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Basic Principles of Celestial Navigation James A
Basic principles of celestial navigation James A. Van Allena) Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242 ͑Received 16 January 2004; accepted 10 June 2004͒ Celestial navigation is a technique for determining one’s geographic position by the observation of identified stars, identified planets, the Sun, and the Moon. This subject has a multitude of refinements which, although valuable to a professional navigator, tend to obscure the basic principles. I describe these principles, give an analytical solution of the classical two-star-sight problem without any dependence on prior knowledge of position, and include several examples. Some approximations and simplifications are made in the interest of clarity. © 2004 American Association of Physics Teachers. ͓DOI: 10.1119/1.1778391͔ I. INTRODUCTION longitude ⌳ is between 0° and 360°, although often it is convenient to take the longitude westward of the prime me- Celestial navigation is a technique for determining one’s ridian to be between 0° and Ϫ180°. The longitude of P also geographic position by the observation of identified stars, can be specified by the plane angle in the equatorial plane identified planets, the Sun, and the Moon. Its basic principles whose vertex is at O with one radial line through the point at are a combination of rudimentary astronomical knowledge 1–3 which the meridian through P intersects the equatorial plane and spherical trigonometry. and the other radial line through the point G at which the Anyone who has been on a ship that is remote from any prime meridian intersects the equatorial plane ͑see Fig. -
Capricious Suntime
[Physics in daily life] I L.J.F. (Jo) Hermans - Leiden University, e Netherlands - [email protected] - DOI: 10.1051/epn/2011202 Capricious suntime t what time of the day does the sun reach its is that the solar time will gradually deviate from the time highest point, or culmination point, when on our watch. We expect this‘eccentricity effect’ to show a its position is exactly in the South? e ans - sine-like behaviour with a period of a year. A wer to this question is not so trivial. For ere is a second, even more important complication. It is one thing, it depends on our location within our time due to the fact that the rotational axis of the earth is not zone. For Berlin, which is near the Eastern end of the perpendicular to the ecliptic, but is tilted by about 23.5 Central European time zone, it may happen around degrees. is is, aer all, the cause of our seasons. To noon, whereas in Paris it may be close to 1 p.m. (we understand this ‘tilt effect’ we must realise that what mat - ignore the daylight saving ters for the deviation in time time which adds an extra is the variation of the sun’s hour in the summer). horizontal motion against But even for a fixed loca - the stellar background tion, the time at which the during the year. In mid- sun reaches its culmination summer and mid-winter, point varies throughout the when the sun reaches its year in a surprising way. -
Phases of the Moon by Patti Hutchison
Phases of the Moon By Patti Hutchison 1 Was there a full moon last night? Some people believe that a full moon affects people's behavior. Whether that is true or not, the moon does go through phases. What causes the moon to appear differently throughout the month? 2 You know that the moon does not give off its own light. When we see the moon shining at night, we are actually seeing a reflection of the Sun's light. The part of the moon that we see shining (lunar phase) depends on the positions of the sun, moon, and the earth. 3 When the moon is between the earth and the sun, we can't see it. The sunlit side of the moon is facing away from us. The dark side is facing toward us. This phase is called the new moon. 4 As the moon moves along its orbit, the amount of reflected light we see increases. This is called waxing. At first, there is a waxing crescent. The moon looks like a fingernail in the sky. We only see a slice of it. 5 When it looks like half the moon is lighted, it is called the first quarter. Sounds confusing, doesn't it? The quarter moon doesn't refer to the shape of the moon. It is a point of time in the lunar month. There are four main phases to the lunar cycle. Four parts- four quarters. For each of these four phases, the moon has orbited one quarter of the way around the earth. -
Technical Memorandum
Technical Memorandum To: Thaddeus Johnson, Jessica Kronenwetter, Kevin Work, William Chadwick, Brian Middleton, Kevin Ludlum, and Seth Iacangelo (NOAA/OSPO, GOES-R/MOST) From: Fangfang Yu, Xiangqian Wu and Xi Shao (NOAA/STAR) Subject: ABI Lunar Trending Image Collection Requirements in the Operational Period Date: 05/01/2018 Rev: Rev 2.0 Cc: Jon Fulbright (NOAA GOES-R/PRO) This technical memo lists the set of lunar trending requirements for the GOES-16 ABI operational period, which can be summarized as followed: Scan pattern: (1) the unclipped Moon can be scanned with either MESO1 or MESO2; and (2) the Moon should be located near the center of the MESO swath at the north-south direction for all the ABI bands. Location: (1) the Moon should appear within the ABI field of regard (FOR); (2) the center of the Moon should be at least 0.013 radians away from the Earth limb for all the ABI bands; and (3) the edge of the Moon should be at least 0.002 radians away from the MESO frame boundary at the east-west direction. Frequency per month: 2-4 trending events per lunar phase. Phase Angle Range: (1) the highest priority two lunar trending events shall have the smallest absolute phase angle as possible between Earth and Moon, but not less than 5.0 degrees. These two trending events shall be on opposite sides of the Earth. (2). The other two lunar trending events with relatively lower priority shall have an absolute phase angle as close as possible to 60 degrees between Earth and Moon, but not more than 90.0 degrees. -
Entrance Pupil Irradiance Estimating Model for a Moon-Based Earth Radiation Observatory Instrument
remote sensing Article Entrance Pupil Irradiance Estimating Model for a Moon-Based Earth Radiation Observatory Instrument Wentao Duan 1, Shaopeng Huang 2,3,* and Chenwei Nie 4 1 School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710054, China; [email protected] 2 Institute of Deep Earth Science and Green Energy, Shenzhen University, Shenzhen 518060, China 3 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109, USA 4 Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100094, China; [email protected] * Correspondence: [email protected] Received: 26 January 2019; Accepted: 6 March 2019; Published: 10 March 2019 Abstract: A Moon-based Earth radiation observatory (MERO) could provide a longer-term continuous measurement of radiation exiting the Earth system compared to current satellite-based observatories. In order to parameterize the detector for such a newly-proposed MERO, the evaluation of the instrument’s entrance pupil irradiance (EPI) is of great importance. The motivation of this work is to build an EPI estimating model for a simplified single-pixel MERO instrument. The rationale of this model is to sum the contributions of every location in the MERO-viewed region on the Earth’s top of atmosphere (TOA) to the MERO sensor’s EPI, taking into account the anisotropy in the longwave radiance at the Earth TOA. Such anisotropy could be characterized by the TOA anisotropic factors, which can be derived from the Clouds and the Earth’s Radiant Energy System (CERES) angular distribution models (ADMs). -
The Moon and Eclipses
Lecture 10 The Moon and Eclipses Jiong Qiu, MSU Physics Department Guiding Questions 1. Why does the Moon keep the same face to us? 2. Is the Moon completely covered with craters? What is the difference between highlands and maria? 3. Does the Moon’s interior have a similar structure to the interior of the Earth? 4. Why does the Moon go through phases? At a given phase, when does the Moon rise or set with respect to the Sun? 5. What is the difference between a lunar eclipse and a solar eclipse? During what phases do they occur? 6. How often do lunar eclipses happen? When one is taking place, where do you have to be to see it? 7. How often do solar eclipses happen? Why are they visible only from certain special locations on Earth? 10.1 Introduction The moon looks 14% bigger at perigee than at apogee. The Moon wobbles. 59% of its surface can be seen from the Earth. The Moon can not hold the atmosphere The Moon does NOT have an atmosphere and the Moon does NOT have liquid water. Q: what factors determine the presence of an atmosphere? The Moon probably formed from debris cast into space when a huge planetesimal struck the proto-Earth. 10.2 Exploration of the Moon Unmanned exploration: 1950, Lunas 1-3 -- 1960s, Ranger -- 1966-67, Lunar Orbiters -- 1966-68, Surveyors (first soft landing) -- 1966-76, Lunas 9-24 (soft landing) -- 1989-93, Galileo -- 1994, Clementine -- 1998, Lunar Prospector Achievement: high-resolution lunar surface images; surface composition; evidence of ice patches around the south pole. -
Lunar Motion Motion A
2 Lunar V. Lunar Motion Motion A. The Lunar Calendar Dr. Bill Pezzaglia B. Motion of Moon Updated 2012Oct30 C. Eclipses 3 1. Phases of Moon 4 A. The Lunar Calendar 1) Phases of the Moon 2) The Lunar Month 3) Calendars based on Moon b). Elongation Angle 5 b.2 Elongation Angle & Phase 6 Angle between moon and sun (measured eastward along ecliptic) Elongation Phase Configuration 0º New Conjunction 90º 1st Quarter Quadrature 180º Full Opposition 270º 3rd Quarter Quadrature 1 b.3 Elongation Angle & Phase 7 8 c). Aristarchus 275 BC Measures the elongation angle to be 87º when the moon is at first quarter. Using geometry he determines the sun is 19x further away than the moon. [Actually its 400x further !!] 9 Babylonians (3000 BC) note phases are 7 days apart 10 2. The Lunar Month They invent the 7 day “week” Start week on a) The “Week” “moon day” (Monday!) New Moon First Quarter b) Synodic Month (29.5 days) Time 0 Time 1 week c) Spring and Neap Tides Full Moon Third Quarter New Moon Time 2 weeks Time 3 weeks Time 4 weeks 11 b). Stone Circles 12 b). Synodic Month Stone circles often have 29 stones + 1 xtra one Full Moon to Full Moon off to side. Originally there were 30 “sarson The cycle of stone” in the outer ring of Stonehenge the Moon’s phases takes 29.53 days, or ~4 weeks Babylonians measure some months have 29 days (hollow), some have 30 (full). 2 13 c1). Tidal Forces 14 c). Tides This animation illustrates the origin of tidal forces. -
Lunar Standstills and Chimney Rock
Lunar Standstills and Chimney Rock Thomas Hockey To understand the motion of something, we require a reference. For a car, it’s the road. For the hands of a clock, it’s the numbered dial behind them. In the case of the Moon seen in the sky, nature provides a terrific reference: It’s the background of stars. The stars are so distant that their motions through space are imperceptible to the naked eye over human history. Thus we speak of the “fixed stars.” Imagine that the spherical Earth is surrounded by a shell of fixed stars. It isn’t really, of course. (The stars are at varying distances from the Earth, they aren’t physically attached to anything, etc.) Still, that’s what it looks like! During the course of the night, this shell appears to partly rotate around us, due to the Earth—the thing that’s really rotating—turning completely once each twenty-four-hour day. You can even infer the place in the sky about which the shell seems to be spinning. It’s a point, directly north, about one third of the way from the horizon at Chimney Rock to the point overhead. Look for the star of modest brightness (the “North Star”) that nearly marks its exact location. This North Celestial Pole [NCP] is just the extension of the Earth’s North Pole (one of two poles defining the axis about which the Earth rotates), infinitely into the sky. (The South Celestial Pole [SCP] is forever below the southern horizon at Chimney Rock.) We can do better than just imagining! A few hours spent stargazing under the real sky will convince you that this is true. -
Using the SFA Star Charts and Understanding the Equatorial Coordinate System
Using the SFA Star Charts and Understanding the Equatorial Coordinate System SFA Star Charts created by Dan Bruton of Stephen F. Austin State University Notes written by Don Carona of Texas A&M University Last Updated: August 17, 2020 The SFA Star Charts are four separate charts. Chart 1 is for the north celestial region and chart 4 is for the south celestial region. These notes refer to the equatorial charts, which are charts 2 & 3 combined to form one long chart. The star charts are based on the Equatorial Coordinate System, which consists of right ascension (RA), declination (DEC) and hour angle (HA). From the northern hemisphere, the equatorial charts can be used when facing south, east or west. At the bottom of the chart, you’ll notice a series of twenty-four numbers followed by the letter “h”, representing “hours”. These hour marks are right ascension (RA), which is the equivalent of celestial longitude. The same point on the 360 degree celestial sphere passes overhead every 24 hours, making each hour of right ascension equal to 1/24th of a circle, or 15 degrees. Each degree of sky, therefore, moves past a stationary point in four minutes. Each hour of right ascension moves past a stationary point in one hour. Every tick mark between the hour marks on the equatorial charts is equal to 5 minutes. Right ascension is noted in ( h ) hours, ( m ) minutes, and ( s ) seconds. The bright star, Antares, in the constellation Scorpius. is located at RA 16h 29m 30s. At the left and right edges of the chart, you will find numbers marked in degrees (°) and being either positive (+) or negative(-). -
SOLSTICE PROJECT RESEARCH Lunar Markings on Fajada Butte, Chaco Canyon, New Mexico
SOLSTICE PROJECT RESEARCH Papers available on this site may be downloaded, but must not be distributed for profit without citation. Lunar Markings on Fajada Butte, Chaco Canyon, New Mexico By A. Sofaer, Washington, D.C. R. M. Sinclair, National Science Foundation, Washington, D.C. L. E. Doggett, U. S. Naval Observatory, Washington, D.C. Appeared in Archaeoastronomy in the New World, ed. A.F. Aveni, pp. 169- 86. Cambridge University Press. Reprinted with permission from Cambridge University Press. Fajada Butte is known to contain a solar marking site, probably constructed by ancient Pueblo Indians, that records the equinoxes and solstices (Sofaer et al. 1979 a). Evidence is now presented that the site was also used to record the 18.6-year cycle of the lunar standstills. Fajada Butte (Figure 1) rises to a height of 135 m in Chaco Canyon, an arid valley of 13 km in northwest New Mexico, that was the center of a complex society of precolumbian culture. Near the top of the southern exposure of the butte, three stone slabs, each 2-3 m in height and about 1,000 kg in weight, lean against a cliff (Figures 2, 3). Behind the slabs two spiral petroglyphs are carved on the vertical cliff face. One spiral of 9 1/2 turns is elliptical in shape, measuring 34 by 41 cm (Figure 4). To the upper left of that spiral is a smaller spiral of 2 1/2 turns, measuring 9 by 13 cm (Figure 4). Fig. 1 Fajada Butte from the north. The solar/lunar marking site is on the southeast summit. -
Astronomy: Space Systems
Solar system SCIENCE Astronomy: Space Systems Teacher Guide Patterns in the night sky Space exploration Eclipses CKSci_G5Astronomy Space Systems_TG.indb 1 27/08/19 8:07 PM CKSci_G5Astronomy Space Systems_TG.indb 2 27/08/19 8:07 PM Astronomy: Space Systems Teacher Guide CKSci_G5Astronomy Space Systems_TG.indb 1 27/08/19 8:07 PM Creative Commons Licensing This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. You are free: to Share—to copy, distribute, and transmit the work to Remix—to adapt the work Under the following conditions: Attribution—You must attribute the work in the following manner: This work is based on an original work of the Core Knowledge® Foundation (www.coreknowledge.org) made available through licensing under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. This does not in any way imply that the Core Knowledge Foundation endorses this work. Noncommercial—You may not use this work for commercial purposes. Share Alike—If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one. With the understanding that: For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to this web page: https://creativecommons.org/licenses/by-nc-sa/4.0/ Copyright © 2019 Core Knowledge Foundation www.coreknowledge.org All Rights Reserved. Core Knowledge®, Core Knowledge Curriculum Series™, Core Knowledge Science™, and CKSci™ are trademarks of the Core Knowledge Foundation. -
The Lunar Cycle: a Cue for Amphibian Reproductive Phenology?
ARTICLE IN PRESS Animal Behaviour xxx (2009) 1–9 Contents lists available at ScienceDirect Animal Behaviour journal homepage: www.elsevier.com/locate/yanbe The lunar cycle: a cue for amphibian reproductive phenology? Rachel A. Grant a,*, Elizabeth A. Chadwick b,1, Tim Halliday a a Department of Life Sciences, The Open University b School of Biosciences, Cardiff University article info Lunar cycles give rise to cues that can be recognized by animals, including changes in light intensity, Article history: geomagnetism and gravity. Many environmental variables affect reproductive timing in amphibians and Received 16 July 2008 we tested the hypothesis that lunar cycles provide one of the cues for amphibian breeding phenology. For Initial acceptance 12 August 2008 several species of anurans, the number of individuals arriving, amplexed or spawning at breeding sites in Final acceptance 8 May 2009 Italy and the U.K. were recorded each day over several breeding seasons. Data on various aspects of Available online xxx reproductive phenology were also collated from the published literature, for several anuran and urodele MS. number: 08-00454 species. Large arrival, amplexus and spawning events were more frequent around the full moon than the new moon in anurans, although the date that the first spawn was observed showed no lunar periodicity. Keywords: Anurans could be responding directly to lunar light, or could have a lunar-synchronized endogenous anuran cycle. First sightings and peak arrivals of urodeles occurred more frequently around new and full moons, breeding but less frequently during the third quarter of the lunar cycle, while departure dates did not show lunar Bufo bufo geomagnetism periodicity.