p The Sky, Stars, and Celestial Sphere
The Sky, Stars, Magnitudes, Celestial Sphere

Much of our initial discussion of Astronomy will concern the motion of objects in the sky. Therefore, we shall introduce some terminology and a coordinate system that allow us to specify succinctly the location of particular objects in the heavens.

The Sky and Stars

We look up through an atmosphere 100km deep. Space is nearly empty beyond that, Stars are many light years apart.

CONSTELLATIONS--term originally used to define groups of stars in the sky often named after mythical creatures by the ancients.

Many of the constellations in books of today were named in Mesopotamia over 5000 years ago.

Constellation we know as Orion was known as Al Jabbar (the giant). (...yes, think NBA's lifetime scoring leader).

Originally these were loose groups of stars and not always precisely defined. (Member stars could be part of different constellations)

There are now 88 official IAU constellations, but they now represent regions of the sky

ASTERISMS--smaller groupings within constellations (e.g. Big Dipper, in Ursa Major (the great bear))

2-D projection of 3-D distribution: often the stars have nothing to do with each other gravitationally, they just appear close together when projected on the sky.

Constellation names are mostly Greek, but star names are mostly Arabic. Naming stars is not useful, as there are too many. System is to name the constellation and the order by brightness with Greek letter : e.g. Alpha Scorpii, which represents the brightest star in Scorpii. Beta Scorpii the second brightest etc. But to do real science we need a quantitative system of measurement. One commonly used scale is called the magnitude scale.

Magnitude and Brightness of Stars

Hipparchus (160-127 BC) classified stars in terms of magnitudes and amazingly we still use a version of this today.

Brightest stars as we see them get a higher magnitude rank (like a tennis ranking). The brightest stars get the lowest numbers.

Magnitude scale has negative numbers for the very brightest stars. The sun is -26, since it is so bright as compared to Sirius which is -1.46. Faintest stars that we can see with powerful telescopes are about 28th magnitude.

These are the apparent visual magnitudes in that they describe what we see. They depend on the location of the star as well as the star type. A more distant star of the same type as the sun will be fainter.

Quantitatively we define the intensity as the light energy from a star to hit one square meter in 1 second (per solid angle).

The magnitude system is such that if 2 stars differ by 1 magnitude, their intensity ratio is 2.5.

If they differ by 2 magnitudes, their intensity ratio is 2.5 x 2.5. Etc.

The simple formula is then

I1/I2= 2.5^(m2-m1)

We can then convert the intensity ratio to the magnitude difference (using a calculator).

The one advantage of this system is that it compresses a large range of intensities in small range of magnitudes. For example: 25 magnitudes is a factor of 10^9 in intensity.

Note further that the the inverse of this relation is straightforward to derive. Take the base 10 logarithm, of both sides and we have

Log (I1 / I2) = (m2-m1) Log (2.5)

using the property that Log x^n = n Log x. Noting that Log (2.5) = 0.4, we have

2.5 Log (I1 / I2) = (m2-m1).

This allows us to get the magnitude, given the brightness ratio.

  • Note that the apparent magnitude limit of our eye is about 6. Thus we cannot see objects with apparent magnitudes greater than 6.

    The Celestial Sphere

    Imagine objects to be attached to a sphere surrounding the earth. This construction is called the celestial sphere. At any one time we see no more than half of this sphere, but sometimes the imaginary half-sphere over our heads is referred to just as the celestial sphere, without the "half" mentioned. (see adjacent figure).

    The point on the celestial sphere that is directly over our heads at a given time is termed the zenith. The imaginary circle passing through the North and South points on our horizon and through the zenith is termed the celestial meridian. We will introduce additional terminology associated with the celestial sphere later.

    Motion in the Sky

    It is clear after only minimal observation that objects change their position in the sky over a period of time. This motion is conveniently separated into two parts:
    1. The entire sky appears to turn around imaginary points in the northern and southern sky once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours.

      Note that the points on the celestial directly north and south do not move much with the diurnal motion because they are are along the spin axis of the Earth. In fact that is how north and south on the earth are defined--the anti-polar directions along the spin axis. The two anti-podal points which don't move are called the north celestial pole and south celestial pole respectively. The north direction points toward Polaris = north star Pawnee Indian name for Polaris is "star that does not walk around."

      Note that the directions we use every day have astronomical definitions.

    2. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon.

    Actually, all objects are slowly changing their relative positions on the celestial sphere, but for most the motion is so slow that it cannot be detected over time spans comparable to a human lifetime; only the "wanderers" have sufficiently fast motion for this change to be easily visible.

    Celestial Coordinate Systems

    We can define a useful coordinate system for locating objects on the celestial sphere by projecting onto the sky the latitude-longitude coordinate system that we use on the surface of the earth. As illustrated in the adjacent figure, this allows us to define "North and South Celestial Poles" (the imaginary points about which the diurnal motion appears to take place) and a "Celestial Equator".

    The figure illustrates that these imaginary objects are the exact analogs of the corresponding imaginary objects on the surface of the earth. Thus, we shall be able to specify the precise location of things on the celestial sphere by giving the celestial analog of their latitudes and longitudes, or something related to those quantities.

    Angles on the sky

    Just as we have directions of latitude and longitude on the earth, we have similar scales on the sky. Since the celestial sphere does not incorporate the distance of a particular object in its location on the sky, to locate an object we must refer to its angular coordinates.

    Similarly, the distance between objects on the sky can be measured as a projected angular distance with vertex of the angle at our location.

    There are 360 degrees in a circle, and 90 degrees in a right angle. Each degree can be further broken up into 60 arc minutes and each minute can be divided into 60 arc seconds. Thus there are 3600 arc seconds per degree.

    If you view a quarter, from the length of a football field it s1 arc minute (= 1') in diameter, that is, it "subtends" 1 arc minute at this distance or has an angular diameter of 1 arc minute.

    A pencil dot subtends about 1 arc second (1") at the same distance.

    The angular diameter of the moon is 0.5 degrees.

    The angular distance between two objects is defined as the the angular separation of two objects on the sky.


    What We See of the Sky Depends on our Latitude

    Our latitude is the angular distance between the north celestial pole, and the northern direction of the horizon.

    If we were in Australia right now the south celestial pole would be above our horizon, while the north celestial pole would be below.

    If we can see the North star from our location we can always measure our latitude since, to a good approximation the north star is at the north celestial pole. This does not help us in the Southern hemisphere!

    Latitude also determine which constellations we see. north circumpolar constellations never set in the northern hemisphere. The south circumpolar constellations never set in the southern hemisphere.

    Comment: lots of terminology but necessary to fix the language in which we will discuss the motion of bodies. Note differences between 1) terminology, 2) observational classification of what is seen, and 3) conceptual understanding.

    The "Path of the Sun" on the Celestial Sphere

    We distinguish between rotation (or spin) of a body and orbit (or revolution). Rotation is the turning of a body around its own axis. Orbit is the motion of the body around a point located outside the body. The rotation of the earth gives us our days, and the orbit around the sun gives us our yearly seasons. Another important imaginary plane on the celestial sphere is the plane of the "ecliptic" or "Path of the Sun", which is the imaginary path that the Sun follows on the celestial sphere over the course of a year. As the diagram at left indicates, the apparent position of the sun with respect to the background stars (as viewed from Earth) changes continuously as the Earth moves around its orbit, and will return to its starting point when the Earth has made one revolution in its orbit.
    Thus, the Sun traces out a closed path on the celestial sphere once each year. This apparent path of the Sun on the celestial sphere is called the ecliptic. Because the rotation axis of the Earth is tilted by 23.5 degrees with respect to the plane of its orbital motion (which is also called the ecliptic), the path of the Sun on the celestial sphere is a circle tilted by 23.5 degrees with respect to the celestial equator (see diagram at right).

    The ecliptic is important observationally, because the planets, the Sun (by definition), and the Moon are always found near the ecliptic. As we shall see later, this is because all of these objects have orbits that lie nearly in the same spatial plane.

    East and West on the Celestial Sphere

    It is useful to define east and west directions on the celestial sphere, as illustrated in the following figure.

    Thus, objects to the west of the Sun on the celestial sphere precede the Sun in the diurnal motion of the celestial sphere (they "rise" before the Sun and "set" before the Sun). Likewise, objects to the east of the Sun trail the Sun in the diurnal motion (they "rise" after the Sun and "set" after the Sun). Generally, one object is west of another object if it "rises" before the other object over the eastern horizon as the sky appears to turn, and east of the object if it "rises" after the other object.

    The Motion of the Planets on the Celestial Sphere

    Mercury, Venus, Mars, Jupiter, Saturn are visible to the naked eye but they produce no light of their own. It is all reflected sunlight. Uranus is sometime bright enough to be seen but is only around magnitude 5.6 at its brightest. Telescopes are always needed to see Pluto and Neptune.

    All planets move in nearly circular orbits around the sun. Farther planets orbit more slowly, and all move in same direction around the sun.

    The planets always appear near the ecliptic because they orbit the sun in nearly the same plane as the earth orbits the sun, so their apparent path around the Earth is almost in the same plane.

    Venus and Mercury are closer to sun than earth so do not wander far from sun in their orbits as seen on the sky. Mercury remains less than 28degrees from the sun at all times.

    Venus can appear as bright as -4 magnitudes. It is quite bright around sunset for about 1/2 the year in the western sky.

    Zodiac is formally defined as a band of 18 degrees centered on the ecliptic which marks the wedge around the ecliptic that the planets follow. The band is divided into 12 segments, named for constellations along the ecliptic.

    A horoscope is technically a map of the position of the sun, planets and moon among the constellations of the Zodiac at a particular time.

    this has no possible relation to any human character or behavior or anything. Astrology has no basis in scientific fact. It is merely a superstition that modern science left in the dust centuries ago.

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