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Can I invoke the standard statement which used to be used for freeware ;

You are, of course, welcome to consult and make use of my pages at will. However, if you have found them useful in any appreciable way, please consider sending a small disbursement (even something as small as 1 Euro/Pound/Dollar/etc. would be received with appreciation).

B. Daugherty, 31 MH, Portsmouth PO5 3JG, Britain.

The Celestial Sphere


Celestial Sphere

It is convenient to consider the totally false, but useful, model of a celestial sphere. Under this model, the Earth is at the center of the Universe and all the stars are attached to a sphere which rotates around the Earth. All the stars will remain fixed on this sphere.

Using this model, you can even calculate where the stars are in the daytime sky, although you obviously can't see them, and which stars lie adjacent to the Sun at any one time. The ancients were capable of carrying out these calculations and brought about the dreaded superstition of astrology. Astrological star signs are intended to indicate which constellation the Sun is in at a particular time. You would be able to see in which constellation the Sun is if an eclipse occured, but our model allows us to accurately calculate the position by extrapolation from what we see in the Night Sky.

The Sun, Moon and planets will move across the Sky on any one night (or day) because they are attached to the Celestial Sphere.

Knowing the motion of the Sun across the sky during the day will tell you how the stars and other objects will appear to move across the Night Sky. The Sun moves from East to West (Australia is always ahead of us, timewise, and America is behind us. The stars and other objects will likewise move from East to West during the night.

Due to the way that the planets are arranged roughly in a plane in the Solar System, they will appear in the sky within roughly the same region of the sky that you can view the Sun - obviously at different times of the day, but along an arc to the South, anyway.

The Moon is also roughly found in the same position of the Sky as the Sun and the planets. This is pure coincidence and leads to solar eclipses, which are likewise pure coincidences due to a temporary similarity in the apparent size of the Sun and Moon in the sky.

It is noted that as time goes by, the Sun, Moon and planets move their position on the Celestial Sphere (in this respect, they are definitely different to the stars which stay absolutely fixed).

The Sun will actually move in a fairly steady way across the sphere, at a rate of about 1 degree per day. Given that after one year it will be back at the same position on the sphere, you can work this out for yourself : given that

one year = 365 days and there are 360 degrees in a full circle.

The path that the Sun takes across the Celestial Sphere is called the ecliptic.

The Moon will move right round the celestial sphere in about a month, i.e. about 15° in 24 hours.

Under the Celestial Sphere model, the planets will appear to move along the Celestial Sphere in a strange manner, sometimes reversing their direction with respect to the Celestial Sphere.

Just to emphasize what I am saying here : I do not mean reversing their motion as seen by us. The Celestial Sphere and all objects on it will rotate across the sky in the same direction during any one night or day, i.e. from east to west. However, movement on the Celestial Sphere will alter the time that we observe this east to west motion. The Moon, for example, progresses across the Celestial Sphere in the same direction during the course of a month causing it to rise later and later each day. The planets, on the other hand, will behave differently from the Moon - they might rise later and later for a particular period, and then started rising earlier and earlier, before resuming its 'later and later' behavior, and so on.

Polaris (the North Star) lies almost at the North Celestial Pole (at this level, we will mostly use the assumption that it is exactly at the Pole, for simplification). In the South, the long axis of Southern Cross points towards nearly due South (and also towards the Magellanic Clouds). The actual Pole Star is Sigma Octantis, which is (just) visible with the naked eye (magnitude 5.5).

Quick Quiz    
  a)   Person A views Sirius due South at 23:30 GMT. Person B sees Sirius due South at 23:36 GMT. Is person B east or west of person A ?

Declination and Right Ascension

On to this Celestial Sphere, we project coordinates which are just a projection of our own latitude and longitude.

The projection of latitude onto the Celestial Sphere is known as Declination, with O° called the Celestial Equator and 90° the Celestial Pole(s). Unless we are at our North or South Pole, the Celestial Pole will not be overhead, and we will be able to see below the Celestial Equator if we look in a particular direction (i.e. Southern direction for Northern Hemisphere and vice-versa). When I say 'see' I also mean this to cover the daytime sky Northern Declination is classified as a positive value, e.g. +30° whereas Southern Declination is stated with a negative sign, e.g. -30°.

The analogy of longtitude is called Right Ascension.

And by analogy with longitude, we need to define a point as the 'zero' of Right Ascension. The Greenwich Meridian was defined as the zero of longitude for arbitrary reasons. The 'zero' of Right Ascension is a bit more logical. The First Point of Aries is relevant here - this is the position occupied by the Sun at the time of the spring (vernal) equinox (around March 21), when it will lie on the Celestial Equator.

A line from one celestial pole thru this First Point of Aries to the other celestial pole will define the 'zero' of Right Ascension.

In a like manner, the position of the Sun on the Autumnal Equinox is known as the First Point of Libra, but this is now in Virgo..

Whereas longitude is divided into 360 degrees, Right Ascension is normally denoted in two ways

  • as hours and minutes : these hours increasing as you move along the Celestial Sphere in an easterly direction, from 0 to 24. Each hour is divided into 60 minutes. You can see that hours of Right Ascension are directly related to hours of time, e.g. objects at 3 hours Right Ascension will be seen overhead three hours later than they are viewed overhead at Greenwich.

  • degrees Whereas longitude is given as so many degrees East or West of Greenwich, Right Ascension will be stated as between 0 and 360 measured in an easterly direction.

When we need to, we can use simple arithmetic to find the conversion

1 hour of Right Ascension corresponds to 15°

1° corresponds to 4 minutes of Right Ascension

We need to point out that the use of degrees is related to the angle subtended around the central axis of the Earth, and will only have 'mathematical' relevance w.r.t. viewing objects in the sky itself when the objects are near the Equator (think of the way that lines of longitude converge towards each other as we move away from the Equator).

Quick Quiz    
  a)   Observer A sees a star due South at 19:40 GMT. Observer B sees the same star due South at 19:46 GMT. By how many degrees of longitude do they differ ?  
b)    c)     d)    e)   

Quick Quiz    
  a)   Observer A is 0.5 ° west of Observer B. What is the time lapse between both Observers viewing the same star due South, and which Observer sees the star due South first ?  

b)  An observer at Greenwich sees Sirius due South at 02:58 GMT on December 4th. A second observer is viewing the sky from a longitude of 2.5° W. At what time would this second observer view Sirius when it was due South on December 4th. ?   c)     d)    e)   

Range of Sky Visible

The altitude of Polaris, i.e. its height above the horizon in degrees will be equal to the degrees of latitude from which it is viewed. At the equator, it will be on the horizon, at the North Pole it will be directly overhead, and from Portsmouth (at say 50°) it will be 50° above the horizon. Determination of longitude might have been a major problem for mariners, but not latitude.

On the above diagram above, some people wonder why the Celestial Equator line does not go thru the center of the circle. There are two ways of looking at this

  • You could consider that the Celestial Equator line should really go through the center but it has been translated to its current position to make all the relevant angles clearer
  • Or, similar to the way that light rays from the Sun are considered to be parallel anywhere on Earth because the Sun is so far away, then lines representing the Celestial Sphere on the above diagram could be considered to be parallel anywhere across the circle.

Circumpolar stars are those stars which are in the sky all year round. From a given latitude, circumpolar stars will have a declination of magnitude greater than the colatitude, which is defined as

90 - latitude

For example, from Portsmouth, all stars with a magnitude of declination greater than

90 - 50 = 40°

will be circumpolar, i.e all stars with a declination in the range

+40° to +90°

On the other hand, there are stars which will never be seen from a particular latitude (excluding an observer on the Equator). From a given latitude, you can at some time of the year view stars which have a declination of

90 - latitude

below the celestial equator.

For example, from Portsmouth, we will be able to view stars as far as

90 - 50 = 40°

below the Celestial Equator, i.e all stars with a declination in the range

40° to - 40°

will be seen at some time in the year, but will not be in the sky all year round.

From Portsmouth, we will be unable to see the most southerly stars, with a declination of between -40° and -90°.

Quick Quiz

a)   Would a star of declination +30 degrees be circumpolar from a latitude of 57 degrees North ? ?  

b)  At 57 degrees North, a star just skims the observer's northern horizon. What is the declination of this star ?  

c)   Would a star at +14 ° be circumpolar from Resolute in Canada at a latitude of 75° ?

d)    e)   


The Sun moves in an easterly direction along the Celestial Sphere, at a rate of approximately one degree a day. Its path on the Celestial Sphere is called the ecliptic.

The Sun takes one year to move along the ecliptic before coming back to where it started. Since this corresponds to 360 °, and since there are 365 days in a year, you can see that this approximates to about 1° a day.

As it moves along the ecliptic, the Sun's declination will also vary between +23.5° and -23.5°.

It is at its highest declination (+23.5°) on about 22 June - Midsummer's Day in the Northern Hemisphere, when we have the maximum amount of daylight. It is at its lowest declination around 22 December, when we have the least number of hours of daylight in the year. Since the amount of daylight begins to increase from then onwards, Christmas is appropriately place as a midwinter festival, just when things are 'improving'. Both June 22 and December 22 are referred to as solstices, although in popular non-astronomical usage, this word is used primarily for the winter date.

When the Sun is placed on the Celestial Equator, as it is twice a year, we have the equinoxes, - when everywhere on Earth will have 12 hours of daylight and 12 hours of nighttime in a full day (apart from the poles). The sun will rise at 06:00 local solar time and set at 18:00 local solar time. This event occurs on, or about, 21 March (vernal equinox) and 22 September (autumnal equinox) - these given names are obviously only valid for the Northern hemisphere. The altitude of the noon Sun will be equal to the colatitude. Incidentally, at the poles, the Sun will circle the horizon for the entire 24 hours.

This variation in declination is caused by the inclination of Earth's axis (i.e. it is inclined at the angle of 23.5°). It is this inclination that causes the seasons. As mentioned in Kepler's Laws, the seasons are not caused by the Earth's varying distance from the Sun.

Referring to the dreaded topic of astrology for a moment, it is worth mentioned that the zodiac is the set of constellations thru which the Sun moves during its motion along the ecliptic. A star sign of 'Taurus' for example is intended to indicate that the Sun is actually in the constellation of Taurus during this particular period. Although you can't see the constellations in the daytime, you can work this information out from the stars that are viewed during the night time coupled with knowledge of the behavior of the Celestial Sphere.

This is knowledge that the ancients possessed and thus allowed them to invent astrology. Unfortunately, the Earth has precessed since their time (just like the axis of a spinning top will move) so that the ecliptic is no longer exactly aligned as it once was with respect to the background stars.

As already stated, the point at which the Sun lies on the Celestial Equator during spring is known as thr First Point of Aries, but nowadays it actually lies in Pisces. About 10 000 years ago, it lay in Taurus (at a time when the bull was a major religious object), it passed into Aries just when sheep and lambs became religious symbols, and then into Pisces as fish became religious symbols ('fishers of men' etc.). It is moving towards the constellation of Aquarius - the 'Age of Aquarius' for those who are old enough to know what I am talking about. Whatever the truth, or not, of the religious associations I have just mentioned, they provide a good way of remembering the sequence of these particular constellations in the sky.

Originally, at the solstices the Sun was in Cancer in the Northern Summer Day and in Capricorn during the Northern Winter, thus the names Tropic of Cancer and Tropic of Capricorn. And during the autumnal equinox, the Sun was in Libra, which is a possible reason which it is identified with a balance scales.

Although the zodiac has 'moved' since the time astrology was invented, the signs are only out by about one month, so this knowledge can still be useful to the extent of telling a 'beginner' which constellations are likely to be seen at a particular time of the year. For example, 'Taurus' is a spring star sign -despite the shift in the zodiac it will still be hidden by the daytime sky during, generally speaking, summertime. Therefore we expect it to be prominent in the Night Sky during winter. Likewise Winter star signs like Aquarius are visible in the Night Sky during Summer, but they will be low down - we know they are low down because when the Sun is in Aquarius, in Winter, we know from experience that the Sun is low down at this time of the year.


The zenith is the point directly overhead for a particular observer. At a given latitude, a star can be seen overhead if it has a declination of a magnitude equal to the said latitude.

The zenith is at 90° if you were to use altazimuth coordinates. Under this system the two coordinates are

  • Altitude or Elevation   the angle above the observer's horizon

  • Azimuth   the angle between North and the point on the horizon below the object, measured clockwise.

From Britain, Vega is almost overhead during the Summer and Capella is overhead during the Winter. While one is overhead, the other will be near the horizon (they are both about the same distance from Polaris).


The Meridian is the line of Right Ascension thru the Celestial Pole, the Zenith and onwards. When an object is on the meridian (i.e. your meridian), it is at it highest point in the sky - from your viewing position. The technical term is - it culminates.

Sidereal and Synodical Periods

Sidereal Period the rotational or revolutionary period with respect to the Stars. This period is not the one which is immediately detected by us, we tend to rely on the synodical period.

Synodical Period   the period of a particular body, as perceived by us, in simple terms. For a more scientific definition : a synodic period is the amount of time between similar arrangements of the Earth, Sun and a third body.

Solar Day   The synodical period of rotation, i.e. the solar day, is 24 hours long, whereas the sidereal day is about 4 minutes less. The solar day is longer because the Earth has to rotate just a bit longer to align the Sun up in the sky, due to its own revolution around the Sun. Because of this difference between the solar day and the sidereal day, the stars appear to us to rise 4 minutes earlier each day and our view of the Celestial Sphere varies during a year.

Quick Quiz

a)   An observer observes Sirius due South at 02:58 GMT on December 4th. At what time would the observer observe Sirius to be due South on December 6th. ? ?  



d)    e)   


The Earth's axis will circle over a period of 26,000 years, in the same way that a spinning top leaning at an angle can have its axis of rotation circle. This is precession.

At the time of the ancient Egyptian civilization, the Pole Star was Thuban in Draco. It came closest to the pole in 2830 BC when it was 10' away.

Polaris is currently about one degree from the Celestial Pole and by 2100 it will have moved to about half a degree distant from it, after which it will move away again. Polaris first became a 'useful' pole star around 1400s, just at the right time for European voyages of discovery.

Some Pole Stars of the future:

  • 4000 AD : Γ Cephei
  • 10,000 AD : Deneb
  • 14,000 AD : Vega (with South Pole Star being Canopus
  • 26,000 AD : Polaris


Its origins have already been mentioned under ecliptic.

It should be mentioned that Scorpius is referred to as Scorpio in astrology.

Crab Nebula

Big Red Spot on Jupiter