Lunar Velocity Research Articles

New Methods for Data Stacking and P‐ and S‐wave Arrival Time Determination Using the Deep Moonquake Apollo Recordings

AbstractA new method of simultaneous time domain cross‐correlation of multiple components of motion at multiple seismic stations is developed for P‐ and S‐wave identification for determination of arrival times of deep moonquakes using Apollo Passive Seismic Experiment (APSE) data. Deep moonquakes occur in selenographically isolated clusters, allowing the stacking of a large number of moonquakes in each cluster to improve signal‐to‐noise ratio. The method developed here seeks to improve upon multichannel cross‐correlation (MCCC) of a single component of motion and multiple events used in past work by incorporating all components and stations simultaneously. This multicomponent multichannel cross‐correlation (MCMCCC) method not only maximizes the inherent correlation between the 12 components (three components of motion at each of four stations) across all events in a given cluster, but also establishes representative stacked traces of moonquakes within each cluster. Additionally, the MCMCCC method utilizes components and events with the highest data quality to guide the inclusion of lower quality components and events (or events with fewer components). A closure difference residual time is introduced to identify moonquake events with better data and/or close source locations, to further improve the signal‐to‐noise ratio of stacked traces. A multicomponent short‐term to long‐term average algorithm is also developed to objectively determine P‐ and S‐wave arrivals that best align with their travel time curves based on lunar velocity models, simultaneously for all 12 components of motion. Newly computed deep moonquake cluster stacks and some updated deep moonquake cluster locations are presented, which improve upon past results.

Babylonian astronomy: a new understanding of column \u03a6

The most discussed and mysterious column within the Babylonian astronomy is column Φ. It is closely connected to the lunar velocity and to the duration of the Saros. This paper presents new ideas for the development and interpretation of column Φ. It combines the excellent Goal-Year method (for the prediction of Lunar Six time intervals) with old ideas and practices from the “schematic astronomy”. Inspired by the old “TU11” rule for prediction of times of lunar eclipses, it proposes that column Φ, in a similar way, used the sum of the Lunar Four to predict times of lunar eclipses as well as the duration of one, 6, and 12 months by means of what usually is called “R–S” schemes. It also explains fully the structure and development of such schemes, a fact that strongly supports the new interpretation of column Φ.

Relativistic tests with lunar laser ranging

This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein’s theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein’s theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein’s theory are detected. A relative temporal variation of the gravitational constant is estimated as , the test of the equivalence principle gives and the Nordtvedt parameter , the PPN-parameters β and γ are determined as and and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of , β and γ, the initial value of the core rotation vector is constrained to a reasonable model value for the estimation of and geodetic precession. A constrained z-component of the initial lunar velocity is used for the estimation of the geodetic precession.

Eclipse theory in the Jing chu li: Part I. The adoption of lunar velocity

This paper investigates the methods of eclipse prediction in China before the fourth century AD, with a detailed example of the eclipse theory in the Jing chu li (Luminous Inception System ). As the official calendar of the Jin dynasty and the Kingdom Wei during the three kingdoms period, the Jing chu li was used for more than 200 years after it was adopted in 237 AD. From the San tong li (Triple Concordance System ) of the Western Han to the Jing chu li, methods for predicting eclipses developed in three important ways: (i) from predicting only lunar eclipses to the prediction of both solar and lunar eclipses; (ii) from relying only on the mean periods of the sun and the moon to taking into consideration the variation in lunar velocity; and (iii) from estimating only a rough date to predicting the exact time of eclipses. This paper addresses two questions: first, how did ancient Chinese astronomers use cycles to predict eclipses in the Han dynasty? Second, how did astronomers such as Liu Hong and Yang Wei revise early eclipse prediction methods? The original text of the Jing chu li is analyzed to show how Yang Wei combined lunar velocity theory with the traditional method of predicting eclipses using cycles.

Studies in Babylonian Lunar Theory: Part II. Treatments of Lunar Anomaly

This paper is the second of a multi-part examination of the creation of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies. This was accomplished in the construction of the System A lunar theory by an unknown author, almost certainly in the city of Babylon and probably early in the 4th century B.C. The present paper focuses mainly on System A and the likely process of its construction. The first three sections are largely descriptive – first of the basic concepts which underlie the theory; then of the component schemes comprising the theory; and finally of two distinctive texts which suggest how the theory was constructed. The crux of the paper is Sect. 4, which describes how the theory seems likely to have been constructed. Here the crucial insight in separating the effects of lunar and solar anomaly appears to have been recognizing that – of all the measurable intervals bounded by eclipses – only 235 months exhibits a variation due solely to lunar anomaly, and that by means of an elegant mathematical model the amplitudes of 223 and 12 months could be deduced from its amplitude. The rest of the section describes the likely details of the derivation of the Φ ~ Λ scheme, and the extension of the methodology to the other components of the theory. It concludes with a demonstration that Φ and its dependent schemes were anchored through the Φ ~ W scheme to the syzygy on –403 Aug 18 (GN 7391) which concluded the shortest 6-month interval in the first 24 saros cycles since –746 (and in fact in the 900 years separating Nabonassar and Ptolemy). The next three sections address a number of largely technical details and amplifications of the theory, beginning with the schemes describing the variation of lunar velocity (column F) in Sect. 5. Section 6 addresses issues concerning the interpretation of Φ and the so-call Saros Text (BM 36705), while Sect. 7 discusses System B’s corresponding treatment of the effects of lunar anomaly, illustrating both its derivative nature and mathematically less rigorous structure. Section 8 examines the accuracy of the two theories, showing that the System A theory was both remarkably accurate and superior to System B. The final section offers some brief remarks on the power and elegance of the mathematical treatment of the problem by the author of System A.

On the Extreme Lunar Velocities

The problem addressed in this paper is an accurate determination of the apparent extreme angular velocities of the Moon as observed from the Earth.1 As our historical records show in East and West alike, Man has constantly been busy with the most remarkable, daily behaviour of our closest celestial neighbor with its greatest apparent motion against the background of the stars. Different from the Sun's daily motion which is all the year round nearly uniform, the markedly variable lunar velocities were easily perceptible from even very crude ancient observations. However, the actual, quantitative recognition that the Moon's motion is not constant, came, according to the natural principles of astronomy, necessarily long after the Moon's periodic relation to the Sun, the synodic period, had been firmly established. This historical process seems to be best followed in China.

An inquiry into the lunar interior: A nonlinear inversion of the Apollo lunar seismic data

This study discusses in detail the inversion of the Apollo lunar seismic data and the question of how to analyze the results. The well‐known problem of estimating structural parameters (seismic velocities) and other parameters crucial to an understanding of a planetary body from a set of arrival times is strongly nonlinear. Here we consider this problem from the point of view of Bayesian statistics using a Markov chain Monte Carlo method. Generally, the results seem to indicate a somewhat thinner crust with a thickness around 45 km as well as a more detailed lunar velocity structure, especially in the middle mantle, than obtained in earlier studies. Concerning the moonquake locations, the shallow moonquakes are found in the depth range 50–220 km, and the majority of deep moonquakes are concentrated in the depth range 850–1000 km, with what seems to be an apparently rather sharp lower boundary. In wanting to further analyze the outcome of the inversion for specific features in a statistical fashion, we have used credible intervals, two‐dimensional marginals, and Bayesian hypothesis testing. Using this form of hypothesis testing, we are able to decide between the relative importance of any two hypotheses given data, prior information, and the physical laws that govern the relationship between model and data, such as having to decide between a thin crust of 45 km and a thick crust as implied by the generally assumed value of 60 km. We obtain a Bayes factor of 4.2, implying that a thinner crust is strongly favored.

A new seismic velocity model for the Moon from a Monte Carlo inversion of the Apollo lunar seismic data

A reanalysis of the Apollo lunar seismic data and the subsequent application of an inverse Monte Carlo method to P and S‐wave arrival times has resulted in a more detailed lunar velocity structure than previously obtainable. The velocity is seen to increase from the surface down to the base of the crust at 45±5 km depth. The results furthermore indicate a constant velocity upper mantle extending to 560±15 km km depth, separated from a more complex high velocity middle mantle by an increase in velocity of 1.0 km/s. In addition, the moonquake locations have been improved. The shallow moonquakes are found to be located in the depth range 50–220 km. The majority of deep moonquakes are concentrated in the depth range 850–1000 km with an apparently rather sharp lower boundary.

Babylonian Lunar Theory ReconsideredZur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische Berechnung von Mondphasen. Lis Brack-Bernsen

Previous articleNext article No AccessEssay ReviewsBabylonian Lunar Theory Reconsidered Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische Berechnung von Mondphasen. Lis Brack-Bernsen John M. SteeleJohn M. Steele Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Isis Volume 91, Number 1Mar., 2000 Publication of the History of Science Society Article DOIhttps://doi.org/10.1086/384630 Views: 1Total views on this site Citations: 1Citations are reported from Crossref Copyright 2000 History of Science Society, Inc.PDF download Crossref reports the following articles citing this article: Book Reviews, Interesting Publications, Treasurer's Report, Notes on Contributors, Forthcoming Articles, HESS Officers, Earth Sciences History 19, no.22 (Jan 2000): 216–250.https://doi.org/10.17704/eshi.19.2.1282qp4336862030

Computational Astronomy: Five Centuries of Finding True Syzygy

Medieval astronomers were aware of the difficulties and enormous effort needed to follow the rules for determining astronomically significant events and, from Ptolemy on, it was generally understood that numerical tables could be constructed that represented the underlying geometrical models adequately. This chapter explores the specific case of finding the time from mean to true syzygy. The earliest solution to the syzygy problem that found in the form of a table appears in a work of Ibn al- Kammād called al-Muqtabis. This is one of his three known works, preserved uniquely in a Latin manuscript: Biblioteca Nacional de Madrid, ms 10023. John of Saxony, one of the Parisian astronomers who adapted the Alfonsine Tables and composed canons to it, offered a more sophisticated solution using Ptolemy's lunar models. He made allowances for the variation in the lunar velocity in the time interval between mean and true syzygy.Keywords: al-Muqtabis; Ibn al- Kammād; John of Saxony; Latin manuscript; medieval astronomers; Ptolemy's lunar models; syzygy problem

The Lunar Velocity Function in System B First-Crescent Ephemerides

CentaurusVolume 37, Issue 1 p. 1-51 The Lunar Velocity Function in System B First-Crescent Ephemerides Leigh Riley, Leigh Riley 10 Walsh Ave., Thornbury, 3071. Australia.Search for more papers by this author Leigh Riley, Leigh Riley 10 Walsh Ave., Thornbury, 3071. Australia.Search for more papers by this author First published: January 1994 https://doi.org/10.1111/j.1600-0498.1994.tb00001.x AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume37, Issue1January 1994Pages 1-51 RelatedInformation

Solar and lunar velocities in the Alfonsine Tables

Although not previously noticed, the solar and lunar velocity tables in the 1483 edition of the Alfonsine Tables differ from the corresponding tables in the 1518 edition (Venice) which are identical to those that appear in the Toledan Tables and the z i j of al-Batt a n i . The velocity tables in the unpublished Hebrew version of the Alfonsine Tables, composed in 1460 (Avignon), agree with the 1483 edition, and the Hebrew translator tells us that these tables (together with some others) were added to the Alfonsine Tables by Christian scholars after the time of Alfonso. A discussion of the underlying parameters is also presented.

Lunar and planetary seismology

The last 4 years have been very significant for new results in lunar seismology and the emergence of a definite program in planetary seismology. Since 1970, four stations with seismic sensors have been placed on the moon at Apollo 14, 15, 16, and 17 sites. When combined with the seismic station operating at the Apollo 12. site since November 1969, these have formed an excellent network. The network has detected a large number of moonquakes and meteoroid impacts. In addition to these there have been nine artificial impacts (ascent stage of the lunar module (LM) and Saturn third‐stage booster (S4B)) of known energies, impact times, and locations. Data from all sources have been analyzed to determine the lunar velocity structure, the seismicity, and the properties of the lunar interior. This has been a pioneering program in extending the direct seismological exploration to another planetary body with both surprising and very significant results.

The 25-km Discontinuity: Implications for Lunar History

The lunar velocity profile and laboratory data on terrestrial and lunar rocks are constraints on models of lunar history. They show that shock-induced microcracks are absent from the rocks present in the moon today at depths of 25 to 60 kilometers. All possible causes of this observation are examined, and the most likely explanations are that either the rocks at depths of 25 to 60 kilometers formed after the major impacts ceased or the microcracks have annealed at temperatures of about 600 degrees C over geologically long times.