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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. -
Solar Engineering Basics
Solar Energy Fundamentals Course No: M04-018 Credit: 4 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 22 Stonewall Court Woodcliff Lake, NJ 07677 P: (877) 322-5800 [email protected] Solar Energy Fundamentals Harlan H. Bengtson, PhD, P.E. COURSE CONTENT 1. Introduction Solar energy travels from the sun to the earth in the form of electromagnetic radiation. In this course properties of electromagnetic radiation will be discussed and basic calculations for electromagnetic radiation will be described. Several solar position parameters will be discussed along with means of calculating values for them. The major methods by which solar radiation is converted into other useable forms of energy will be discussed briefly. Extraterrestrial solar radiation (that striking the earth’s outer atmosphere) will be discussed and means of estimating its value at a given location and time will be presented. Finally there will be a presentation of how to obtain values for the average monthly rate of solar radiation striking the surface of a typical solar collector, at a specified location in the United States for a given month. Numerous examples are included to illustrate the calculations and data retrieval methods presented. Image Credit: NOAA, Earth System Research Laboratory 1 • Be able to calculate wavelength if given frequency for specified electromagnetic radiation. • Be able to calculate frequency if given wavelength for specified electromagnetic radiation. • Know the meaning of absorbance, reflectance and transmittance as applied to a surface receiving electromagnetic radiation and be able to make calculations with those parameters. • Be able to obtain or calculate values for solar declination, solar hour angle, solar altitude angle, sunrise angle, and sunset angle. -
3.- the Geographic Position of a Celestial Body
Chapter 3 Copyright © 1997-2004 Henning Umland All Rights Reserved Geographic Position and Time Geographic terms In celestial navigation, the earth is regarded as a sphere. Although this is an approximation, the geometry of the sphere is applied successfully, and the errors caused by the flattening of the earth are usually negligible (chapter 9). A circle on the surface of the earth whose plane passes through the center of the earth is called a great circle . Thus, a great circle has the greatest possible diameter of all circles on the surface of the earth. Any circle on the surface of the earth whose plane does not pass through the earth's center is called a small circle . The equator is the only great circle whose plane is perpendicular to the polar axis , the axis of rotation. Further, the equator is the only parallel of latitude being a great circle. Any other parallel of latitude is a small circle whose plane is parallel to the plane of the equator. A meridian is a great circle going through the geographic poles , the points where the polar axis intersects the earth's surface. The upper branch of a meridian is the half from pole to pole passing through a given point, e. g., the observer's position. The lower branch is the opposite half. The Greenwich meridian , the meridian passing through the center of the transit instrument at the Royal Greenwich Observatory , was adopted as the prime meridian at the International Meridian Conference in 1884. Its upper branch is the reference for measuring longitudes (0°...+180° east and 0°...–180° west), its lower branch (180°) is the basis for the International Dateline (Fig. -
The Correct Qibla
The Correct Qibla S. Kamal Abdali P.O. Box 65207 Washington, D.C. 20035 [email protected] (Last Revised 1997/9/17)y 1 Introduction A book[21] published recently by Nachef and Kadi argues that for North America the qibla (i.e., the direction of Mecca) is to the southeast. As proof of this claim, they quote from a number of classical Islamic jurispru- dents. In further support of their view, they append testimonials from several living Muslim religious scholars as well as from several Canadian and US scientists. The consulted scientists—mainly geographers—suggest that the qibla should be identified with the rhumb line to Mecca, which is in the southeastern quadrant for most of North America. The qibla adopted by Nachef and Kadi (referred to as N&K in the sequel) is one of the eight directions N, NE, E, SE, S, SW, W, and NW, depending on whether the place whose qibla is desired is situated relatively east or west and north or south of Mecca; this direction is not the same as the rhumb line from the place to Mecca, but the two directions lie in the same quadrant. In their preliminary remarks, N&K state that North American Muslim communities used the southeast direction for the qibla without exception until the publication of a book[1] about 20 years ago. N&K imply that the use of the great circle for computing the qibla, which generally results in a direction in the north- eastern quadrant for North America, is a new idea, somehow original with that book. -
2 Coordinate Systems
2 Coordinate systems In order to find something one needs a system of coordinates. For determining the positions of the stars and planets where the distance to the object often is unknown it usually suffices to use two coordinates. On the other hand, since the Earth rotates around it’s own axis as well as around the Sun the positions of stars and planets is continually changing, and the measurment of when an object is in a certain place is as important as deciding where it is. Our first task is to decide on a coordinate system and the position of 1. The origin. E.g. one’s own location, the center of the Earth, the, the center of the Solar System, the Galaxy, etc. 2. The fundamental plan (x−y plane). This is often a plane of some physical significance such as the horizon, the equator, or the ecliptic. 3. Decide on the direction of the positive x-axis, also known as the “reference direction”. 4. And, finally, on a convention of signs of the y− and z− axes, i.e whether to use a left-handed or right-handed coordinate system. For example Eratosthenes of Cyrene (c. 276 BC c. 195 BC) was a Greek mathematician, elegiac poet, athlete, geographer, astronomer, and music theo- rist who invented a system of latitude and longitude. (According to Wikipedia he was also the first person to use the word geography and invented the disci- pline of geography as we understand it.). The origin of this coordinate system was the center of the Earth and the fundamental plane was the equator, which location Eratosthenes calculated relative to the parts of the Earth known to him. -
Celestial Coordinate Systems
Celestial Coordinate Systems Craig Lage Department of Physics, New York University, [email protected] January 6, 2014 1 Introduction This document reviews briefly some of the key ideas that you will need to understand in order to identify and locate objects in the sky. It is intended to serve as a reference document. 2 Angular Basics When we view objects in the sky, distance is difficult to determine, and generally we can only indicate their direction. For this reason, angles are critical in astronomy, and we use angular measures to locate objects and define the distance between objects. Angles are measured in a number of different ways in astronomy, and you need to become familiar with the different notations and comfortable converting between them. A basic angle is shown in Figure 1. θ Figure 1: A basic angle, θ. We review some angle basics. We normally use two primary measures of angles, degrees and radians. In astronomy, we also sometimes use time as a measure of angles, as we will discuss later. A radian is a dimensionless measure equal to the length of the circular arc enclosed by the angle divided by the radius of the circle. A full circle is thus equal to 2π radians. A degree is an arbitrary measure, where a full circle is defined to be equal to 360◦. When using degrees, we also have two different conventions, to divide one degree into decimal degrees, or alternatively to divide it into 60 minutes, each of which is divided into 60 seconds. These are also referred to as minutes of arc or seconds of arc so as not to confuse them with minutes of time and seconds of time. -
Positional Astronomy Coordinate Systems
Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. -
On the Choice of Average Solar Zenith Angle
2994 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 On the Choice of Average Solar Zenith Angle TIMOTHY W. CRONIN Program in Atmospheres, Oceans, and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts (Manuscript received 6 December 2013, in final form 19 March 2014) ABSTRACT Idealized climate modeling studies often choose to neglect spatiotemporal variations in solar radiation, but doing so comes with an important decision about how to average solar radiation in space and time. Since both clear-sky and cloud albedo are increasing functions of the solar zenith angle, one can choose an absorption- weighted zenith angle that reproduces the spatial- or time-mean absorbed solar radiation. Calculations are performed for a pure scattering atmosphere and with a more detailed radiative transfer model and show that the absorption-weighted zenith angle is usually between the daytime-weighted and insolation-weighted zenith angles but much closer to the insolation-weighted zenith angle in most cases, especially if clouds are re- sponsible for much of the shortwave reflection. Use of daytime-average zenith angle may lead to a high bias in planetary albedo of approximately 3%, equivalent to a deficit in shortwave absorption of approximately 22 10 W m in the global energy budget (comparable to the radiative forcing of a roughly sixfold change in CO2 concentration). Other studies that have used general circulation models with spatially constant insolation have underestimated the global-mean zenith angle, with a consequent low bias in planetary albedo of ap- 2 proximately 2%–6% or a surplus in shortwave absorption of approximately 7–20 W m 2 in the global energy budget. -
M-Shape PV Arrangement for Improving Solar Power Generation Efficiency
applied sciences Article M-Shape PV Arrangement for Improving Solar Power Generation Efficiency Yongyi Huang 1,*, Ryuto Shigenobu 2 , Atsushi Yona 1, Paras Mandal 3 and Zengfeng Yan 4 and Tomonobu Senjyu 1 1 Department of Electrical and Electronics Engineering, University of the Ryukyus, Okinawa 903-0213, Japan; [email protected] (A.Y.); [email protected] (T.S.) 2 Department of Electrical and Electronics Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui-city, Fukui 910-8507, Japan; [email protected] 3 Department of Electrical and Computer Engineering, University of Texas at El Paso, TX 79968, USA; [email protected] 4 School of Architecture, Xi’an University of Architecture and Technology, Shaanxi, Xi’an 710055, China; [email protected] * Correspondence: [email protected] Received: 25 November 2019; Accepted: 3 January 2020; Published: 10 January 2020 Abstract: This paper presents a novel design scheme to reshape the solar panel configuration and hence improve power generation efficiency via changing the traditional PVpanel arrangement. Compared to the standard PV arrangement, which is the S-shape, the proposed M-shape PV arrangement shows better performance advantages. The sky isotropic model was used to calculate the annual solar radiation of each azimuth and tilt angle for the six regions which have different latitudes in Asia—Thailand (Bangkok), China (Hong Kong), Japan (Naha), Korea (Jeju), China (Shenyang), and Mongolia (Darkhan). The optimal angle of the two types of design was found. It emerged that the optimal tilt angle of the M-shape tends to 0. The two types of design efficiencies were compared using Naha’s geographical location and sunshine conditions. -
The Celestial Sphere
The Celestial Sphere Useful References: • Smart, “Text-Book on Spherical Astronomy” (or similar) • “Astronomical Almanac” and “Astronomical Almanac’s Explanatory Supplement” (always definitive) • Lang, “Astrophysical Formulae” (for quick reference) • Allen “Astrophysical Quantities” (for quick reference) • Karttunen, “Fundamental Astronomy” (e-book version accessible from Penn State at http://www.springerlink.com/content/j5658r/ Numbers to Keep in Mind • 4 π (180 / π)2 = 41,253 deg2 on the sky • ~ 23.5° = obliquity of the ecliptic • 17h 45m, -29° = coordinates of Galactic Center • 12h 51m, +27° = coordinates of North Galactic Pole • 18h, +66°33’ = coordinates of North Ecliptic Pole Spherical Astronomy Geocentrically speaking, the Earth sits inside a celestial sphere containing fixed stars. We are therefore driven towards equations based on spherical coordinates. Rules for Spherical Astronomy • The shortest distance between two points on a sphere is a great circle. • The length of a (great circle) arc is proportional to the angle created by the two radial vectors defining the points. • The great-circle arc length between two points on a sphere is given by cos a = (cos b cos c) + (sin b sin c cos A) where the small letters are angles, and the capital letters are the arcs. (This is the fundamental equation of spherical trigonometry.) • Two other spherical triangle relations which can be derived from the fundamental equation are sin A sinB = and sin a cos B = cos b sin c – sin b cos c cos A sina sinb € Proof of Fundamental Equation • O is -
The Solar Resource
CHAPTER 7 THE SOLAR RESOURCE To design and analyze solar systems, we need to know how much sunlight is available. A fairly straightforward, though complicated-looking, set of equations can be used to predict where the sun is in the sky at any time of day for any location on earth, as well as the solar intensity (or insolation: incident solar Radiation) on a clear day. To determine average daily insolation under the com- bination of clear and cloudy conditions that exist at any site we need to start with long-term measurements of sunlight hitting a horizontal surface. Another set of equations can then be used to estimate the insolation on collector surfaces that are not flat on the ground. 7.1 THE SOLAR SPECTRUM The source of insolation is, of course, the sun—that gigantic, 1.4 million kilo- meter diameter, thermonuclear furnace fusing hydrogen atoms into helium. The resulting loss of mass is converted into about 3.8 × 1020 MW of electromagnetic energy that radiates outward from the surface into space. Every object emits radiant energy in an amount that is a function of its tem- perature. The usual way to describe how much radiation an object emits is to compare it to a theoretical abstraction called a blackbody. A blackbody is defined to be a perfect emitter as well as a perfect absorber. As a perfect emitter, it radiates more energy per unit of surface area than any real object at the same temperature. As a perfect absorber, it absorbs all radiation that impinges upon it; that is, none Renewable and Efficient Electric Power Systems. -
Local Sidereal Time (LST) = Greenwich Sidereal Time (GST) +
AST326, 2010 Winter Semester • Celestial Sphere • Spectroscopy • (Something interesting; e.g ., advanced data analyses with IDL) • Practical Assignment: analyses of Keck spectroscopic data from the instructor (can potentially be a research paper) − “there will be multiple presentations by students” • Telescope sessions for spectroscopy in late Feb &March • Bonus projects (e.g., spectroscopic observations using the campus telescope) will be given. Grading: Four Problem Sets (16%), Four Lab Assignments (16%), Telescope Operation – Spectrograph (pass or fail; 5%), One Exam(25%), Practical Assignment (28%), Class Participation & Activities (10%) The Celestial Sphere Reference Reading: Observational Astronomy Chapter 4 The Celestial Sphere We will learn ● Great Circles; ● Coordinate Systems; ● Hour Angle and Sidereal Time, etc; ● Seasons and Sun Motions; ● The Celestial Sphere “We will be able to calculate when a given star will appear in my sky.” The Celestial Sphere Woodcut image displayed in Flammarion's `L'Atmosphere: Meteorologie Populaire (Paris, 1888)' Courtesy University of Oklahoma History of Science Collections The celestial sphere: great circle The Celestial Sphere: Great Circle A great circle on a sphere is any circle that shares the same center point as the sphere itself. Any two points on the surface of a sphere, if not exactly opposite one another, define a unique great circle going through them. A line drawn along a great circle is actually the shortest distance between the two points (see next slides). A small circle is any circle drawn on the sphere that does not share the same center as the sphere. The celestial sphere: great circle The Celestial Sphere: Great Circle •A great circle divides the surface of a sphere in two equal parts.