John Pazmino
 NYSkies Astronomy Inc
 2001 May 26
Parameters for sky motion and aspect
    These are notes for my talk before the Observing Group on Saturday
26 May 2001 on 'sky orientation'. This relates to the sky's aspect and
motion as governed by several parameters. There are five motions of
the sky.
    Diurnal - hourly during a given day
    Annual - seasonal at a given hour
    Planetary - motion of planet, comet, &c against the stars
    Latitude - change of location on Earth
    Precession - secular alteration of coord grid
Celestial sphere
    The heavens look like an immense globe around us. We are at the
very center of this globe. The globe, the CELESTIAL SPHERE, was once
thought to be a real construction but of course it is not. Never the
less it remains today a very handy mechanical way of understanding the
motion and aspect of the sky.
    The celestial sphere is of arbitrarily huge radius, infinite if
you want to call it, so that in comparison to it the whole solar
system is but a point. Our travels on the Earth and the motion of the
Earth around the Sun have no effect of perspective on the stars. The
deployment of the stars on the celestial sphere gives no hint of
finite distance by which we can glean a 3D picture of the universe.
    The stars, nebulae, galaxies are fixed as if tacked or glued to
the inner surface of the celestial sphere. As the celestial sphere
moves, all of the stars move with it as a single unit. This is the
idea of FIXED STARS.
    Like the Earth, the celestial sphere has an EQUATOR and NORTH and
Right ascension and declination
    Skipping all the history, these are the equivalent in the sky of
Earth latitude and longitude. They can be tabulated or plotted on an
atlas chart. RIGHT ASCENSION is the 'longitude' coordinate.
DECLINATION is the 'latitude' part.
    Declination is measured in degrees of arc. Positive declination is
north of the equator; negative, south. The north pole of the heavens
is at +90 deg declination.
    Right Ascension is dimensioned in time units like a clockface. The
complete circuit of 'longitude' has 24 hours in stead of 360 degrees.
The hours are divided into minutes and seconds, just like those of
    Imagine the celestial sphere to have a solid outer shell with the
fixed stars on it. Lining this shell is a transparent skin with the
coordinate grid on it. Missing out the details, this inner skin turns
within the outer shell so that the coord lines slide across the stars.
    The numerical reading of a star's coordinates will alter over time
altho the very star is not itself moving. The effect is very slow,
only about 50 arcseconds at most per year. With passage of many 
decades the shift in right ascension and declination can be serious 
enough to redraw a chart with the updated alignment of the coord grid. 
For most stargazing purposes you can ignore precession and use a chart 
drawn for, nowayears, the year 2000. 
    The year for which the coord grid is laid on a chart is the EPOCH
and for the next couple decades the epoch of 2000 will serve us well.
In the mid 20th century thru about 1980 the epoch of 1950 was widely
used. You'll find a deep litterature of maps with this epoch.
    Precession is important foe interpreting old literature. If you
read of a comet in a 1920 magazine and plot its path on a map with
epoch 2000 grid, the path will be badly displaced. You must either
convert the 1920 coords to the 2000 epoch or get a map for the 1920 
    This is actually easiest done by computer being that planetarium
programs have precession built in. You set the program to 1920 and 
apply the positions from the 1920 epoch.
    SIlly factoid. The constellation boundaries are defined from a map
of 1875 epoch (No, I don't know why, when this was done in 1930.) If 
you look carefully at a contemporary map with these boundaries, they 
do NOT quite align with the coord grid. 
    Note that the epoch is NOT the instant date of a chart! The epoch
refers to the alignment of the grid on the chart by which objects are
plotted into it. The instant date, which can include all fields of a
date and hour, refers to the data themselfs, the trail of a comet or
location of a nova.
    Early astronomers recognized seven bodies in the heavens which
wandered against the stars as if crawling on the celestial sphere.
These were PLANETS, which then included Sun and Moon. Their positions
evolved over the days so they can not be marked on a map for permanent
or longterm use. A map with the planets marked on it is valid only for
a single date.
    Comets and asteroids also wander among the stars and they can be
plotted only for specific dates on a map of the heavens.
Planetary motion
    This is the true motion of a planet, comet, asteroid thru the
stars. It is a perspective effect combining the Earth's and other
body's real orbital motion around the Sun. The path in the stars of a
given planet has some cycle to it so you can dope out where it will be
in the past or future.
    The motion of a comet is very irregular and, until parabolic and
highly elongated ellipses were understood, they were utterly
unpredictable. Even when a comet returns to the Earth's vicinity due
to its closed orbit, the path from return to return is vastly
    However, taking all the planets together, even just the five
classical ones, their positions among the stars at a given date is
totally unique and will never be repeated. This results from the
periods of the planets being irrational ratios of each other.
Timescale of planetary motion
    Planets and most asteroids move slowly enough so that a position
for them plotted at any hour during a given day is good for the entire
day. Thus a chart showing a planet's place for 0h UT is good for any
night hour in New York during the 24 hours surrounding 0h UT.
    Near-Earth asteroids and many comets move so swiftly against the
stars that the hour is important. A comet marked for 0h UT may have
scudded many degrees from its place if you try to view it several
hours away from 0h UT.
    The Moon moves against the stars quite 1/2 degree per hour. For
casual moonviewing this is not too important, specially since you
recognize the Moon in the sky regardless of its exact coordinates. On
the other hand for conjunctions and specially for eclipses and
occultations the hour can be vital.
    The aspect of the sky due to latitude is more likely a step change
and not a gradual motion. You board a plane in New York for your
winter home in Bonaire. When you get off the plane you're at latitude
10 or so degrees north, in stead of New York's 40ish degrees. On the
first clear night you see an very different sky overhead.
    Latitude rotates the celestial sphere about the east-west line so 
that the altitude of the north pole is alway equal to your latitude. 
Polaris in New York (close enough to the pole) is 40 degrees up. In
Bonaire it's about 10 degrees up. The celestial equator, about 50
degrees up in the south at New York, is 80 degrees up from Bonaire.
    Stars beyond the southern horizon from New York now rise and set
and are visible at some set of date & hour. Stars which in New York
circle the north pole without setting now do set below the north
horizon for certain dates & hours.
    If you're used to seeing a constellation from New York you may
find it tilted into some unrecognizable angle. Wholly unseen zones of
the sky are now in sight with their unknown stars.
    As a rule, the area of sky visible from a given latitude, at some
date and hour, extends from the elevated pole (north in this case) to a 
distance away from the opposite pole which is equal to your latitude. 
The zone within that distance surrounding the opposite pole remains 
latent from you. Example, in New York we can see, at some moment, 
everything from Polaris all the way to 40 degrees away from the south 
pole. Stuff within 40 degrees of the south pole are latent because 
they never rise. 
    Equivalently, the area visible extends from the elevated pole to a
declination in the opposite hemisphere equal to 90 degrees minus your
latitude. So from New York the farthest south we can see is -50 deg
declination, that is (90 deg) - (40 deg), with opposite sign. 
Southern sky
    All of astronomy as handed down to us comes from cultures in the
mid northern latitudes. These include Mesopotamia, Greece, Egypt,
Europe, and to some extent China and Japan. These peoples did not know
of the far south stars except for occasional explorations well south
of their home ports.
    The SOUTHERN SKY is the region of the heavens farther south than -
45 degrees declination. This is entirely a boreocentric thing, you
understand. This zone includes Carina, Crux (southern cross), much of
Centaurus, Ara, as well as many constellation concocted long after
classical era.
    By similar logic the SOUTHERN MILKY WAY is the reach of the Milky
Way south of -45 deg declination.
Altitude and azimuth
    The location of a star in the local sky is a function of latitude,
date, and hour. That is, three parameters must be specified to
uniquely lock the sky into its proper aspect.
    Once this is done, the local or horizon coordinates can be
calcked. It may be that the target you want to look at is below the
horizon and out of sight or may be hidden behind local obstructions
like towers or trees.
    The angular displacement from the horizon is the ALTITUDE in
degrees of arc. 0 deg is the horizon. 90 deg is directly overhead in
the ZENITH. If you have to cite a depression below the horizon, use
negative angles. The point directly underfoot is the NADIR at -90 deg
    AZIMUTH is much like compass directions. 0 deg is north; 90 deg is
east; 180, south; 270, west. If you picture a clockface with 12
o'clock in the north, then each hour round thru east, south, and west
is 30 deg of azimuth.
Altitude and elevation 
    In astronomy, altitude is the angular position of a point in the
sky up (or down) from the horizon. ELEVATION is the linear height of
the observer above some base level, such as that of the open sea.
Altitude is in degrees of angle while elevation is in meters (or some
oldstyle unit) of linear height.
    In aviation and some navigation the two terms are exactly swopped.
Elevation is the angle and altitude is the height! As long as you 
stick to straight astronomy you'll have no troubles. 
Diurnal motion
    Reflection of Earth's rotation to produce day and night. Because
the Sun is among the stars as it rises and sets, so all the stars and
other celestial bodies partake in this daily cycle of rising and
setting. The stars in the east (all of this is for New York latitude)
wheel up from the horizon and arc toward the right (south). Stars in 
the south migrate from left (east) to right (west). 
    Stars in the west wheel down toward the horizon and arc to the
right (north). Those in the north circulate around the north pole, near the
star Polaris (there happens to be no bright south star) in the
counterclockwise sense. They drift upward while on the right of the
pole and downward while on the the left.
    Starglobes, solid spheres viewed from the outside, were made to 
study and understand the sky motions. They have to turn clockwise, as 
seen from its own north pole, to properly show the star motion. 
    Eventually a flat dial version of a starglobe was invented to tell
time with a hand to point to the Sun. (Our civil time is based on the
Sun's progress over us.) On such dials, the hand has to rotate, ahem,
clockwise in concordance with a solid starglobe. Whence comes our
convention for clockwise and counterclockwise rotation.
    Diurnal rotation allows you to see much more than just half of the
heavens during a night. Stars in the west set first, followed by those
now in the south. Stars below the horizon in the east will rise later
in the night.
    We can not see the stars all the time due to the atmospheric
scattering and dispersion of sunlight, causing a veiling of the stars
when the Sun is near or above the horizon. On the Moon, with no air,
the stars are visible all the time, right up to the edge of the Sun.
Annual motion
    Reflection of the Earth's motion around the Sun once each year.
(The year is defined as the time to complete one full circuit around
the Sun.) The night side of the Earth faces away from the Sun. Hence
at various places in the orbit, this night side faces outward toward
different parts of the heavens. This makes a given zone of the stars
visible at night only in certain months or seasons.
    An other way of understanding this is to concentrate on the Sun.
The Sun drifts thru the zodiac once each year as our line of sight to
it rotates around the Sun. Stars near the Sun will be masked by
daytime. Those far away will be seen at night.
    This exclusion zone around the Sun is carried by the Sun as it
migrates thru the zodiac. Stars ahead, east, of it will be covered by
the exclusion zone in the coming days. Stars now in the zone and not
visible will leave it off of its western side and become visible.
    Thus the stars in our night sky are merely those which at the
instant day are far from the daytime zone surrounding the Sun. And so
at a given hour, say 20h local time, month by month the stars drift
westward into the daytime zone and new stars drift up out of the east.
    This is an analog model of the heavens as seen form a particular
latitude. It is useful within 5 or so degrees of the home latitude for
general starbrowsing. It consists of a base plate of stars centered on
the north pole (for north latitudes) and an overlay plate with a
horizon cutout. Round the edges of both plates are the dates of the
year and hours of the day.
    The dates are attached to the star plate; hours, horizon plate.
You line up the desired hour and date by rotating the two plates. They 
are pivoted at the north pole. Friction holds them still so they don't 
spin unintentionally.
    The stars within the horizon cutout, or mask on some models, are
those above your horizon for the selected date and hour. The field is
the entire hemisphere of the celestial sphere above you.
    Essentially all planispheres are intended for longterm use. They 
plot only the fixed stars, no planets or other moving or shortlife 
objects. Some do have surfaces that allow temporarily marking a comet
or nova, then erasing it later.
    The map projection is generally a very distorted one so stars near
the edge of the planisphere are spread much too far apart compared to
those near the center. But this distortion helps keep the planisphere
within size for handling and carrying. It can take some mental
gymnastics to correlate the flat presentation of the sky on the
planisphere with the rounded dome over you! What most stargazers do is
turn the gadget so the part of the horizon they are facing is at the
bottom. They then concentrate on the stars in this direction from the
horizon to overhead. The zenith is more or less in the middle of the
horizon mask, but it could be quite excentric if the map distortion is
too severe.
    A few models have interchangeable horizon plates to allow use in
different latitudes. The normal model is for a fixed single latitude,
usually in the mid 30s and low 50s of north latitude and mid 20s of
south latitude.
Portrait or atlas chart
    This is a chart aligned with north at the top and west to the
right. It ignores the actual orientation and location of the field in
your local sky. This chart is like a plate in an atlas in that it can
be detailed with many labels, symbols, grids, and other details.
    Some charts for use in the southern hemisphere have south at the
top and west at the left; the northern chart is turned end for end and the
lettering is then rectified.
    A portrait map can have a path or trail on it, like for a comet. 
Skyscape or horizon chart
    This chart is drawn to match up directly with the stars over your
local horizon. They tend to be lightly lettered and free of clutter.
They are commonly used to plot planets for a specific date and hour to
correlate with your horizon. This is important for twilight hours when
there are few stars visible in the bright sky.
    A skyscape chart is valid only for a given date, hour, and
latitude if it has any planets on it.
    If it has only fixed stars, the horizon chart can be used for a
set of date-hour combos. In fact for each day of the year, all 365 of
them, there is a corresponding hour, so there are 365 combos of
validity for this chart. An arbitrary setting of a planisphere has the 365
sets of date-hour on the scales around the perimeter of the device.
    Many of these combos will be useless for falling within strong 
twilight or in daylight.
Trail and snapshot
    If you plot the position of a planet on a starchart for a single
date, this is a snapshot of the heavens for that date. You do this to
help find the planet (comet, &c) on that date or to record its
position as you saw it on that date. This is like taking a photograph
of the sky and noting the planets on the image.
    If you plot a planet for a series of dates you get a trail or path
of that planet. The chart is valid between the earliest and latest
date at the ends of the trail. This is good for planet finding during
a season or a comet during its visit to the Earth and Sun. This is
like taking sequential pictures of the sky, then superimposing the
images. On the composite you got the sequential positions of the
Angular scale
    Linear scale on a starchart is meaningless due to the indefinitely
large radius of the celestial sphere. All charts are dimensioned and
measured off of by angles.
    Like Earth maps a starmap may be of any scale suitable for its
purpose. An allsky map showing the whole dome may fit on a letter
page, with scale of 1 degree per millimeter. A map of a galaxy cluster
may cover a few arcminutes of sky with a scale of 10 arcseconds per
    Every good chart should have on it or in the caption the explicit
scale. If there is a chance that the chart will be photocopied to a
zoomed in or out size, an actual ruler is needed so it partakes in the
photocopying. In some cases the scale is obvious, like when 
recognizable star patterns are included or when the entire sky is 
Correlating map and sky
    If possible choose or make (by a computer program) a map fitted 
for the purpose at hand. This is not always possible or practical. You 
may have but the map in a magazine or handout. IF you generate your 
own chart, leave out extraneous and superfluous lines, symbols, 
labels. This removes clutter and makes the chart far easier to read. 
    It's your own choice to use a chart with dark stars on a light
background or one with light stars on a dark background. Computer
produced maps tend to have the dark on light simply to save ink and,
for some printers, avoid wetting the printout. With a computer
generated map you can reverse the color by means of an artist program.
Almost all have an 'inverse' or 'negative' color function.
    The scale tells how much of the sky is comprehended by the map.
Say it is a field 30 degrees by 20 degrees. You must visualize on the
sky a rectangle of this angular extent.
    Your closed fist held at armslength spans 10 degrees across the
knuckles. The fingers spread out as far as they can spans 20 degrees
from thumb to pinky. A ruler at armslength measures degrees by the
centimeter marks; this is a bit sloppy but in a pinch it works.
    Dimension lines within major constellations can be used to assess
angular extent. The sides of the Great Square of Pegasus, for
instance, are about 15 degrees. The Belt of Orion is 3 degrees. From
Polaris to the nearer 'Pointer' star of the Big Dipper is about 30
degrees. Stargazing books usually have such handy measures in the
constellation descriptions.
Distance and direction
    All 'distances' on the celestial sphere are in angular, not
linear, measure. This is similar to the use on Earth of the arcminute
in navigation. An arcminute on the Earth is defined to be the
'nautical mile', nearly 1,800 meters. Hence, we say a comet stands 8-
1/2 degrees from a certain star.
    Directions on the sky can really be confusing! About any given
point you can specify a direction, just like you do on Earth, by a
compass rose. You may use compass points or compass degrees. The comet
noted above is 8-1/2 degrees to the southwest of that certain star. Or
it's in direction 235 degrees from that star.
    The directional angles are the same as on Earth. North is zero;
east, 90 degrees; and so on.
    Be careful! North is NOT toward the horizon in the north!! It is
ALWAYS toward Polaris, which is about 1/2 way up in the Earth's north.
You can check this by aligning a chart with the coord grid on it with
the stars and seeing where north is; it will in general not be where
you think it should be.
    West is in the direction the diurnal motion carries the stars. It
is NOT toward the west point on the horizon!! Again check this with a
gridded map against the stars. 
    Note that on the sky 'east' and 'west' are seemingly flipped
relative to a map of the Earth. The US east coast is on the right side
of an Earth map. The east coast of Cygnus in the sky is toward the
left on a starchart
    Use horizontal directions, like 'above' and 'left of' ONLY for
casual discourse. Be SURE to understand that these instructions are
valid ONLY for the peculiar date, hour, and latitude of the instant.
The Moon
    Assume the Moon is in the south, like a first quarter near sunset.
As you look at it, north is to the top and west is to the right. At
first quarter the right side of the Moon is lighted by the Sun. This
is the west side. In this situation you are considering the Moon as a
disc pasted on the sky so directions in it are those of a compass rose 
centered on it. This scheme of directions is the ASTRONOMICAL system. 
    If you think of the Moon as a globe or world, then on that globe
west is on the left. Imagine momentarily that the skin of the Earth is
transplanted onto the Moon so you see the US on the Moon. The west
coast of the US is indeed on the left. This system is the
ASTRONAUTICAL scheme and is used in space explorations.
    A similar argument applies to the Sun or any planet presenting a
globe to your sight (even a telescopic one). You should be careful to
note which scheme you're using!
Orientation or field rotation
    As the celestial sphere rotates above us any section of it, like
constellation, may be tilted one way or an other. The constellations
do NOT always stand in their portrait orientations. You have to tilt
your atlas chart to line up the stars on it with those in the sky.
    You must point north of the chart to north in the sky. For a
section in the south, north is up. Those in the west have north to
their upper right; the portrait chart has to tilted clockwise about
1/8 turn.
    Constellations in the east have north to their upper left. Tilt
the chart counterclockwise about 1/8 turn.
    Constellations in the north, for New York, pose a special problem. You
must tilt the chart so its north points to Polaris and NOT the north point
on the horizon. Stars 'under' Polaris have the chart more or less upright
with north at the top. Those 'above' Polaris have the chart turned end for
end with north at the bottom.
    Stars to the left of Polaris have the chart's north to the right
And those on the right of Polaris have chart north pointing left.
Inverted field
    Most binoculars and monoculars leave the orientation of the field
alone. What's on top in the sky is on top in the instrument. Except
for enlargement and amplification, you can directly match star for star
the instrument's field with the sky.
    Most astronomy telescopes INVERT the field. The view is rotated so
many degrees relative to the part of the sky aimed at. The angle of
rotation differs with the optical path inside the telescope, the tilt of
the eyepiece on the side or back of the tube, and the placement of your
eye against the eyepiece. That is, you may stand on one side or the other
of the telescope and thusly work an extra rotation of the field as
compared to the sky.
    Note well that an inverted field does NOT automagicly have south
at the top! Until a couple years ago it would be a miraculous
instrument which can always make south be at the top of the field!
Today with electronic field manipulation you can always have south --
or north! -- at the top of your field.
    To match up an atlas chart with the telescope view you must turn
it round in its own plane but NOT flip over on its back. It really
helps if the chart is drawn to a scale similar to that of your
telescope, like an eyepiece impression of a star cluster.
Flipped field
    Some telescopes in addition to rotating the field, flip or mirror
it. In this case you must flip the chart over and view it thru its
back. A flashlight or lighttable will be handy here. You can tell if
the field ia flipped if NO rotation of the atlas chart brings the 
field into alignment with it. Be SURE you are in fact positively 
identifying the stars within the field. 
    There is an easy way to tell if your instrument does a flip of the 
field. Count the number of reflections in the optical path from the 
entrance of the starlight into the instrument to its exit thru the
eyepiece. You may have to study the cutaway or optical layout diagram in
the instruction book. Be sure to include the mirrors in attachments,
usually a diagonal.
    If the count is EVEN, and zero is for this purpose an even number,
there is NO mirror or flip of the field. If the count is ODD, you got
a flipped field.
    A straight-thru refractor (0 reflections) and a Newton reflector
(2 reflections) have NO flip, only pure rotation. A Schmidt-Cassegrain
with its usual diagonal has three reflections, an odd number, and so
gives a flipped field.
Flipped charts
    Some starchart programs include a 'mirror' or 'flip' function that on
screen and printout makes a flipped field. The lettering is right way
round. If your program can not do this you can send the chart to an 
artist program. Just about every artist program has a 'flip' or 
'mirror' function. However, any lettering on the chart will also be
     A few outfits that distribute charts by mail or website offer a
set of flipped maps. Others will provide them on request.
Exploring sky orientation
    The runaway simplest and fastest way to play with sky orientation
is with the program SkyGlobe. This is a DOS program that runs perfectly
well under all flavors of Windows. It must be in a full-screen panel.
    It is widely distributed as shareware on software websites; do a
search for 'SkyGlobe'. It comes down to you as a zipped file so you do
need PKUNZIP or WinZIP to rehydrate it into executable form. It doesn't
matter whether you get the latest, apparently final, version 3.6 or 
the earlier one, version 3.5.
    SkyGlobe is operated entirely from the keyboard with most of the
common features requiring but a single keypress. There are no menus
or dialog boxes or gadgets to distract you. The code is very tight and
    SkyGlobe presents the naked eye sky. Planets remain symbolic dots
under high zoom and stars are included to only 7th magnitude. The
more showy deepsky objects are marked as symbols and the Milky Way
is a stylized band.
    The display is deeply customizable. You can save up to 10 displays
for later loading with all the custom features preserved. Scene #0 is
the 'home' scene because it loads when SkyGlobe starts. 
    The planet motions are rather accurate over the range of (if I
remember correctly) 5,000 BC to 9,000 AD. You can not add new orbits.
Version 3.6 allow you to load a prepared table of positions so they 
are marked on the sky.