## Observing Fundamentals

Here you will find explanations of the terms used elsewhere

### Angles

Angles are used to measure the difference in two directions, or apparent distances on the celestial sphere. The usual unit is the degree, 1/360 of a circle. 90° is a right angle. Angles may also be measured in time units, with 24 hours to 360°, or 1 hour = 15° Degrees and hours may be divided either decimally, or sexagesimally, into minutes and seconds. Angles are also measured in radians, which is the ratio of the length of circumference divided by the radius. 2π radians is a complete circle, and 1 rad = 57.3°, approximately.

The angle subtended by parts of the hand may be used to estimate angles. The distance between my eye and hand with my arm extended is about 21 inches. The width of my palm, 3.5 inches, subtends an angle of about 10°. Each finger then subtends 2.5°, and my span, end of thumb to end of index finger, 20° Since people have about the same proportions, these angles will be about the same for everyone. This will be sufficient to estimate angular distances without other aid.

Angular distances are surprisingly difficult to estimate without mechanical aid, because of perceptual distortions related to the Horizon Illusion. The same angle can appear much larger near the horizon than near the zenith.

### Motions

The view into the night sky extends to infinity, the rotation of the earth towards the east causes the sky to revolve once per day, and the motion of the earth in its orbit changes the stellar background of the sun. These real appearances seem to the observer, imagining himself stationary, as the apparent motions in terms of which it is customary to describe astronomical phenomena. The celestial sphere is imagined as the inside of a globe, which rotates once per day from east to west, while the sun moves eastward on the sphere, completing a revolution in one year. Apparent phenomena are described much more easily on this latter basis, without affecting our knowledge of the true relations.

The stars remain fixed. The sun, moon and planets move, generally eastward, in a band on either side of the ecliptic, or path of the sun, called the zodiac ("circle of animals") divided into twelve equal constellations of 30° each; these are not the same as the actual groupings of stars or areas of the celestial sphere, and are used only in visual astronomy as a convenience. The normal eastward motion is called direct, the occasional westward motion of the outer planets retrograde, which is only a result of the faster movement of the earth in its orbit overtaking these planets when they are opposite to the sun. The moon moves fastest of all, completing its journey in 29.5 days. The sun requires 365.25 days.

### Observer's Reference Frame

Imagine yourself standing facing south. East is at your left hand, West your right, and North behind you. These cardinal points should be known to you before you begin observing. North can be accurately determined by the direction of Polaris at night. The identification of Polaris should be your first goal. The meridian is a straight line on the celestial sphere (a great circle) from the South point, through your zenith, through the North Celestial Pole (NCP) near Polaris, to the North point. The directions East and West are used to describe the directions counter to and with the diurnal motion of the celestial sphere from East to West.

Altitude (a) is the angle from the horizon vertically up to a point on the celestial sphere on a vertical circle. 0° is on the horizon, 90° is at the zenith, directly overhead. Azimuth (Z) is the angle measured clockwise from North to the foot of the vertical circle through the point. 0° is North, 90° is East, 180° is South, and 270° is West. Sometimes, azimuths are measured from South instead of from North. The reference should always be stated, but assume it is from North if there is no reason to assume otherwise.

Altitude and azimuth are the altazimuth coordinates or the observer's reference frame. They can be used to specify precisely the direction in which to look.

The altitude of the NCP is equal to the observer's latitude, and its azimuth is 0° If you are south of the equator, the NCP is at a negative altitude, and the South Celestial Pole (SCP) is at your latitude south. The celestial sphere rotates about an axis through the NCP and the SCP.

The estimation of altitudes above the horizon is affected by illusions related to the Horizon Illusion. Without training, such estimates may be seriously in error.

### Celestial Reference Frame

The location of points on the celestial sphere can be specifed by angular coordinates called right ascension (α) and declination (β). Unlike the altitude and azimuth, these do not change for a fixed point on the celestial sphere, such as a star. Right ascension is like longitude, and declination like latitude, on the earth, and are measured analogously. The reference point is called the Vernal Equinox, which is located on the equator, a great circle 90° from the poles. The equator crosses the meridian at an altitude equal to 90° minus your latitude. The ecliptic crosses the equator from below to above at the Vernal Equinox, moving towards the East. Right Ascension is measured in hours in the same direction, from 0 to 24 hours. It is the time in hours that a body rises after the Vernal Equinox.

The Vernal Equinox makes one complete revolution in the sky in about four minutes less than one day. As the days pass, everything happens four minutes earlier per day, and new stars appear in the East and disappear in the West at the same times each evening. This is, of course, due to the steady eastward motion of the sun on the celestial sphere. The angle of the Vernal Equinox from the midnight point is called the Celestial Time. At 12 hours celestial time, the Vernal Equinox is on your meridian. Obviously, if you know where the Vernal Equinox is, you can figure out where everything else is.

This celestial reference frame is called equatorial coordinates, and is unaffected by the rapid durnal motion.

### Angular Distance Between Points

The angular distance between two points on the celestial sphere is easy to find if the coordinates of the points are known. The right ascension α and the declination δ are nearly constant for stars. These coordinates can be found in star lists, or approximate values can be scaled from charts. The coordinates of the sun, moon and planets change with time, but can be found from the Astronomical Almanac. The same method of finding the distance can also use altitude and azimuth, but these coordinates change fastest of all. Let us suppose that we know the right ascension and declination, or analogous coordinates, for the two points under consideration.

First, change the coordinates to decimal degrees. Remember that 1 hour of right ascension is equivalent to 15°. We need the declinations of the two points, positive or negative, δ1 and δ2, and the difference in right ascensions (α1 - α2). All calculations, including the conversion to degrees, should be done with a scientific calculator. Many calculators offer shortcuts in the conversion from degress, minutes and seconds to decimal degrees.

Now evaluate the expression sin δ1 sin δ2 + cos δ1 cos δ2 cos (α1 - α2). The inverse cosine of this value is the distance between the two points. If one of the declinations is negative, the first term will also be negative; take care with this. The cosine of the difference in right ascensions is usually positive, but can be negative if the right ascensions differ by more than 6h, for example. The product of the cosines of the declinations is always positive. Where the two points are close together, there will be no trouble, but the method will work in any case if signs are properly handled. The formula can be derived by taking the dot product of unit vectors in the directions of the points.

This method can be adapted to find the approximate great-circle distances on the earth from longitudes and latitudes by multiplying the angle in radians by the mean radius of the earth, about 6380 km or 3980 mi.

### Linear Distances

In observational astronomy, only angular distances on the celestial sphere are observed. The actual linear distances to stars and other objects can be found only by careful study and analysis, beginning with the parallactic displacement of an object with respect to more distant objects, which was only observed in the 19th century after a long search. Now there are methods of estimating great distances, and the overwhelming size of the universe is clearly revealed. For these methods, refer to a text on astronomy. The light year, ly, is the distance travelled by a light impulse in a year, about 9.46 x 1015 metres (63,000 times the distance to the sun). A more professional unit is the parsec, the distance at which the annual parallactic displacement is 1 second of arc, or 3.26 ly. The nearest star is 4.3 ly away. Deneb in Cygnus is 1800 ly distant, and the closest spiral galaxy, the Andromeda galaxy, is some 200,000 ly away. The universe is sufficiently large that any life elsewhere is safe from human interference.

### Magnitudes

Stars are point sources of light. No amount of magnification makes them anything but points. Sun and moon exhibit discs apparent to the eye; the planets also show discs when magnified. The total amount of visible light from a celestial body is specified by its magnitude number. The lower the number, the brighter the object. Stars were originally qualtitatively classified from first to sixth magnitude, from the brightest to those just visible. Now that brightness is quantitatively specified, the range goes from less than one up to larger numbers for the dimmest stars that can be seen with any sort of aid. Stars visible without aid still range from about 0 magnitude to 6th magnitude.

The five steps from magnitudes 1 to 6 are conventionally taken as steps of equal ratios of brightness, with an overall ratio of 1 to 100. Hence, each magnitude is a factor of the fifth root of 100, or 2.51.

The faintest star that can be seen depends on the background brightness of the sky. In a city, under clear conditions, stars to the 3rd magnitude only are easily visible without aid.

There are no more than two dozen stars of magnitude 1.5 and brighter, and it is very useful to be able to recognize the bright stars visible from your latitude, which will serve as major landmarks. The five naked-eye planets, Mercury, Venus, Mars, Jupiter and Saturn, are all brighter than most stars, though the brightnesses of Mars and Mercury can vary greatly. Venus is magnitude -4, Jupiter -2. Mercury and Venus are seen only near the sun at twilight and dawn, Mars is noticeably red, and all three superior planets can appear opposite the sun. All planets move only in the zodiac, which is another key to identification.

Remember that the larger the magnitude number, the less bright the object. Small magnitudes correspond to bright objects. Sirius, magnitude -1.5, is the brightest star (other than the sun). The apparent brightness of a star depends not only on its actual brightness, but also on its distance from us. The brightness decreases as the square of the distance. Most bright stars are bright because they are close, not because they are intrinsically brighter. The absolute magnitude of a star is its magnitude when seen at a distance of 9.46 x 1016 metres, or 32.6 light years. The absolute magnitude of the sun is about 4.83, of Sirius 1.42, and of Deneb -7.5. The distance in light years is 32.6 x 10(M - m)/5.024, if M and m are the absolute and apparent magnitudes. For Deneb, m = 1.25, so it is 1800 ly away.

### Other Objects

Sun and moon, stars and planets are the familiar occupants of the sky. The Great Nebula in Andromeda is an external galaxy. It appears as a hazy oblong patch visible only against a dark sky or in binoculars, and does not move on the celestial sphere. Comets are rare visitors that appear in strange places and move strangely. They usually appear as hazy circular patches, ghostly against a black sky. Sometimes they are bright enough to be seen without aid, and develop tails of debris. Meteors are phenomena of the earth's atmosphere, tiny specks vaporized and heated to incandescence by air friction making brief streaks across the sky. The skies are so constant than any change is remarkable. Events other than those mentioned are extremely rare.

Binoculars reveal star clusters, both distant globular clusters and nearer open clusters like the Pleiades and Hyades, as well as double stars and the surface of the moon. Small telescopes reveal essentially the same thing, but higher magnification can show a little planetary detail such as the rings of Saturn, and closer double stars. Most of the astronomical pictures seen in popular publications were taken with very large telescopes at very high magnifications using long photographic exposures and computer-enhanced imagery. Nebulosity, in particular, is very difficult to see with the eye because its surface brightness is low.

### Colors

Casually observed, practically all celestial bodies shine with white light. However, there are faint tints that are the more remarkable for their rareness. In Orion, Betelgeuse and Rigel are quite different. Betelgeuse is golden, Rigel is brilliant bluish-white. Aldebaran is yellow, Antares is red. The different colors of Jupiter, Saturn and Mars can be distinguished. When one says Antares is red, do not expect something like a traffic light--these are subtle distinctions, and all the more interesting for that. In the dark, the color sensitivity of the eye changes as well, and this affects what is seen.

The brightly colored scenes seen on the Internet and books of deep space objects do not show real colors, but enhanced artificial colors that distinguish the different qualities of the radiation more clearly. Most of the objects are very difficult to see even in a large telescope, and have to be captured with long exposures. They would not look this way to an unaided eye closer to them, since many are very faint.

### Sources of Information

1. Ian Ridpath, ed., Norton's 2000.0 Star Atlas and Reference Handbook, 18th ed. (New York: John Wiley and Sons, 1989)
2. J. B. Sidgwick, Observational Astronomy for Amateurs, 3rd. ed. (New York: Dover, 1980)
3. Robert Burnham, Jr., Burnham's Celestial Handbook, revised ed. in 3 vols. (New York: Dover, 1978)
4. The Astronomical Almanac for the Year 2001, (Washington: U.S.G.P.O., 2000)
5. P. K. Seidelmann, ed., Explanatory Supplement to the Astronomical Almanac (Mill Valley, CA: University Science Books, 1992)
6. R. N. Mayall and M. W. Mayall, eds., Olcott's Field Book of the Skies, 4th ed. (New York: G. P. Putnam's, 1954)
7. R. H. Allen, Star Names, Their Lore and Meaning (New York: Dover, 1963, republ. of 1895 edition)
8. Spirit Level Sensitivity