- versus moonlight interpreter in monthly oscillator entrainment

  5. Ritter, A., & Tessmar-Raible, K. (2024). Time me by the moon. EMBO Reports, 25(8), 3169–3176. https://doi.org/10.1038/s44319-024-00196-5

    Ritter and Tessmar-Raible review the evolution and function of lunar timing systems across organisms. This is a synthesis, not a new human experiment or proof that the same mechanism operates across species.

    Open source: Time me by the moon

  6. Wehr, T. A. (2018). Bipolar mood cycles and lunar tidal cycles. Molecular Psychiatry, 23(4), 923–931. https://doi.org/10.1038/mp.2016.263

    A retrospective series of 17 selected patients explores mood-cycle timing and lunar tidal periods. The observations generate hypotheses; they do not establish gravitational causation, a population-wide mental-health effect or a treatment recommendation.

    Open source: Bipolar mood cycles and lunar tidal cycles

  7. Alberghina, D. (2025). A rhythmic dance: how lunar cycles influence reproductive behavior in vertebrates. Frontiers in Mammal Science, 4, 1690167. https://doi.org/10.3389/fmamm.2025.1690167

    Alberghina’s mini review surveys vertebrate reproductive timing literature. Comparative observations depend on species and setting. The review supplies context for hypotheses; it does not independently demonstrate a human reproductive mechanism.

    Open source: A rhythmic dance: how lunar cycles influence reproductive behavior in vertebrates

  8. Dopico, X. C., Evangelou, M., Ferreira, R. C., Guo, H., Pekalski, M. L., Smyth, D. J., Cooper, N., Burren, O. S., Fulford, A. J., Hennig, B. J., Prentice, A. M., Ziegler, A. G., Bonifacio, E., Wallace, C., & Todd, J. A. (2015). Widespread seasonal gene expression reveals annual differences in human immunity and physiology. Nature Communications, 6(1), 7000. https://doi.org/10.1038/ncomms8000

    Dopico and colleagues report seasonal expression in 5,136 of 22,822 genes tested in the BABYDIET blood-cell dataset, with comparisons across other cohorts and tissues. The proportion refers to that analysis, not every gene in every person. Seasonal immune patterns do not validate lunar, zodiac or individual energy predictions.

    Open source: Widespread seasonal gene expression reveals annual differences in human immunity and physiology

  9. Meyer, C., Muto, V., Jaspar, M., Kussé, C., Lambot, E., Chellappa, S. L., Degueldre, C., Balteau, E., Luxen, A., Middleton, B., Archer, S. N., Collette, F., Dijk, D. J., Phillips, C., Maquet, P., & Vandewalle, G. (2016). Seasonality in human cognitive brain responses. Proceedings of the National Academy of Sciences, 113(11), 3066–3071. https://doi.org/10.1073/pnas.1518129113

    Meyer and colleagues examine task-related fMRI responses at different times of year after a controlled laboratory protocol. Seasonal brain-response differences do not mean that each person’s attention or memory performance peaks at a solstice or equinox. This study does not establish a lunar effect.

    Open source: Seasonality in human cognitive brain responses

  10. Hohm, I., Wormley, A. S., Schaller, M., & Varnum, M. E. W. (2024). Homo temporus : Seasonal Cycles as a Fundamental Source of Variation in Human Psychology. Perspectives on Psychological Science, 19(1), 151–172. https://doi.org/10.1177/17456916231178695

    Hohm and colleagues review seasonal variation and propose meteorological, ecological and sociocultural pathways for further study. This synthesis does not validate astrology, a universal seasonal energy schedule or an individual forecast.

    Open source: Homo temporus : Seasonal Cycles as a Fundamental Source of Variation in Human Psychology
PEER-REVIEWED RESEARCH

Women's Health & Moon Cycles

Science is uncovering that the ancient connection between women's cycles and the Moon is real — it's just that modern light pollution may be dimming it. Explore the peer-reviewed research below.

Powered by OpenAlex — open scholarly data
✦CORRELATIO • FULL MOON RESEARCH

It's a Full Moon tonight — 50% illuminated

Tonight’s phase is astronomical context for exploring the literature. It does not predict your sleep, hormone levels or mood. Compare study-specific findings with their limitations and null results.

Menstrual Synchrony

Inspect selected observations of menstrual timing and lunar phase, including sampling, intermittent associations and uncertain mechanisms.

✦PAPIRUS • HELFRICH-FÖRSTER (2021)
OPEN ACCESS

Women temporarily synchronize their menstrual cycles with the luminance and gravimetric cycles of the Moon

C. Helfrich-Förster, S. Monecke, I. Spiousas, T. Hovestadt, O. Mitesser, T. A. Wehr•Science Advances•2021Source identity checked 2026-10-11

Intermittent associations in selected records; a human causal mechanism remains unresolved.

Selected long-term records from 22 women showed intermittent timing associations. The analysis does not establish universal synchronization, a gravity receptor, clinical benefit or an individual prediction.

✦PAPIRUS • HELFRICH-FÖRSTER (2025)
OPEN ACCESS

Synchronization of women’s menstruation with the Moon has decreased but remains detectable when gravitational pull is strong

Charlotte Helfrich-Förster, Esther D. Domenie, Oliver Mitesser, Thomas Hovestadt, Alberto Ferlin, Thomas A. Wehr, Rodolfo Costa, Sara Montagnese•Science Advances•2025Source identity checked 2026-10-11

Historical timing associations and proposed explanations require separate causal tests.

The authors compare selected long-term menstrual records across historical periods. They propose light exposure and gravitational timing as explanations for changed associations; this observational comparison does not isolate those causes or validate a cycle prediction.

✦PAPIRUS • ALBERGHINA (2025)
OPEN ACCESS

A rhythmic dance: how lunar cycles influence reproductive behavior in vertebrates

Daniela Alberghina•Frontiers in Mammal Science•2025Source identity checked 2026-10-11

A vertebrate literature review supplies context rather than a new human causal test.

Alberghina’s mini review surveys vertebrate reproductive timing literature. Comparative observations depend on species and setting. The review supplies context for hypotheses; it does not independently demonstrate a human reproductive mechanism.

Biological Mechanisms

Explore species-specific lunar timing mechanisms and their limits. Marine experiments should not be generalized to human physiology.

✦PAPIRUS • ECOCHARD (2024)
OPEN ACCESS

Evidence that the woman’s ovarian cycle is driven by an internal circamonthly timing system

René Ecochard, Joseph B. Stanford, Richard J. Fehring, Marie Schneider, Shahpar Najmabadi, Claude Gronfier•Science Advances•2024Source identity checked 2026-10-11

Cycles and women are different sampling units; an internal-timer hypothesis is not a demonstrated lunar mechanism.

Ecochard and colleagues analyze 26,912 cycles from 2,303 European women and 4,786 cycles from 721 North American women. Time-series characteristics support an internal timing hypothesis. The reported lunar alignment differs between populations; these records do not demonstrate a molecular lunar sensor or an effective fertility intervention.

✦PAPIRUS • POEHN (2022)
OPEN ACCESS

A Cryptochrome adopts distinct moon- and sunlight states and functions as sun- versus moonlight interpreter in monthly oscillator entrainment

Birgit Poehn, Shruthi Krishnan, Martin Zurl, Aida Coric, Dunja Rokvic, N. Sören Häfker, Elmar Jaenicke, Enrique Arboleda, Lukas Orel, Florian Raible, Eva Wolf, Kristin Tessmar-Raible•Nature Communications•2022Source identity checked 2026-10-11

A marine-worm mechanism requires separate evidence before any human inference.

Experiments on Platynereis dumerilii and its L-Cryptochrome examine species-specific light responses relevant to reproductive timing. The marine bristle-worm findings do not establish a corresponding sensor in humans.

✦PAPIRUS • RITTER (2024)
OPEN ACCESS

Time me by the moon

Andrés Ritter, Kristin Tessmar-Raible•EMBO Reports•2024Source identity checked 2026-10-11

A comparative review identifies questions and mechanisms within their studied organisms.

Ritter and Tessmar-Raible review the evolution and function of lunar timing systems across organisms. This is a synthesis, not a new human experiment or proof that the same mechanism operates across species.

Sleep & Mood

Compare reported sleep and clinical associations with null findings, study design and sample limitations. These papers do not establish universal effects.

✦PAPIRUS • WEHR (2018)
OPEN ACCESS

Bipolar mood cycles and lunar tidal cycles

T A Wehr•Molecular Psychiatry•2018Source identity checked 2026-10-11

Selected clinical time series do not establish a general causal effect.

A retrospective series of 17 selected patients explores mood-cycle timing and lunar tidal periods. The observations generate hypotheses; they do not establish gravitational causation, a population-wide mental-health effect or a treatment recommendation.

Seasonal Rhythms

Inspect seasonal associations within particular tissues, tasks, cohorts and locations. These studies and reviews concern annual variation; they do not validate lunar effects, astrology or a personal energy forecast.

✦PAPIRUS • DOPICO (2015)
OPEN ACCESS

Widespread seasonal gene expression reveals annual differences in human immunity and physiology

Xaquin Castro Dopico, Marina Evangelou, Ricardo C. Ferreira, Hui Guo, Marcin L. Pekalski, Deborah J. Smyth, Nicholas Cooper, Oliver S. Burren, Anthony J. Fulford, Branwen J. Hennig, Andrew M. Prentice, Anette-G. Ziegler, Ezio Bonifacio, Chris Wallace, John A. Todd•Nature Communications•2015Source identity checked 2026-10-11

Seasonal gene-expression associations depend on tissue, cohort, geography and analysis.

Dopico and colleagues report seasonal expression in 5,136 of 22,822 genes tested in the BABYDIET blood-cell dataset, with comparisons across other cohorts and tissues. The proportion refers to that analysis, not every gene in every person. Seasonal immune patterns do not validate lunar, zodiac or individual energy predictions.

✦PAPIRUS • MEYER (2016)
OPEN ACCESS

Seasonality in human cognitive brain responses

Christelle Meyer, Vincenzo Muto, Mathieu Jaspar, Caroline Kussé, Erik Lambot, Sarah L. Chellappa, Christian Degueldre, Evelyne Balteau, André Luxen, Benita Middleton, Simon N. Archer, Fabienne Collette, Derk-Jan Dijk, Christophe Phillips, Pierre Maquet, Gilles Vandewalle•Proceedings of the National Academy of Sciences•2016Source identity checked 2026-10-11

Seasonal task-related brain responses are distinct from improved task performance.

Meyer and colleagues examine task-related fMRI responses at different times of year after a controlled laboratory protocol. Seasonal brain-response differences do not mean that each person’s attention or memory performance peaks at a solstice or equinox. This study does not establish a lunar effect.

✦PAPIRUS • HOHM (2024)
OPEN ACCESS

Homo temporus : Seasonal Cycles as a Fundamental Source of Variation in Human Psychology

Ian Hohm, Alexandra S. Wormley, Mark Schaller, Michael E. W. Varnum•Perspectives on Psychological Science•2024Source identity checked 2026-10-11

A framework for studying seasonal variation, with geographical and cultural moderators.

Hohm and colleagues review seasonal variation and propose meteorological, ecological and sociocultural pathways for further study. This synthesis does not validate astrology, a universal seasonal energy schedule or an individual forecast.

◐ EVIDENCE CHECK

Myth vs. Evidence

Common claims about the Moon and women's health, examined against the peer-reviewed research.

Explore the Research

Search across 250+ million scholarly works via OpenAlex. Your query is automatically scoped to lunar and moon cycle research.

✦METHODOLOGIA • OPENALEX & PEER REVIEW

About This Research

All studies referenced on this page are peer-reviewed, published in indexed scientific journals, and sourced from OpenAlex, an open catalog of the world's scholarly works maintained by the nonprofit OurResearch. DOI links resolve to the original publications. Editorial summaries are our own; always refer to the full papers for methodology and nuanced findings.

✦ITER CAELESTE • THE NEXT ORBIT
Recommended Next Orbit

Keep an exploratory record of daily experience:

Daily Moon Check-In Tracker

DAILY PRACTICE

An Exploratory Daily Record

Record sleep, mood and energy alongside lunar phase and ordinary influences such as work schedules and evening light. A 30-day log spans about one lunar cycle; it cannot establish a biological rhythm or causal effect. Use the record to notice questions, not to validate a prediction.

Start Tracking
Or explore complementary celestial angles:
Market Tides 100-Year BacktestsECONOMETRICS

Explore econometric studies testing whether lunar cycles affect Wall Street equity returns and volatility.

Birth Moon CalculatorNATAL

Calculate your natal phase archetype and compare your baseline with research cohorts.

✦CORPUS SCIENTIAE LUNARIS • KNOWLEDGE GRAPH

Chronobiology & Sleep Science Knowledge Graph

Hierarchical inquiry tree with atomic answers and peer-reviewed academic citations.

Chronobiology

Chronobiology & Lunar Biological Rhythms

Astrometry

Astrometric Coordinates: Tropical vs. Sidereal & Constellations

Ephemeris

Orbital Mechanics, Libration & Harmonics