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Ast 443 / Phy 517
AST 443 / PHY 517 Astronomical Observing Techniques Prof. F.M. Walter I. The Basics The 3 basic measurements: • WHERE something is • WHEN something happened • HOW BRIGHT something is Since this is science, let’s be quantitative! Where • Positions: – 2-dimensional projections on celestial sphere (q,f) • q,f are angular measures: radians, or degrees, minutes, arcsec – 3-dimensional position in space (x,y,z) or (q, f, r). • (x,y,z) are linear positions within a right-handed rectilinear coordinate system. • R is a distance (spherical coordinates) • Galactic positions are sometimes presented in cylindrical coordinates, of galactocentric radius, height above the galactic plane, and azimuth. Angles There are • 360 degrees (o) in a circle • 60 minutes of arc (‘) in a degree (arcmin) • 60 seconds of arc (“) in an arcmin There are • 24 hours (h) along the equator • 60 minutes of time (m) per hour • 60 seconds of time (s) per minute • 1 second of time = 15”/cos(latitude) Coordinate Systems "What good are Mercator's North Poles and Equators Tropics, Zones, and Meridian Lines?" So the Bellman would cry, and the crew would reply "They are merely conventional signs" L. Carroll -- The Hunting of the Snark • Equatorial (celestial): based on terrestrial longitude & latitude • Ecliptic: based on the Earth’s orbit • Altitude-Azimuth (alt-az): local • Galactic: based on MilKy Way • Supergalactic: based on supergalactic plane Reference points Celestial coordinates (Right Ascension α, Declination δ) • δ = 0: projection oF terrestrial equator • (α, δ) = (0,0): -
Equatorial and Cartesian Coordinates • Consider the Unit Sphere (“Unit”: I.E
Coordinate Transforms Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. declination the distance from the center of the (δ) sphere to its surface is r = 1) • Then the equatorial coordinates Equator can be transformed into Cartesian coordinates: right ascension (α) – x = cos(α) cos(δ) – y = sin(α) cos(δ) z x – z = sin(δ) y • It can be much easier to use Cartesian coordinates for some manipulations of geometry in the sky Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. the distance y x = Rcosα from the center of the y = Rsinα α R sphere to its surface is r = 1) x Right • Then the equatorial Ascension (α) coordinates can be transformed into Cartesian coordinates: declination (δ) – x = cos(α)cos(δ) z r = 1 – y = sin(α)cos(δ) δ R = rcosδ R – z = sin(δ) z = rsinδ Precession • Because the Earth is not a perfect sphere, it wobbles as it spins around its axis • This effect is known as precession • The equatorial coordinate system relies on the idea that the Earth rotates such that only Right Ascension, and not declination, is a time-dependent coordinate The effects of Precession • Currently, the star Polaris is the North Star (it lies roughly above the Earth’s North Pole at δ = 90oN) • But, over the course of about 26,000 years a variety of different points in the sky will truly be at δ = 90oN • The declination coordinate is time-dependent albeit on very long timescales • A precise astronomical coordinate system must account for this effect Equatorial coordinates and equinoxes • To account -
The Determination of Longitude in Landsurveying.” by ROBERTHENRY BURNSIDE DOWSES, Assoc
316 DOWNES ON LONGITUDE IN LAXD SUIWETISG. [Selected (Paper No. 3027.) The Determination of Longitude in LandSurveying.” By ROBERTHENRY BURNSIDE DOWSES, Assoc. M. Inst. C.E. THISPaper is presented as a sequel tothe Author’s former communication on “Practical Astronomy as applied inLand Surveying.”’ It is not generally possible for a surveyor in the field to obtain accurate determinationsof longitude unless furnished with more powerful instruments than is usually the case, except in geodetic camps; still, by the methods here given, he may with care obtain results near the truth, the error being only instrumental. There are threesuch methods for obtaining longitudes. Method 1. By Telrgrcrph or by Chronometer.-In either case it is necessary to obtain the truemean time of the place with accuracy, by means of an observation of the sun or z star; then, if fitted with a field telegraph connected with some knownlongitude, the true mean time of that place is obtained by telegraph and carefully compared withthe observed true mean time atthe observer’s place, andthe difference between thesetimes is the difference of longitude required. With a reliable chronometer set totrue Greenwich mean time, or that of anyother known observatory, the difference between the times of the place and the time of the chronometer must be noted, when the difference of longitude is directly deduced. Thisis the simplest method where a camp is furnisl~ed with eitherof these appliances, which is comparatively rarely the case. Method 2. By Lunar Distances.-This observation is one requiring great care, accurately adjusted instruments, and some littleskill to obtain good results;and the calculations are somewhat laborious. -
Sidereal Time Distribution in Large-Scale of Orbits by Usingastronomical Algorithm Method
International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value (2013): 6.14 | Impact Factor (2013): 4.438 Sidereal Time Distribution in Large-Scale of Orbits by usingAstronomical Algorithm Method Kutaiba Sabah Nimma 1UniversitiTenagaNasional,Electrical Engineering Department, Selangor, Malaysia Abstract: Sidereal Time literally means star time. The time we are used to using in our everyday lives is Solar Time.Astronomy, time based upon the rotation of the earth with respect to the distant stars, the sidereal day being the unit of measurement.Traditionally, the sidereal day is described as the time it takes for the Earth to complete one rotation relative to the stars, and help astronomers to keep them telescops directions on a given star in a night sky. In other words, earth’s rate of rotation determine according to fixed stars which is controlling the time scale of sidereal time. Many reserachers are concerned about how long the earth takes to spin based on fixed stars since the earth does not actually spin around 360 degrees in one solar day.Furthermore, the computations of the sidereal time needs to take a long time to calculate the number of the Julian centuries. This paper shows a new method of calculating the Sidereal Time, which is very important to determine the stars location at any given time. In addition, this method provdes high accuracy results with short time of calculation. Keywords: Sidereal time; Orbit allocation;Geostationary Orbit;SolarDays;Sidereal Day 1. Introduction (the upper meridian) in the sky[6]. Solar time is what the time we all use where a day is defined as 24 hours, which is The word "sidereal" comes from the Latin word sider, the average time that it takes for the sun to return to its meaning star. -
Sidereal Time 1 Sidereal Time
Sidereal time 1 Sidereal time Sidereal time (pronounced /saɪˈdɪəri.əl/) is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky. Just as the Sun and Moon appear to rise in the east and set in the west, so do the stars. A sidereal day is approximately 23 hours, 56 minutes, 4.091 seconds (23.93447 hours or 0.99726957 SI days), corresponding to the time it takes for the Earth to complete one rotation relative to the vernal equinox. The vernal equinox itself precesses very slowly in a westward direction relative to the fixed stars, completing one revolution every 26,000 years approximately. As a consequence, the misnamed sidereal day, as "sidereal" is derived from the Latin sidus meaning "star", is some 0.008 seconds shorter than the earth's period of rotation relative to the fixed stars. The longer true sidereal period is called a stellar day by the International Earth Rotation and Reference Systems Service (IERS). It is also referred to as the sidereal period of rotation. The direction from the Earth to the Sun is constantly changing (because the Earth revolves around the Sun over the course of a year), but the directions from the Earth to the distant stars do not change nearly as much. Therefore the cycle of the apparent motion of the stars around the Earth has a period that is not quite the same as the 24-hour average length of the solar day. Maps of the stars in the night sky usually make use of declination and right ascension as coordinates. -
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. -
A Short Guide to Celestial Navigation5.16 MB
A Short Guide to elestial Na1igation Copyright A 1997 2011 (enning -mland Permission is granted to copy, distribute and/or modify this document under the terms of the G.2 Free Documentation -icense, 3ersion 1.3 or any later version published by the Free 0oftware Foundation% with no ,nvariant 0ections, no Front Cover 1eIts and no Back Cover 1eIts. A copy of the license is included in the section entitled "G.2 Free Documentation -icense". ,evised October 1 st , 2011 First Published May 20 th , 1997 .ndeB 1reface Chapter 1he Basics of Celestial ,aEigation Chapter 2 Altitude Measurement Chapter 3 )eographic .osition and 1ime Chapter 4 Finding One's .osition 0ight Reduction) Chapter 5 Finding the .osition of an Advancing 2essel Determination of Latitude and Longitude, Direct Calculation of Chapter 6 .osition Chapter 7 Finding 1ime and Longitude by Lunar Distances Chapter 8 Rise, 0et, 1wilight Chapter 9 )eodetic Aspects of Celestial ,aEigation Chapter 0 0pherical 1rigonometry Chapter 1he ,aEigational 1riangle Chapter 12 )eneral Formulas for ,aEigation Chapter 13 Charts and .lotting 0heets Chapter 14 Magnetic Declination Chapter 15 Ephemerides of the 0un Chapter 16 ,aEigational Errors Chapter 17 1he Marine Chronometer AppendiB -02 ,ree Documentation /icense Much is due to those who first bro-e the way to -now.edge, and .eft on.y to their successors the tas- of smoothing it Samue. Johnson Prefa e Why should anybody still practice celestial naRigation in the era of electronics and 18S? 7ne might as Sell ask Shy some photographers still develop black-and-Shite photos in their darkroom instead of using a digital camera. -
1 the Equatorial Coordinate System
General Astronomy (29:61) Fall 2013 Lecture 3 Notes , August 30, 2013 1 The Equatorial Coordinate System We can define a coordinate system fixed with respect to the stars. Just like we can specify the latitude and longitude of a place on Earth, we can specify the coordinates of a star relative to a coordinate system fixed with respect to the stars. Look at Figure 1.5 of the textbook for a definition of this coordinate system. The Equatorial Coordinate System is similar in concept to longitude and latitude. • Right Ascension ! longitude. The symbol for Right Ascension is α. The units of Right Ascension are hours, minutes, and seconds, just like time • Declination ! latitude. The symbol for Declination is δ. Declination = 0◦ cor- responds to the Celestial Equator, δ = 90◦ corresponds to the North Celestial Pole. Let's look at the Equatorial Coordinates of some objects you should have seen last night. • Arcturus: RA= 14h16m, Dec= +19◦110 (see Appendix A) • Vega: RA= 18h37m, Dec= +38◦470 (see Appendix A) • Venus: RA= 13h02m, Dec= −6◦370 • Saturn: RA= 14h21m, Dec= −11◦410 −! Hand out SC1 charts. Find these objects on them. Now find the constellation of Orion, and read off the Right Ascension and Decli- nation of the middle star in the belt. Next week in lab, you will have the chance to use the computer program Stellar- ium to display the sky and find coordinates of objects (stars, planets). 1.1 Further Remarks on the Equatorial Coordinate System The Equatorial Coordinate System is fundamentally established by the rotation axis of the Earth. -
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. -
Exercise 1.0 the CELESTIAL EQUATORIAL COORDINATE
Exercise 1.0 THE CELESTIAL EQUATORIAL COORDINATE SYSTEM Equipment needed: A celestial globe showing positions of bright stars. I. Introduction There are several different ways of representing the appearance of the sky or describing the locations of objects we see in the sky. One way is to imagine that every object in the sky is located on a very large and distant sphere called the celestial sphere . This imaginary sphere has its center at the center of the Earth. Since the radius of the Earth is very small compared to the radius of the celestial sphere, we can imagine that this sphere is also centered on any person or observer standing on the Earth's surface. Every celestial object (e.g., a star or planet) has a definite location in the sky with respect to some arbitrary reference point. Once defined, such a reference point can be used as the origin of a celestial coordinate system. There is an astronomically important point in the sky called the vernal equinox , which astronomers use as the origin of such a celestial coordinate system . The meaning and significance of the vernal equinox will be discussed later. In an analogous way, we represent the surface of the Earth by a globe or sphere. Locations on the geographic sphere are specified by the coordinates called longitude and latitude . The origin for this geographic coordinate system is the point where the Prime Meridian and the Geographic Equator intersect. This is a point located off the coast of west-central Africa. To specify a location on a sphere, the coordinates must be angles, since a sphere has a curved surface.