Basic Observational Knowledge

Astronomy, like all fields, assumes a certain literacy in terms unique to the field. Because of the great age of this science, some terms are antique and used in ways which may differ from the usage of the same or similar term in other fields.

Angular measure

The sky consists of 4π steradians (a unit of solid angle) "surface", or approximately 41253 square degrees. Considering the Moon has a typical diameter in the sky of half a degree, or an areal dimension of about 0.2 square degrees, one can see that the sky is a rather roomy place.

Like on a circle, angular measure in the sky is conducted in degrees, with a Great Circle (a circle containing the center of the celestial sphere) divided into 360 degrees. A degree is divided into 60 arcminutes, and a minute is divided into 60 arcseconds. The arcsecond is the typical "working unit" of angular measure for astronomical images. It is the typical smallest unit of resolution that is delivered by a large telescope due to blurring by atmospheric "seeing" without active or adaptive telescope corrections. There are 3600 arcseconds in a degree, or 206265 arcseconds in a radian. The smallness of this dimension can be visualized by noting that an arcsecond is about the apparent size of the thickness of a human hair about 100 feet away. A human with excellent vision can see, unaided, angular separations down to about 2 arcminutes.

But in astronomy, a second angular measure is also frequently encountered: seconds or minutes of separation in time. This arises because the Earth is in rotational motion compared to the sky, and thus a telescope, fixed to the Earth, sees objects move across its field of view. Without a clock-drive locking a telescope to the sky, objects separated East to West will drift through a telescope field, and the East-West angular distance can be quoted in the time difference between passage of the two objects in the telescopic field.

Coordinates in fact are generally specified with the North/South component, the Declination, quoted in units of arc, and the East/West component, the Right Ascension, quoted in units of time. Thus coordinates appear in the form

Vega    18:36:56.34     +38:47:01.3     J2000.0
In this typical catalog entry, the Right Ascension (RA) of Vega is read as 18 hours, 36 minutes, 56.34 seconds (implicitly, of time) and the Declination (Dec) of Vega is +38 degrees, 47 minutes, 01.3 seconds (implicitly, of arc). Since there are 24 hours in a circle and 360 degrees, on the equator one second of time equals fifteen seconds of arc. This is often confusing! In addition, since lines of constant declination for declination north or south of the equator are not great circles, the conversion constant varies as one goes off the equator. Along the constant latitude arclength (which is not a great circle!) 1 second of time = 15 seconds of arc * cosine(Declination). Because of this roughly order of magnitude difference in scales, coordinates are typically cited to one more digit past the decimal in RA than in Dec, so that the precision is the same as seen on the sky.

Coordinate systems

The coordinate system on which objects are measured is defined by the projection of the Earth's rotational axis into the sky, defining the Celestial Equator and the Celestial Poles. This provides an absolute reference for a North-South coordinate, as with Latitude on the Earth -- this is called the Declination. The East-West coordinate reference is more involved. Happily, whereas the East-West reference choice on the Earth was essentially a political one, with (from time to time) the chief naval power defining the origin (the Prime Meridian) in the sky there is a convenient reference provided by the intersection of the Celestial Equator with the plane of the Earth's orbit around the Solar System (the Ecliptic). The coordinate measured westerly from one of these intersections (the "vernal" or spring equinox point, where the Sun crosses from south to north in the sky) is called the Right Ascension.

Unhappily, none of these beautiful geometrical abstractions are perfectly fixed: in fact all are slowly in motion -- a fact realized even as early as Hipparcos among the ancient Greeks. The Earth's axis wobbles like a top, slowly precessing around a 48 degree diameter circle in the sky over a period of about 25,800 years (the Precession of the Equinoxes). There is a much smaller wiggle (only about 23 arcseconds) with several periods, the dominant being 18.6 years (the Nutation). These are both produced by tugs on the Earth's tidal bulge from both the Moon and the Sun, producing free body precession.

The result is that the coordinate lines themselves are in motion, which is quite awkward and unpleasant. Fortunately the motion is slow. As a result, over time "Standard" coordinate frames are defined (1875, 1900, 1925, 1950, 2000 are common ones, with 1950 and 2000 the only two currently in active use) representing a mean coordinate frame with respect to the Nutation during that calendar year. Typically the 1950 and 2000 Equinox systems will be quoted as B1950 and J2000 or ICRS 2000 to make clear the actual standard catalog and parameters which defines the frame. The differences between different definitions for a standard Equinoctial year are small: Both J2000 and its successor definition ICRS 2000 are widely used and the (slightly differing) frame definitions result in positional differences that vary by about a twentieth of an arcsecond, thus they are functionally identical to all but astrometry specialists.

Given historical example, probably the astronomical community will decide on a exact specifics of a 2050 standard Equinox around the 2030 timeframe and use it for the following half century.

The system is further complicated by the fact that objects on this celestial grid are themselves in motion. Nearby stars move around at speeds of a fraction of an arcsecond per year (some high proper motion stars move much faster), and thus one must determine where in fact they were at a historical observation, or where they will be at a future planned one. Galaxies, fortunately, are sufficiently far away that over human time intervals, absent extremely-high-precision interferometric techniques -- they appear almost fixed -- in fact distant quasars are now used to define the fixed reference frame on which an Equinox definition is superimposed. The motion of stars is called the proper motion and is available in catalogs, typically quoted in units of milliarcseconds per year for both the E/W and N/S component.

When quoting a position, the time of the position at which the object has a given place is called the Epoch. The time of the coordinate grid itself is called the Equinox. Popular usage, even among astronomers, often confuses these two. When obtaining coordinates to point a telescope, one would preferably obtain both the current coordinate grid (the Equinox of date) and the current positions of the object itself given its motions (the Epoch of date) for setting the telescope position. Often the proper motions may be unavailable, and thus the catalog epoch is used, but the (usually larger) correction for the current Equinox is used. This is why the position reported when you are at the telescope and looking at an object differs from the catalog position. It will typically be reported as the Equinox of Date unless otherwise indicated.

At the level of precision necessary to acquire an object at the telescope, simple converters will handle the job of converting between different Equinoxes quite effectively. The HBO telescope allows one to specify the Equinox attached to a coordinate pair when setting a target point. Numerous precession calculators are also online to do this task.

At the telescope, these coordinate systems are related to the Sidereal Time which is the coordinate of Right Ascension currently crossing the meridian of the sky.

Other positional corrections

The above discussion yields an astrometric coordinate for a specified equinox describing an object. But observing an object through a telescope will yield an apparent position that is slightly displaced. Since it is the apparent coordinate that is observed, if one wishes to measure the highest accuracy astrometric coordinate, any distortions must be understood and backed out, or else local astrometric references in an image chosen and used to calibrate the astrometric system within. The largest terms of deviation from astrometric to apparent coordinates are:

Refraction Atmospheric refraction makes an object appear higher in elevation than it really is. An object appearing to be on the horizon is actually 34 arcminutes (slightly larger than the diameter of the Sun or Moon) below it, so the effect is (relatively) enormous at the horizon itself. At intermediate elevations, however, more typical corrections are about 1 arcminute (5 arcminutes at 10 degrees elevation).

Astronomical Aberration The Earth is a moving target for starlight, and its motion causes an apparent change in the direction in which targets appear to be seen. The effect is small because the speed of light is so large compared to the motion of the Earth, but it does create an annual term of 20 arcseconds amplitude in the apparent place of a star. A much smaller effect is seen from the Earth's rotation: an observer on the equator will see an additional daily 0.32 arcsecond term.

Nutation (as mentioned previously) accounts for an approximately 23 arcsecond variation with a principal period of 18.6 years.

Summary
Term Period Scale
Precession 24000 years Up to 50 arcseconds/year
Refraction --- typically 1 arcminute
Aberration 1 year 20 arcseconds
Nutation 18.6 years 23 arcseconds

In addition, telescopes themselves and their coordinate scales are imperfectly made: one must make allowances for the fact that the RA and Dec axes on a telescope are never perfectly orthogonal, that the principal optical axis of the telescope is not exactly orthogonal to the Dec axis, that the telescope's RA axis does not point perfectly towards the pole, and that there is mechanical flexure of the components of the telescope as it is moved about. These factors are not typically quoted in an object's "apparent" coordinates, because they are unique to a given instrument at a particular time. When a telescope is computer-controlled, the software may provide for the correction of these terms automatically.

Brightness Systems

In optical astronomy, object brightness is generally given in units called "magnitude". The term derives from historical usage that the brightest stars in the sky were of the "first magnitude", and so forth down to sixth magnitude, the limit that the unaided eye can see. It was only in the 18th century that it was shown that the eye responds to light in an approximately logarithmic way and that stars of 6th magnitude were about 100 times fainter than stars of 1st magnitude. Another century would elapse before truly quantitative studies of brightness would begin and formalize the system.

The magnitude system is anchored by standard stars. The definitions have changed over time but the original system was set essentially so that Vega defined the zero magnitude point in various colors. One of the more widely used reference catalogs of standard stars are the Landolt standards (Landolt, A.U., 1992, AJ, 104, 340) which are scattered about the sky near the celestial equator. Differential photometry between stars in an image frame is easy. Tieing them to an absolute photometric system is somewhat more involved, depending on the precision required.


(Girardi, Bertelli, Bressan et al, 2002, A&A, 391, 195)

Magnitudes are quoted according to passbands, generally for the Johnson-Cousins-Glass system (indicated by capital letters from the set UBVRIJHK). There are many filter systems in astronomy, but this is the oldest and still among the most widely used.

Since the scale is logarithmic with a factor of 100 between 1st and 6th (a five-magnitude gap), there is a factor of ten in intensity for every 2.5 magnitudes. This is formallly stated as: $m_{\rm A} - m_{\rm B} = -2.5 \times \log_{10} ( F_{\rm A} / F_{\rm B} )$ where $m$ refer to magnitudes and $F$ to fluxes.

Note that one unusual aspect of the magnitude system is that brighter objects have more negative magnitudes -- thus the "sense" of the system is opposite from almost all other measurement systems.

The approximate rule of thumb is that a zero magnitude star in the green light (i.e., the "V" filter for the Johnson-Cousins system) delivers about 1000 photons per second per square centimeter per Angstrom to the top of the Earth's atmosphere -- see EstimatingPhotons. One can thus make estimates of the number of photons received in an astronomical measurement knowing the brightness in advance.

Other wavelength regimes have their own measurement systems, though generally these fall into two categories: raw photon counts, as tend to be used for extremely high energy (gamma ray or x ray) astronomy, and the Jansky system (a unit which denotes $1\times10^{-26} \rm{W}/(\rm{m}^2 \rm{Hz})$, used in the infrared and radio regime.

Time

Astronomers generally record time when making observations in "Universal Time" (UTC), upon which the world's standard time zones are synchronized. Eastern Standard Time (EST) is UTC - 5 hours; Eastern Daylight Time (EDT) is UTC - 4 hours.

The UTC system is based on the international second. The Earth is not so kind as to keep itself synchronized from year to year with a day based on fixed seconds, so periodically "leap seconds" are added to (and possibly subtracted from, though that has not happened yet) to the UTC scale to keep this fixed time scale synchronized with the Earth's rotation to within 0.9 second (see table of leap seconds here). Calculating an interval of time over several years, therefore, requires keeping track of additional leap seconds. The atomic coordinate time standard without leap seconds is International Atomic Time (TAI) which will therefore drift over time with respect to the Earth's irregular rotation. The offset between TAI and UTC is always an integral number of seconds.

There are further complications. The Earth is in motion about the Sun, thus "arrival times" of light may vary by up to twice the Earth-Sun light time, or 16 minutes, for objects on the ecliptic over the course of a year. Measured velocities are also shifted by this motion. Times of periodic phenomena need to be corrected to a fixed point (typically the solar system barycenter) to remove this periodic term.

At the final level of refinement, there is an additional correction term imposed by the General Relativistic time dilatation caused by the gravity well of the Solar system. Barycentric Coordinate Time (TCB) is defined as a proper time experienced by a clock traveling with the Solar system but outside its gravity well. The correction is small: only about half a second per year difference between an Earth clock and a TCB clock. Only very high-precision work requires attention to this and related niceties.

When reporting a series of times, it is inconvenient to specify dates and times in the usual manner: it becomes difficult to easily calculate time differences or plot these on a chart. The usual astronomical convention is to convert dates and times to the decimalized "Julian Date," abbreviated JD. The Julian date represents the number of days and fraction thereof since noon Universal Time, January 1, 4713 BCE on the Julian calendar. Contemporary values of the Julian Day are above 2.4 million. There is a quirk with the structure of the Julian Day: it begins at noon, not midnight.

For convenience with contemporary observations, astronomers often use the "Modified Julian Date", or MJD, which is simply the Julian Date minus 2400000.5. The MJD, because of the 0.5 in the subtraction, begins at midnight, not noon, just as in conventional timekeeping.

There are numerous calculators both online and available through programs to reduce observations to JD or MJD forms. One provided by the US Naval Observatory may be found here.

Exercises

  1. How many astronomical images that cover the diameter of the Moon would be required to map the sky? The Palomar Sky Survey mapped most of the sky using 6x6 degree photographic plates (which is a very large field) in the 1950s. How many of these plates were necessary to cover the sky?
  2. Look up the coordinates for the star Arcturus using SIMBAD. Precess the coordinates from the ICRS Equinox 2000 coordinates to current. If you enter equinox 2000 coordinates into a telescope pointing system, how far off will you be (assume no proper motion). A typical field of view is 10 arcminutes. Will you still see Arcturus?
  3. What is the difference between Arcturus' position in Equinox 2000 coordinates between Epoch 2000 and Epoch of date? Over a century, how far does Arcturus move?

-- DonBarry - 2013-08-30

 
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