Introductory Astronomy: 

The Celestial Sphere

Motions Visible Without Optical Aid


Daily Motion Long-term Motion
Sun E to W in about 12 hours from sunrise to sunset. Length of day varies from season to season and with latitude. W to E along the ecliptic 1 degree per day. The height of the sun in the sky at noon is at maximum in the summer, minimum in winter (excludes tropical regions). The sun returns to the same constellation in 1-year intervals.
Moon E to W in about 12 hours, 25 minutes from moonrise to moonset. Moonrise is about 50 minutes later each day. Like the sun, this timing is modulated by the season and your latitude on Earth. W to E within 5 degrees of the ecliptic. It takes 27.3 days to travel 360 degrees with respect to the stars, but phases repeat on a 29.5-day cycle.
Planets E to W in about 12 from rising to setting (again modulated by season and latitude). Additional, very small variations are caused by the planets's own motions against the background stars. W to E within 7 degrees of the ecliptic. The average speed varies according to planet. It is fastest for Mercury and slowest for Saturn (slower for Uranus, Neptune, Pluto but we can't see them with our eyes). All the planets have periods where they go retrograde (E to W) with timing different for each planet.
Stars E to W in about 12 hours (modulated by season, by latitude, and by where the star is on the sky: circumpolar stars, for instance, do not rise and set, but they will travel in a circle around the pole, 180 degrees in 12 hours minus about 4 minutes.) Star rise is about 4 minutes (3m 56s) earlier each day. The stars remain fixed on the celestial sphere with respect to themselves. The earth's pole describes a circular wobble of 23.5 degree amplitude centered on a point in the constellation of Draco every 26,000 years (often called "precession of the equinoxes").

Long time exposures taken at night illustrate daily motion:
South Pole Star Trails 1 | South Pole Star Trails 2 | North Pole Star Trails

The Celestial Sphere


The red "Ecliptic" is the sun's path. The sun is at the vernal equinox around March 21 and travels eastward (increasing right ascension).

Just the celestial sphere plus the ecliptic, with solstices and equinoxes marked.


Drawn for northern latitudes, these are the paths the sun takes across the sky on the equinoxes and solstices. Can you see that the summer path is longer (and therefore that the summer sun stays in the sky longer)?

This figure illustrates that, depending on your latitude, some stars will be "circumpolar" and will never set. Remember: your latitude = the altitude of the north celestial pole.

Examples relating observer's coordinates (altitude) with celestial coordinates (declination) for various latitudes on earth. We consider only maximum altitudes, i.e., points on the meridian.
Observer's Latitude Altitude of North Celestial Pole (Az.=0) Altitude of South Celestial Pole (Az.=180) Altitude of Celestial Equator (Az.= 0 or 180) Declination of North horizon Declination of South horizon Declination of Zenith
0 (Ecuador) 0 0 90 90 -90 0
30 (Caribbean) 30 -30 60 (Az. 180) 60 (i.e. 30 degrees beyond 90) -60 30
60 (Canada) 60 -60 30 (Az. 180) 30 -30 60
90 (North Pole) 90 -90 0 (i.e. the horizon equals the celestial equator) 0 0 90

Formulae that seem obvious from looking at the table above:

This works south of the equator also, but you have to switch all of the "norths" with the "souths". The final point to make about this is that these latitude/declination/altitude correspondences are always true, but that longitude/right ascension correspondences depend on the hour of the day and also the season.

A bit more on seasons


From "New Physical Geography" 1917 edition (copyrighted 1903) by R. S. Tarr. The Macmillan Co. Note that the numbering of the seasons should be reversed if we align with a northern hemisphere bias.

These two figures are supposed to illustrate the same thing: the constant 23.5 degree tilt of the earth. Conceptual danger: these are perspective-foreshortened drawings; the actual orbit of the earth is a near-perfect circle; its distance from the sun varies by a very tiny amount (1.7 percent from the average). Also, the numbers 2 and 4 should be swapped on the cherries in the barrel for northern hemisphere observers (but perfectly correct if you view the solar system so that south is up) [Thanks for pointing that out, James King]. The north pole leans toward the constellation Gemini.

Table of Sun's path along the ecliptic:
Approx. Date Label Sun's Right Ascension Sun's Declination
March 21 Vernal Equinox 0 hours 0 degrees
June 21 Summer Solstice 6 hours +23.5 degrees
Sept 21 Fall Equinox 12 hours 0 degrees
Dec 21 Winter Solstice 18 hours -23.5 degrees

Moon Phases


This is the standard everything-on-one-figure textbook diagram. It's a great summary figure after you have understood moon phases and timing. The view is from the north, looking down for the bottom half of the figure, but the view is from earth for the top row of moons. Diagram is not to scale.

Moon phase information. Can you see how this tabulated information comes from the figure above? Handy phrase for distinguishing whether a moon is waxing or waning (works only in the northern hemisphere): "If the light's on the right, the moon is getting bright!"
Phase Sun-earth-moon angle (degrees) Approx. time that moon crosses your meridian Less 6 hr = rise time Plus 6 hr = set time
New 0 or 360 noon 6 a.m. 6 p.m.
First Quarter 90 6 p.m. noon midnight
Full 180 midnight 6 p.m. 6 a.m.
Third Quarter 270 6 a.m. midnight noon

Shadows and rays of light travel in absolutely straight lines. 1 | 2.

The finite angular size of the sun fuzzes out the shadow somewhat, giving rise to dense shadow (umbra) and incomplete shadow (penumbra) regions of space behind the eclipsing object:

If the sun was a pointlike object, this fuzzing would not occur. The above diagram is (blatantly) not to scale.


Diagram of solar eclipse. Relative scale is correct!


Diagram of lunar eclipse. Relative scale is correct!

2017 eclipse path visualization.

Note that eclipses don't happen every month because the moon's orbit is tilted 5 degrees out of the earth-sun plane. So we really only get eclipse seasons twice a year (when the sun is on the "line of nodes" in the diagram below).

Constellations

All 88 Constellation boundaries. | Constellation map, winter sky | Constellation map, summer sky | Constellation map, north polar region

Star chart version of Hercules.

Antique version of Hercules.