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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 ona 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

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

right ascension).

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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)?

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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:

altitude of NCP = observer's latitudealtitude of SCP = -(observer's latutude)

max. altitude of celestial equator = 90 - (observer's latitude)

Dec. of north horizon = 90 - (observer's latitude)

Dec. of south horizon = -90 + (observer's latitude)

Dec. of zenith = observer's latitude

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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.

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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).

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

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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!"

PhaseSun-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

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Diagram of solar eclipse. Relative scale is correct!

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Star chart version of Hercules.

Antique version of Hercules.

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