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.
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,
, 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.
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
This provides an absolute reference for a North-South coordinate, as with Latitude
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
). 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
to make clear the actual standard catalog and parameters which defines the frame.
The differences between different definitions for a standard Equinoctial year are
and its successor definition
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
. 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
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
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:
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).
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.
(as mentioned previously) accounts for an approximately 23 arcsecond variation
with a principal period of 18.6 years.
|| 24000 years
|| Up to 50 arcseconds/year
|| typically 1 arcminute
|| 1 year
|| 20 arcseconds
|| 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.
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
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
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:
refer to magnitudes and
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
, used in the infrared and radio regime.
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
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
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
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
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
- 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?
- 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?
- 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?