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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): where ascending node of the ecliptic intersects the celestial equator (the first point of Aries = γ)

Reference points

Ecliptic coordinates (λ,β)

• β = 0: plane of the Earth’s orbit around the
Sun

• (λ,β) = (0,0) at γ • ε: inclination of the ecliptic to the celestial

equator, ε=23o26'21".448 - 46".82T - 0".0006T2 + 0".0018T3, (T in Julian Centuries from 2000AD)

• north ecliptic pole: 18h +66o33' (J2000)

Reference points

Altitude-Azimuth (q,f)

• Azimuth q measured east of north • Altitude f measured from horizon to zenith

Reference points

Galactic (lII, bII)

• (lII, bII) = (0,0) is at α=17h42m24s, δ=-28o55'. • North galactic pole: (α,δ) =12h49m, +27o24'
(B1950.0).

• The galactic equator is inclined to the celestial equator by 62.6o.

When

• Solar time • Terrestrial time • Sidereal time

The Second

• The atomic second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of cesium 133.

• The solar second is 1/86,400 of the length of one solar day,
This second is variable in duration, a consequence of the irregular and unpredictable rotation rate of the Earth.

• The ephemeris second is one/31,556,925.9749 of the length of the tropical year 1900 (vernal equinox to vernal equinox).

The atomic second is the same length as the ephemeris second. The mean solar second equalled the atomic second in 1820.

Solar time

• Local time. • The Sun transits (crosses the meridian) at noon, local time.

• The length of the day varies throughout the year.

Civil Time

• the mean angular velocity of the Sun is 15o per hour. • Civil time consists of 24 time zones, each nominally 15o wide, centered on lines of longitude which are multiples of 15o (there are local variations).

– The Eastern time zone is centered on 75o west longitude.
Noon EST occurs when the fictitious mean Sun crosses the 75th degree of longitude.

• The fictitious mean Sun differs from the true Sun in that it has a constant angular velocity across the sky. The difference (in time) between the true Sun and the fictitious mean Sun, the Equation of Time, reaches nearly +/-15 minutes.

  • The Equation of Time
  • Universal Time

• UT is the civil time at 0o longitude (the standard meridian), which passes through Greenwich, England.

• UT is also known as Greenwich mean time (GMT), and is military time Zulu (Z).

• UT is based on the fictitious mean Sun. UT = 12h + the Greenwhich hour angle (GHA) or Right Ascension of the fictitious mean Sun.

• UT1 is UT corrected for the motion of the geographic poles (the
Chandler wobble and similar phenomena).

• UT2 is UT1 with an extrapolated correction for the spindown of the
Earth.

• UTC (Coordinated Universal time) is basically UT1, rounded off. Leap seconds are added to keep UTC within 0.9 sec of UT1. UTC is broadcast by WWV radio. You can see this time on the seismograph in the ESS lobby.

Atomic Time

• TAI • Kept by atomic clocks since 1958 • Stable to 1 part in 1015

– 0.1 nsec/day

• Optical lattice clocks: precise to 1 part in 10-18

– 0.1 sec in the age of the universe

• Unaffected by the vagaries of the Solar System

GPS Time

• = UTC in 1980 • = UTC +18 sec in 2017 • No corrections for leap seconds • = TAI – 17 sec • Accurate to 14 nsec after drift corrections • (=> 4 meter accuracy)

Ephemeris Time

• ET based on the fictitious mean Sun, with the angular velocity of the Sun on 1900 0.5 January. The RA of the fictitious mean Sun =

2

RA=18h38m45.836s + 8,640,184.542s TE + 0.0929s TE

• ET-UT = 24.349s + 72.318sTE + 29.950sTE2 • Ephemeris time was formally abolished in 1984, and replaced with

– Terrestrial Time (TT; formerly Terrestrial Dynamical Time TDT) – Terrestrial Barycentric Time (TBT).

• For all practical purposes, TT = UT1. • TT - TAI = 32s.184

• TE = (JD-2415020.0)/36525, the number of Julian Centuries since 1900 January 0.5

Heliocentric Time

• Time at the center of the Sun

• UT corrected for the light travel time (up to 8.3 minutes on the ecliptic)

Terrestrial Barycentric Time

• TDB = TT + 0.001658 sin(g) + 0.000014 sin(2g) seconds, where

– g = 357o.531 + 0o.9856003 (JD - 2451545.0) – g: mean anomaly of the Earth in its orbit around the Sun.

• TBD is referred to the barycenter of the Solar System. It is an ideal time calculated for an ideal Earth in a circular orbit around the Sun.

• The 1.7 ms periodic deviation is a GR effect due to the variation in the gravitational potential around the Earth's orbit.

• TCB: ideal time corrected for GR effects in a flat space-time frame far from the Solar System. Due to gravitational time dilation, TCB is 49 sec/century faster than TDB.

Recommended publications
  • Ephemeris Time, D. H. Sadler, Occasional

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    EPHEMERIS TIME D. H. Sadler 1. Introduction. – At the eighth General Assembly of the International Astronomical Union, held in Rome in 1952 September, the following resolution was adopted: “It is recommended that, in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0; that the time reckoned in these units be designated “Ephemeris Time”; that the change of mean solar time to ephemeris time be accomplished by the following correction: ΔT = +24°.349 + 72s.318T + 29s.950T2 +1.82144 · B where T is reckoned in Julian centuries from 1900 January 0 Greenwich Mean Noon and B has the meaning given by Spencer Jones in Monthly Notices R.A.S., Vol. 99, 541, 1939; and that the above formula define also the second. No change is contemplated or recommended in the measure of Universal Time, nor in its definition.” The ultimate purpose of this article is to explain, in simple terms, the effect that the adoption of this resolution will have on spherical and dynamical astronomy and, in particular, on the ephemerides in the Nautical Almanac. It should be noted that, in accordance with another I.A.U. resolution, Ephemeris Time (E.T.) will not be introduced into the national ephemerides until 1960. Universal Time (U.T.), previously termed Greenwich Mean Time (G.M.T.), depends both on the rotation of the Earth on its axis and on the revolution of the Earth in its orbit round the Sun. There is now no doubt as to the variability, both short-term and long-term, of the rate of rotation of the Earth; U.T.
  • An Introduction to Orbit Dynamics and Its Application to Satellite-Based Earth Monitoring Systems

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    19780004170 NASA-RP- 1009 78N12113 An introduction to orbit dynamics and its application to satellite-based earth monitoring systems NASA Reference Publication 1009 An Introduction to Orbit Dynamics and Its Application to Satellite-Based Earth Monitoring Missions David R. Brooks Langley Research Center Hampton, Virginia National Aeronautics and Space Administration Scientific and Technical Informalion Office 1977 PREFACE This report provides, by analysis and example, an appreciation of the long- term behavior of orbiting satellites at a level of complexity suitable for the initial phases of planning Earth monitoring missions. The basic orbit dynamics of satellite motion are covered in detail. Of particular interest are orbit plane precession, Sun-synchronous orbits, and establishment of conditions for repetitive surface coverage. Orbit plane precession relative to the Sun is shown to be the driving factor in observed patterns of surface illumination, on which are superimposed effects of the seasonal motion of the Sun relative to the equator. Considerable attention is given to the special geometry of Sun- synchronous orbits, orbits whose precession rate matches the average apparent precession rate of the Sun. The solar and orbital plane motions take place within an inertial framework, and these motions are related to the longitude- latitude coordinates of the satellite ground track through appropriate spatial and temporal coordinate systems. It is shown how orbit parameters can be chosen to give repetitive coverage of the same set of longitude-latitude values on a daily or longer basis. Several potential Earth monitoring missions which illus- trate representative applications of the orbit dynamics are described. The interactions between orbital properties and the resulting coverage and illumina- tion patterns over specific sites on the Earth's surface are shown to be at the heart of satellite mission planning.
  • Goals: 1) Solve a Different Cultures Astronomy Problem. 2) Look at the Interaction Between Science, Religion and Culture

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  • How Long Is a Year.Pdf

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    How Long Is A Year? Dr. Bryan Mendez Space Sciences Laboratory UC Berkeley Keeping Time The basic unit of time is a Day. Different starting points: • Sunrise, • Noon, • Sunset, • Midnight tied to the Sun’s motion. Universal Time uses midnight as the starting point of a day. Length: sunrise to sunrise, sunset to sunset? Day Noon to noon – The seasonal motion of the Sun changes its rise and set times, so sunrise to sunrise would be a variable measure. Noon to noon is far more constant. Noon: time of the Sun’s transit of the meridian Stellarium View and measure a day Day Aday is caused by Earth’s motion: spinning on an axis and orbiting around the Sun. Earth’s spin is very regular (daily variations on the order of a few milliseconds, due to internal rearrangement of Earth’s mass and external gravitational forces primarily from the Moon and Sun). Synodic Day Noon to noon = synodic or solar day (point 1 to 3). This is not the time for one complete spin of Earth (1 to 2). Because Earth also orbits at the same time as it is spinning, it takes a little extra time for the Sun to come back to noon after one complete spin. Because the orbit is elliptical, when Earth is closest to the Sun it is moving faster, and it takes longer to bring the Sun back around to noon. When Earth is farther it moves slower and it takes less time to rotate the Sun back to noon. Mean Solar Day is an average of the amount time it takes to go from noon to noon throughout an orbit = 24 Hours Real solar day varies by up to 30 seconds depending on the time of year.
  • The Determination of Longitude in Landsurveying.” by ROBERTHENRY BURNSIDE DOWSES, Assoc

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    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

    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

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    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.
  • Leapseconds and Spacecraft Clock Kernels LSK and SCLK

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    N IF Navigation and Ancillary Information Facility Leapseconds and Spacecraft Clock Kernels LSK and SCLK January 2020 N IF Topics Navigation and Ancillary Information Facility • Kernels Supporting Time Conversions – LSK – SCLK • Forms of SCLK Time Within SPICE • Backup LSK & SCLK 2 N IF SPICE Time Conversion Kernels Navigation and Ancillary Information Facility In most cases one or two kernel files are needed to perform conversions between supported time systems. • LSK - The leapseconds kernel is used in conversions between ephemeris time (ET/TDB) and Coordinated Universal Time (UTC). • SCLK - The spacecraft clock kernel is used in conversions between spacecraft clock time (SCLK) and ephemeris time (ET/TDB). – It’s possible there could be two or more clocks associated with a given spacecraft. Ephemeris Time, ET and Barycentric Dynamical Time, TDB, are the same LSK & SCLK 3 N IF The Leapseconds Kernel (LSK) Navigation and Ancillary Information Facility The leapseconds kernel contains a tabulation of all the leapseconds that have occurred, plus additional terms. • Used in ET UTC and in ET SCLK conversions. – Subroutines using LSK: STR2ET, TIMOUT, ET2UTC, etc. – Utility programs using LSK: spkmerge, chronos, spacit, etc. • Use FURNSH to load it. • NAIF updates the LSK when a new leap second is announced by the International Earth Rotation Service (IERS). – The latest LSK file is always available from the NAIF server. » The latest is LSK always the best one to use. – Announcement of each new LSK is typically made months in advance using the “spice_announce” system. » http://naif.jpl.nasa.gov/mailman/listinfo/spice_announce – New LSKs take effect ONLY on January 1st and July 1st LSK & SCLK 4 N IF LSK File Example Navigation and Ancillary Information Facility KPL/LSK .
  • The Calendars of India

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  • Astronomical Time Keeping file:///Media/TOSHIBA/Times.Htm

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  • A Short Guide to Celestial Navigation5.16 MB

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    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.
  • Governing the Time of the World Written by Tim Stevens

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