scholarly journals Libration of the Moon: shape of the Earth and motion of the ecliptic plane

1986 ◽  
Vol 114 ◽  
pp. 141-144
Author(s):  
M. Moons
Keyword(s):  
Gravity Field ◽  
Spherical Harmonics ◽  
Fourth Order ◽  
Center Of Mass ◽  
Ecliptic Plane ◽  
The Sun ◽  
Lunar Gravity ◽  
The Moon ◽  
Lunar Gravity Field ◽  
The Earth

Very accurate theories of the libration of the Moon have been recently built by Migus (1980), Eckhardt (1981, 1982) and Moons (1982, 1984). All of them take into account the perturbation due to the Earth and the Sun on the motion of a rigid Moon about its center of mass. Additional perturbations (influence of the planets, shape of the Earth, elasticity of the Moon, …) are also often included.We present here the perturbations due to the shape of the Earth and the motion of the ecliptic plane on our theory which already contains planetary perturbations. This theory is completely analytical with respect to the harmonic coefficients of the lunar gravity field which is expanded in spherical harmonics up to the fourth order. The ELP 2000 solution (Chapront and Chapront-Touzé, 1983) supplies us with the motion of the center of mass of the Moon.

scholarly journals Theory of the Libration of the Moon

1983 ◽  
Vol 74 ◽  
pp. 37-37
Author(s):  
M. Dubois-Moons
Keyword(s):  
Gravity Field ◽  
Orbital Motion ◽  
Lunar Theory ◽  
The Sun ◽  
Lunar Gravity ◽  
The Moon ◽  
Fourth Degree ◽  
Lunar Gravity Field ◽  
The Earth ◽  
Second Degree

AbstractThe paper presents a new theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field. This field is represented through its fourth degree harmonics for the torque due to the Earth (the second degree for the torque due to the Sun). The Moon is assumed to be rigid and its orbital motion is described by the ELP 2000 solution (Chapront and Chapront-Touzé 1981) for the main problem of lunar theory with planetary perturbations and influence of the non-sphericity of the Earth. Comparisons with other theories (Migus 1980 and Eckhardt 1981) are also presented.

scholarly journals Everything Is A Circle: A New Universal Orbital Model

2021 ◽  
Author(s):  
AslıPınar Tan
Keyword(s):  
Solar System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Ecliptic Plane ◽  
The Sun ◽  
The Moon ◽  
Circular Orbits ◽  
Orbital Parameters ◽  
The Earth ◽  
Angular Velocities

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

scholarly journals The Lunar orbit paradox

2013 ◽  
Vol 40 (1) ◽  
pp. 135-146
Author(s):  
Aleksandar Tomic
Keyword(s):  
Inertial Mass ◽  
Lunar Orbit ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Three Body ◽  
Origin Of The Moon ◽  
Force Intensity ◽  
Critical Consideration

Newton's formula for gravity force gives greather force intensity for atraction of the Moon by the Sun than atraction by the Earth. However, central body in lunar (primary) orbit is the Earth. So appeared paradox which were ignored from competent specialist, because the most important problem, determination of lunar orbit, was inmediately solved sufficiently by mathematical ingeniosity - introducing the Sun as dominant body in the three body system by Delaunay, 1860. On this way the lunar orbit paradox were not canceled. Vujicic made a owerview of principles of mechanics in year 1998, in critical consideration. As an example for application of corrected procedure he was obtained gravity law in some different form, which gave possibility to cancel paradox of lunar orbit. The formula of Vujicic, with our small adaptation, content two type of acceleration - related to inertial mass and related to gravity mass. So appears carried information on the origin of the Moon, and paradox cancels.

scholarly journals High-resolution spectroscopy and spectropolarimetry of the total lunar eclipse January 2019

2020 ◽  
Vol 635 ◽  
pp. A156
Author(s):  
K. G. Strassmeier ◽  
I. Ilyin ◽  
E. Keles ◽  
M. Mallonn ◽  
A. Järvinen ◽  
...  
Keyword(s):  
Large Scale ◽  
Solar Spectrum ◽  
High Resolution Spectroscopy ◽  
Strong Increase ◽  
Lunar Eclipse ◽  
The Sun ◽  
The Moon ◽  
Earth’S Atmosphere ◽  
The Earth ◽  
Earth's Atmosphere

Context. Observations of the Earthshine off the Moon allow for the unique opportunity to measure the large-scale Earth atmosphere. Another opportunity is realized during a total lunar eclipse which, if seen from the Moon, is like a transit of the Earth in front of the Sun. Aims. We thus aim at transmission spectroscopy of an Earth transit by tracing the solar spectrum during the total lunar eclipse of January 21, 2019. Methods. Time series spectra of the Tycho crater were taken with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) at the Large Binocular Telescope in its polarimetric mode in Stokes IQUV at a spectral resolution of 130 000 (0.06 Å). In particular, the spectra cover the red parts of the optical spectrum between 7419–9067 Å. The spectrograph’s exposure meter was used to obtain a light curve of the lunar eclipse. Results. The brightness of the Moon dimmed by 10.m75 during umbral eclipse. We found both branches of the O2 A-band almost completely saturated as well as a strong increase of H2O absorption during totality. A pseudo O2 emission feature remained at a wavelength of 7618 Å, but it is actually only a residual from different P-branch and R-branch absorptions. It nevertheless traces the eclipse. The deep penumbral spectra show significant excess absorption from the Na I 5890-Å doublet, the Ca II infrared triplet around 8600 Å, and the K I line at 7699 Å in addition to several hyper-fine-structure lines of Mn I and even from Ba II. The detections of the latter two elements are likely due to an untypical solar center-to-limb effect rather than Earth’s atmosphere. The absorption in Ca II and K I remained visible throughout umbral eclipse. Our radial velocities trace a wavelength dependent Rossiter-McLaughlin effect of the Earth eclipsing the Sun as seen from the Tycho crater and thereby confirm earlier observations. A small continuum polarization of the O2 A-band of 0.12% during umbral eclipse was detected at 6.3σ. No line polarization of the O2 A-band, or any other spectral-line feature, is detected outside nor inside eclipse. It places an upper limit of ≈0.2% on the degree of line polarization during transmission through Earth’s atmosphere and magnetosphere.

scholarly journals Methods to Test the “Dimming Effect” Produced by a Decrease in the Number of Photons Received from Receding Light Sources

2020 ◽  
Author(s):  
Mark Zilberman
Keyword(s):  
Light Source ◽  
Opposite Direction ◽  
Ecliptic Plane ◽  
Light Sources ◽  
The Sun ◽  
Decimal Point ◽  
Relativistic Systems ◽  
The Earth ◽  
New Models ◽  
Direction Opposite

The hypothetical “Dimming Effect” describes the change of the number of photons arriving from a moving light source per unit of time. In non-relativistic systems, the “Dimming effect” may occur due to the growing distance of light sources moving away from the receiver. This means that due to the growing distance, the photons continuously require more time to reach the receiver, which reduces the number of received photons per time unit compared to the number of emitted photons. Understandably, the proposed “Dimming effect” must be tested (confirmed or rejected) through observations. a. This article provides the formula for the calculation of “Dimming effect” values using the redshift parameter Z widely used in astronomy. b. The “Dimming effect” can possibly be detected utilizing the orbital movement of the Earth around the Sun. In accordance to the “Dimming effect”, observers on Earth will view 1.0001 more photons per time unit emitted by stars located near the ecliptic plane in the direction of the Earth orbiting the Sun. And, in contrast, observers will view only 0.9999 photons per time unit emitted by stars located near the ecliptic plane in the direction opposite to the Earth orbiting the Sun. Calculating precise measurements of the same stars within a 6-month period can possibly detect this difference. These changes in brightness are not only for specific stars, as the change in brightness takes place for all stars near the ecliptic in the direction of the Earth’s orbit around the Sun and in the opposite direction. c. The “Dimming effect” can possibly be detected in a physics laboratory using a moving light source (or mirror) and photon counters located in the direction of travel and in the opposite direction. d. In theory, Dilation of time can also be used for testing the existence of the “Dimming effect.” However, in experiments on Earth this effect appears in only the 14th digit after the decimal point and testing does not appear to be feasible. e. Why is it important to test the “Dimming effect?” If confirmed, it would allow astronomers to adjust values of "Standard Candles" used in astronomy. Since “Standard Candles” are critical in various cosmological models, the “Dimming effect” can correct models and/or reveal and support new models. If it is proved that the “Dimming effect” does not exist, it will mean that the number of photons arriving per unit of time does not depend on the speed of the light source and observer, which is not so apparent.

Decapitated Lunar Goddesses in Aztec Art, Myth, and Ritual

1997 ◽  
Vol 8 (2) ◽  
pp. 185-206 ◽  
Author(s):  
Susan Milbrath
Keyword(s):  
Solar Eclipse ◽  
Seasonal Cycle ◽  
Full Moon ◽  
The Sun ◽  
The Moon ◽  
Seasonal Transition ◽  
The Earth ◽  
New Moon ◽  
The Demonic

AbstractAztec images of decapitated goddesses link the symbolism of astronomy with politics and the seasonal cycle. Rituals reenacting decapitation may refer to lunar events in the context of a solar calendar, providing evidence of a luni-solar calendar. Decapitation imagery also involves metaphors expressing the rivalry between the cults of the sun and the moon. Huitzilopochtli's decapitation of Coyolxauhqui can be interpreted as a symbol of political conquest linked to the triumph of the sun over the moon. Analysis of Coyolxauhqui's imagery and mythology indicates that she represents the full moon eclipsed by the sun. Details of the decapitation myth indicate specific links with seasonal transition and events taking place at dawn and at midnight. Other decapitated goddesses, often referred to as earth goddesses with “lunar connections,” belong to a complex of lunar deities representing the moon within the earth (the new moon). Cihuacoatl, a goddess of the new moon, takes on threatening quality when she assumes the form of a tzitzimime attacking the sun during a solar eclipse. The demonic new moon was greatly feared, for it could cause an eternal solar eclipse bringing the Aztec world to an end.

Solar Motion and Lunar Eclipses in Philolaus’ Cosmological System

Apeiron ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dirk L. Couprie
Keyword(s):  
The Other ◽  
The Sun ◽  
The Moon ◽  
Internal Logic ◽  
Wrong Side ◽  
The Earth ◽  
Solar Motion ◽  
Length Of The Day

Abstract In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of the day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean.

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