IAL 2: The Sky

Don't Panic

Sections

  1. Introduction
  2. Parallax
  3. The Celestial Sphere
  4. Location on the Sky and Coordinate Systems
  5. The Sun on the Celestial Sphere
  6. The Seasons
  7. Axial Precession
  8. The Moon, Planets, Asteroids, and Comets on the Celestial Sphere
  9. Constellations: Reading Only
  10. The Modern Astronomical Constellations: Reading Only
  11. Why does Astronomy Still Bother with Constellations? Reading Only

    1st century BCE zodiac

  1. Introduction

    2. This lecture (IAL 2: The Sky) and the next 2 lectures (IAL 3: The Moon: Orbit, Phases, Eclipses and IAL 4: The History of Astronomy to Newton) consist mostly of old astronomy.

    So astronomy mostly from before 1900 and some of it from long before going back millennia.

    Old astronomy is mostly the astronomy of what we see in the sky---the astronomical sky which is mostly above the Earth's atmosphere---the exceptions are objects in low Earth orbits which are NOT entirely above the Earth's atmosphere.

    Old astronomy does NOT concern itself with the internal structure of the astronomical objects.

    Old astronomy is still needed for modern astronomy---and so we still need to know it---but the astrology bits are just for fun: see the zodiac figure above and the figure possibly of Cleopatra (69--30 BCE) below (local link / general link: cleopatra.html).

    Modern astronomy as the main focus starts from IAL 5: Physics, Gravity, Orbits, Thermodynamics, Tides and goes on and on.

  2. Parallax

    3. When we look up at the SKY---beyond the clouds that is---it is all very REMOTE.

    And you know it is REMOTE because the astro-bodies to the naked eye---or even the contact-lens-coated eye---and even to simple instruments show NO parallax.

    1. What Is Parallax?

        Question: What is parallax?

        1. A quick zigzag motion of astro-bodies.
        2. The change in the angular positions of objects as the observer moves.
        3. An over-the-counter medication for constipation.











        Answer 2 is right.

        Answer 3? You're thinking of ex-lax.

      The animation in the figure below (local link / general link: parallax_animation.html) illustrates parallax dynamically and shows that the remoter the object, the smaller the parallax.

      Now note that remote       mountains show NO noticeable parallax to small movements by the Alien in the figure below (local link / general link: parallax_small.html).

      Similarly even if you move       kilometers or all the way across the Earth, you can with simple measurement techniques measure NO parallax for astro-bodies.

      Ergo, the astro-bodies are very remote compared to the size of the Earth.

      Recall that the Sun and planets are of order a few or a few tens of astronomical units away.

      The Moon is much closer at about 60 Earth radii away, but to crude measurements it show NO parallax either.

      The nearest stars are of order a few parsecs away. One needs really precise measurements to detect their parallaxes.

    2. Parallax Measurements:

      Parallax measurements can be used to determine distance by simple geometry: to be specific trigonometry.

      You need to measure the baseline between two angular measurements that are used to determine parallax.

      The larger the baseline, the larger the parallax and, usually, the more accurate the measurement.

      If the baseline is too small, parallax, and therefore distance, CANNOT be measured at all.

      How baseline and parallax are used to obtain distances is illustrated in the figure below (local link / general link: right_triangle.html).

    3. Stellar Parallax and the Parsec:

      The rotation of the Earth on the Earth's axis gives a largish baseline by moving an observer by a distance up to 2 Earth radii.

      But that baseline is still too small to see the parallax of Solar System objects against the background of the fixed stars without fairly advanced techniques.

      See the explication of the fixed stars in the figure below (local link / general link: ptolemy_muse.html).

      The revolution of the       Earth gives a much larger baseline for parallax measurements than any baseline just on the Earth: up to 2 Earth orbit radii: i.e., up to 2 astronomical units.

      The shift in angle by moving 2 astronomical units is certainly a parallax shift. However, ancient tradition in astronomy tells us to consider half that angular shift (i.e., the semi-angle) as the standard astronomical parallax for the astronomical objects, in particular for the case of stars where it is called stellar parallax. Just accept it.

      The Stellar parallax videos below (local link / general link: stellar_parallax_videos.html) give some insight into stellar parallax.

        EOF

      Now the       baseline of 1 astronomical unit, leads to the distance unit the parsec (pc).

      The figure below (local link / general link: parallax_stellar.html) shows how stellar parallax is determined and how the parsec is defined.

    4. Distance Measurements Are Tough, Especially for the Ancients:

      A 2-AU baseline is NOT a large enough baseline for simple methods to detect parallax of even the nearest stars against the background of remote stars.

      But a 2-AU baseline is quite enough to see the parallax of the Solar System objects against the background of the fixed stars even with the naked eye.

      There are complications. The Solar System objects are actually moving in the center-of-mass free-fall inertial frame (COMFFI frame) of the Solar System (which is approximately the location of the Sun, but NOT always inside the Sun) on time scales of the revolution of the Earth: i.e., on the time scale of a year.

      Also before Nicolaus Copernicus (1473--1543), most people thought the Earth was NOT revolving or rotating and that Solar System objects moved essentially around the Earth in some complicated way.

      So it's hard to disentangle parallax effects from other motion effects for Solar System objects---and for the Ancients to even recognize that there were parallax effects.

      The upshot of this discussion is that from simple observations, we CANNOT know the distances to the astro-bodies.

      We have the procedures nowadays to get good distances.

      But those were NOT available to the Ancients who had to largely guess at distances or give up trying to know them. The later ancient Greek astronomers finally got a fairly accurate distance to the Moon of ∼ 60 Earth radii (No-102). But beyond the Moon, the Ancients had NO accurate distances.

      It is true to say that accurate distances are always harder to measure compared to accurate angular positions in whatever age you are living in.

  3. The Celestial Sphere

    4. What of the old celestial sphere?

    1. The Dome of the Sky:

      If you just stay in one region of the Earth, the astro-bodies could be located on a big dome of the sky over the flat Earth.

      The astro-bodies can be seen as traveling over this dome of the sky every day with the Sun, Moon, and planets executing more complicated motions superimposed motions relative to the fixed stars. See the explication of the fixed stars in the figure above (local link / general link: ptolemy_muse.html).

      Without measurable parallaxes or other distance indicators for the astro-bodies, how could you tell that this dome model it was NOT true.

      Perhaps the ancient Sumerians and Babylonians, who never got out of the Tigris-Euphrates River area, perceived the sky this way---we don't know--they didn't tell us---they may have had various ideas.

      For a possible Babylonian cosmology, see the figure below (local link / general link: babylonian_cosmos.html).

    2. The Round Earth and Celestial Sphere of the Stars:

      So the Babylonian astronomers and Babylonians in general probably thought the Earth as a flat Earth.

      In fact, we do think of the astro-bodies carried around on a giant imaginary sphere for the purposes of locating objects on the sky.

      We call this big sphere, following ancient tradition, the celestial sphere.

      No simple observation contradicts this celestial sphere theory as a real model of the cosmos.

      The celestial sphere theory even makes philosophical sense if you know the Earth is ROUND and believe it is at the center of the cosmos. One could reason that the cosmos has spherical symmetry everywhere.

      The idea of a physical celestial sphere---the celestial sphere of the stars---got incorporated in the theory of the cosmos that become dominant in in later Classical Antiquity, the Medieval Islamic world, the Medieval Europe, and Renaissance Europe.

      This theory was part of Aristotelian cosmology which was a geocentric cosmology with a spherical Earth. It had the fixed stars located on a rotating physical celestial sphere---the celestial sphere of the stars.

      For Aristotle (384--322 BCE), the "supreme authority", see the figure below local link / general link: aristotle_supreme.html).

      Why could       Aristotelian cosmology---which is in many respects wrong (the important spherical Earth part was right)---have such a long vogue of about 2000 years---4th century BCE--17th century?

      A key reason is that the ancient Greek astronomers (see subsection Distance Measurements Are Tough, Especially for the Ancients above) and their successors up to 17th century could NOT measure astronomical distances very well.

      In fact, ancient Greek astronomers did try to measure astronomical distances, but the only success was that they did eventually figure out that the Moon distance was ∼ 60 Earth radii: see the figure below (local link / general link: aristarchos_manuscript.html).

      But the       Ancients and their successors up to 17th century never did get any other distances accurately---these distance are much larger, of course, than the distance to the Moon.

      Their geometry was strong, but their instruments were weak.

      The parallaxes of all the astro-bodies beyond the Moon were just too small for techniques from before the 17th century to measure.

      Now Magellan's circumnavigation tended to confirm Aristotelian cosmology---the Earth was round just like Aristotle said it was---but later work by Nicolaus Copernicus (1473--1543), Galileo Galilei (1564--1642), Johannes Kepler (1571--1630), Isaac Newton (1643--1727), and others, relegated Aristotelian cosmology to history.

      The celestial sphere of the stars disappeared as a physical object and became imaginary, infinitely remote celestial sphere on which all astro-bodies are projected for the purposes of location.

    3. The Modern Celestial Sphere:

      Nowadays, the celestial sphere is NOT physical body anymore, of course.

      It is an imaginary sphere quasi-infinitely beyond any physical astro-body.

      The actual astro-bodies are viewed as projected onto the celestial sphere for location purposes. We discuss locating astro-bodies on the celestial sphere below in section Location on the Sky and Coordinate Sytems.

      Some first points about the celestial sphere:

      1. The whole celestial sphere revolves around the Earth once per day as seen from the Earth, of course.

        Actually, once per sidereal day. We'll discuss sidereal day below in section The Sun on the Celestial Sphere.

      2. Physically, we think of the Earth as rotating on its axis (as in the animation below) and NOT of the surrounding universe rotating about us.

      3. But either perspective is a valid geometrical description of motion. For a discussion, see the figure below (local link / general link: /celestial_sphere_rotating.html).

      4. In fact, for most astronomical observational purposes and in often in everyday life, we take the Earth as being at rest and the surrounding universe as rotating about us.

        This is geocentric perspective---which is a very humankind egocentric perspective.

      5. Why then do we say the Earth is "rotating physically"?

        Earth is rotating relative to fundamentally absolutely unrotating observable universe with respect to which all inertial frames do NOT rotate---except maybe in very strong gravitational fields like near black holes???---but yours truly has to guess about this since no one explicates this factoid. The best explication so far (and it does NOT say much) is Wikipedia: Inertial frame of reference: General relativity.

        Recall it is only to relative to inertial frames that accelerations (which includes orbital motions) are caused by forces and only by forces.

        All this explanation is too long to say everytime we need to say it.

        So as a shorthand, we say that the Earth "physically" rotates and the observable universe does NOT "physically" rotate.

        However, we can say either geometrically rotates relative to the other depending on our descriptive needs.

      6. As well as the overall daily motion of the astro-bodies by being carried around by the rotating celestial sphere, the astro-bodies also have motions relative to the celestial sphere.

        The motions are easily observed for astronomical objects in the Solar System since these motions are relatively rapid. We will discuss these motions below (see sections The Sun on the Celestial Sphere The Moon, Planets, Asteroids, and Comets on the Celestial Sphere).

        Extrasolar objects (i.e., astronomical objects outside of the Solar System) also move relative to the celestial sphere, but this motion becomes harder to detect in direct way as the extrasolar objects get farther away since the angular extent of the motions on the sky strongly tends to get smaller with increasing distance.

      7. Why do the angular motions relative to the celestial sphere strongly tend to get smaller with increasing distance?

        Velocities relative to local inertial frames for most observable astro-bodies are of order a few hundred kilometers per second and the biggest ones are of order a few tens of thousands of kilometers per second.

        At distances of kiloparsecs and megaparsecs, the distances traveled by astro-bodies on human time scales at such velocities are minute compared to the distances to the astro-bodies.

        Now angle is ratio of the projected length of an object divided by the distance to it aside from some conversion factor if you are NOT using radian measure.

        So at distances of kiloparsecs and megaparsecs, the angular motions are minute on human time scales.

        Our ability to directly detect these motions is improving, but it is still limited to stars and other astro-bodies in our neighborhood of the Milky Way.

        Indirectly, we can detect motions far away via the Doppler effect (see IAL 7: Spectra) and the cosmological redshift z (see IAL 26: The Discovery of Galaxies and IAL 30: Cosmology).

    4. Celestial Sphere Basics:

      The basic idea of the celestial sphere is illustrated in the figure below (local link / general link: celestial_sphere_000_basic_idea.html).

      As the grid on the adjacent figure (      local link / general link: celestial_sphere_000_basic_idea.html) suggests, you can locate astro-bodies on the celestial sphere by angular position and the angular positions are the same for everyone on Earth because there is NO SIGNIFICANT parallax as you move about the Earth or, for extra-solar-system bodies, as the Earth moves about the Sun.

        Of course, there really is parallax if you use very refined techniques, but even most professional astronomy doesn't have to worry about that parallax too much.

      We will return to locating objects on the celestial sphere below in section Location on the Sky and Coordinate Systems.

      1. Points and Circles on the Celestial Sphere:

        There are special points and circles that we put on the celestial sphere.

        These points and circles help with finding astro-bodies on the celestial sphere and understanding and tracing their motion.

        The figure below (local link / general link: celestial_sphere_001_features.html) explicates the some of the basic of the special points and circles.

      2. A Bit More on Polaris:

        Just a bit more about Polaris, the pole star of our historical period.

        Polaris (α UMi) (or the Pole Star or the North Star) is 44'09'' (44 arcminutes, 9 arcseconds) from the NCP in year 2000 coordinates (more precisely J2000.0 coordinates).

        So it's less than a degree from NCP---which is which is about or less than a finger width at arms length (Hand Angle Measurements).

        Polaris is a moderately bright star (visual magnitude of 2.02), and thus can be used to identify the NCP (which is just an empty point on celestial sphere).

        Polaris is the end star of the handle of the Little Dipper---which is an asterism (i.e., a non-official constellation)---is part of the modern standard constellation Ursa Minor.

        But the Little Dipper is NOT a particularly obvious asterism and NOT the give the easiest way finding of Polaris.

        The easiest ways of finding Polaris are illustrated in the figure below (local link / general link: polaris_ursa_minor_major.html).

      3. The Celestial Sphere Rotates Westward Relative to the Fixed Earth:

        Now the Earth rotates eastward relative to the observable universe, but if you take the fixed Earth as your frame of reference, the whole celestial sphere rotates west.

        But you can only see what is above your local horizon which is the great circle that cuts the celestial sphere in half: above the sky, below the ground.

        So what we usually see: astro-bodies rising east and setting west on the horizon as the sky turns.

        Artificial satellites in low earth orbit can rise and set anywhere if their angular velocity relative to the fixed stars is fast enough.

        This point is illustrated in the figure below (local link / general link: gps_global_positioning_system.html).

        Most         astro-bodies, in fact, don't move much relative the celestial sphere during a day---some do like some artificial satellites, of course.

        Insofar as they are approximated as unmoving on the celestial sphere, astro-bodies are carried around daily on the celestial sphere on circles parallel to the celestial equator.

    5. Complications with Using the Celestial Sphere:

      There are TWO COMPLICATIONS in seeing the circling of the astro-bodies with the celestial sphere:

      1. Bright daylight and clouds usually totally hide astronomical objects. Note especially that most astronomical objects are too dim to be seen against the diffuse sky radiation (i.e., the blue sky) caused sunlight scattering in the Earth's atmosphere.

      2. The celestial sphere is cut in half at an oblique angle by the horizon of the Earth.

        The Earth is round, but to a little human anywhere on the Earth, the Earth seems like an infinite flattish plane.

        Understanding the astronomical sky would be much easier for us little humans if the Earth didn't block our view.

      See the two figures below (local link / general link: celestial_sphere_002_horizon.html; local link / general link: leprechaun.html).

    6. Best Celestial Sphere Video Ever!!!:

      See celestial sphere | 1:45: Best celestial sphere video ever!!! below (local link / general link: celestial_sphere_videos.html). It makes the celestial sphere idea very clear.

    7. Circumpolar Objects and Non-Circumpolar Objects:

      Stars that NEVER cross the horizon line are called circumpolar stars.

      Any object that NEVER crosses the horizon line is a circumpolar object.

      The circumpolar situation is clear in the figure above (local link / general link: celestial_sphere_002_horizon.html) which is repeated below (local link / general link: celestial_sphere_002_horizon.html).

      The       circumpolar objects are those on small circle paths (or for those on the celestial equator on great circle paths) that never cross the horizon---circumpolar in this context means uninterrupted circles around the celestial axis.

      Those circumpolar objects above the horizon are always in the sky though they may be invisible due to daylight or weather conditions.

      Those circumpolar objects below the horizon are never seen by the observer whose latitude defines the horizon's orientation.

      Also clear from the figure above (local link / general link: celestial_sphere_002_horizon.html) is that circumpolar objects have smaller angles to the celestial axis than the angle between the celestial axis and the nearest point on the horizon---an angle which we learn to call the altitude of the celestial axis below in section Location on the Sky and Coordinates.

      What is or is NOT a circumpolar objects is clearly dependent on latitude:

      1. At the North Pole and South Pole, all sky is circumpolar sky.

      2. At the Earth's equator, there is NO circumpolar sky.

      3. In general, the circumpolar sky increases with absolute value of latitude |L| from 0 % at |L| = 0 to 100 % at |L|=90°.

        The general formulae for declination of the circumpolar sky are given in figure above (local link / general link: declination_altitude.html).

      The fraction of sky that is non-circumpolar can all be seen from any given latitude, but only half at any time in the day. The Earth occults the other half. The rotation of Earth allows you to see the whole non-circumpolar sky over the course of a day.

      Astronomical objects that move relative to the celestial sphere can change from between being circumpolar and non-circumpolar. The Sun within the Arctic Circle and Antacrtic Circle can switch its status. Low-Earth-orbit artificial satellites can switch status multiple time during a day.

    8. Two Perspectives on the Celestial Sphere in an Applet:

      The applet in the figure below (local link / general link: naap_rotating_sky_explorer.html) allows one to explore the celestial sphere from the two perspectives:

      1. The perspective with the Earth seen as an infinite plane cutting the celestial sphere in half and a rotating celestial sphere.

      2. The perspective with a rotating Earth as a pinprick at the center of the celestial sphere---well you have to imagine the Earth as a pinprick since for diagramatic reasons its shown as pretty big compared to the celestial sphere.

      The circumpolar and non-circumpolar behaviors are explorable too.

    9. More Illustrations of Circumpolar Behavior:

      A simple case for circumpolar objects is that of an observer at the North Pole or the South Pole. He/she would see one hemisphere of the celestial sphere spin around every day with all star paths parallel to the horizon---all stars are circumpolar stars for this observer.

      The figure below illustrates this case.

      If you are NOT at the North Pole/South Pole, the NCP/SCP is NOT at zenith and the stars do NOT move in circles around zenith.

      They still move in circles around the celestial axis, of course.

      In the Northern Hemisphere looking to the north, the NCP is above the horizon and you see the stars circling it. Those stars sufficiently close to the NCP that they don't pass below the horizon are circumpolar as aforesaid.

      We show a diagram of their motion in the figure below.

      In the Northern Hemisphere looking to the south, the SCP is below the horizon.

      Stars south of the NCP by an angle equal to its altitude (which is equal to its latitude) will NOT be NCP circumpolar stars.

      They must rise and set OR always be below the horizon: i.e., those sufficiently close to the SCP to be SCP circumpolar stars. See the figure below.

      In the figure below (local link / general link: sky_swirl_polaris_animation.html), we show an animation of the NCP circumpolar stars.

      Some of the       Celestial sphere videos (see below local link / general link: celestial_sphere_videos.html) show circumpolar stars in action: Aurora Borealis Night Sky Time Lapse - Northern Lights - Nikon D5100 and Tokina 11 | 5:03 and Frozen South: Antarctica 24 hour Sun 4K | 2:07 for the circumpolar Sun.

      A       long-exposure image shows the motion around the celestial axis too. For an illustration, see the figure below (local link / general link: gemini_north_swirl.html).

    10. What Are the Atltitudes of the NCP and SCP?

      First, we need to say that altitude in astronomy is the angle to an astronomical object measured straight up from the horizon toward zenith.

      Now what are the altitudes of the NCP and SCP?

      Well, the altitude of the NCP from due north and the altitude of the SCP from due south are, respectively,

          AN_NSP = L     and     AS_SCP = -L

      counting the southern latitudes as negative. The figure below (local link / general link: declination_altitude_2.html) proves these formulae.

  4. Location on the Sky and Coordinate Systems

    5. The astro-bodies can be located on the celestial sphere in several different ways.

    We do NOT do a lot with these location methods in IAL since IAL is NOT primarily an observational set of lectures, but we do need them for a few things and we keep them in mind throughout the course.

    Here, we just discuss 3 main ways of locating astro-bodies on the celestial sphere and, briefly, the conversions between the second and third ways.

    1. Constellations as Skymarks:

      A crude, but easily remembered, and highly useful way of locating an astro-body on the celestial sphere is to locate it by what constellation it is in. In modern astronomer jargon, a constellation is NOT a set of stars, but a defined region on the celestial sphere that contains the set of stars making up the historical constellation.

      These constellation regions tile the whole celestial sphere without overlap, and so provide an unambiguous means of locating astro-bodies on the celestial sphere.

      One can say, for example, that the Sun is in Aquarius about March 1 (Se-21) and in Pisces on Mar21 (approximately the vernal equinox). See the figure below (local link / general link: iau_pisces.html).

      Locating astronomical object by constellation is useful for rough work and contemplation by both by amateur and professsional astronomers since some of us know the celestial sphere pretty well and the constellations are SKYMARKS.

      Actually, amateur astronomers are probably better at this than professional astronomers---who are sometimes profoundly ignorant of constellations as SKYMARKS.

      We will look at constellations in section Constellations and the sections following that one.

      To see the       IAU 88 constellations in restful/boring fashion, see The constellations | 12:11 video in Constellation videos below (local link / general link: constellation_videos.html).

    2. The Horizontal Coordinate System:

      A second way locating astro-bodies on celestial sphere is by using horizontal coordinates (AKA local coordinates).

      Horizontal coordinates are good for locating astro-bodies at one instant in time at one place on the Earth.

      They make use of markers and directions that are easily understood by humans without much in the way of elaborate measuring instruments.

      But every astro-body's horizontal coordinates change rapidly with time as the Earth rotates and at any one time are different for different points on Earth.

      So horizontal coordinates are NOT good for catalogs or other long-term records.

      The horizontal coordinates are explained in the figure below (local link / general link: horizontal_coordinates.html) and applet in the figure below that (local link / general link: naap_observer.html).

      The       meridian (AKA celestial meridian) is a LOCAL MERIDIAN. It is illustrated in the figure above (local link / general link: horizontal_coordinates.html).

      The meridian is a great circle on the celestial sphere that passes from due north on your horizon through your zenith and then to due south on your horizon.

      When an astro-body crosses meridian that is called transiting the meridian.

      The act of transiting meridian is called a transit.

      The times of transits for astro-bodies are frequently tabulated or automatically calculated.

    3. The Equatorial Coordinate System:

      The third way to locate astro-bodies is using equatorial coordinates. This way is much more precise than using constellations and is much more time-independent than using horizontal coordinates.

      Equatorial coordinates are used for catalogs and permanent records.

      The equatorial coordinates are explicated and illustrated in the three figures below (local link / general link: celestial_sphere_003_eqcoord.html; local link / general link: celestial_sphere_animation.html; local link / general link: sky_map_all_sky.html).

    4. An Applet Dynamically Illustrating the Relationship Between the Horizontal Coordinate System and the Equatorial Coordinate System:

      The applet in the figure below (local link / general link: naap_equatorial_horizontal.html) dynamically illustrating the relationship between the horizontal coordinate system and the equatorial coordinate system.

    5. The Equatorial Coordinate System in Moderate Detail: NOT lectured on in class:

      Now we describe the equatorial coordinate system in moderate detail. In a classroom lecture, the discussion below is given with the figures above.

      The viewing center of the equatorial coordinates is any place on Earth.

      The equatorial coordinates are analogous to terrestrial latitude and longitude.

      Astro-bodies are located north or south of celestial equator along meridians by a "latitude" angle called declination (dec) which is measured using the units degree (1/360 of a circle), arcminute (1/60 of a degree and abbreviated by a ' symbol), and arcsecond (1/60 of an arcminute and abbreviated by a '' symbol).

      Declination is positive to the north and negative to the south.

      The "longitude" angle is called right ascension (RA) and is measured eastward from the vernal equinox (which we will discuss below) in the weird angle units hours (15 degrees), minutes (1/60 of an hour) and seconds (1/60 of a minute).

      Since the celestial sphere rotates around the Earth every day, all RAs are visible above the horizon.

        If you are NOT on the equator, they are all present somewhere on the sky above the horizon all the time.

        If you are EXACTLY on the equator in an ideal sense, then you can only see half of the RAs at any one time. But because celestial sphere rotates around the Earth once per day, you see all RAs in a day.

      NOT all declinations can be seen from any point on Earth, except from exactly on the equator. The horizon hides some in a way that depends on latitude.

      The equatorial coordinates astro-bodies do change with time.

      Part of this change is due the physical motions of the Earth and the astro-bodies through space.

      For astro-bodies in the Solar System, these changes are relatively fast, and so the equatorial coordinates of the astro-bodies must continually be recalculated. Fortunately, nowadays computers to this for us effortlessly. In the past, such calculations were often the main job of mathematical astronomers.

      For extra-solar-system astro-bodies the changes are relatively slow, and so the equatorial coordinates of the astro-bodies do NOT need continually be recalculation.

      But updates for the nearest extra-solar-system astro-bodies would have to made just for relatively physical motions.

      However, the equatorial coordinates change intrinsically for another reason: the axial precession of the Earth's axis.

      The equatorial coordinates are tied to the Earth's equator and the Earth's axis. The axial precession causes the orientation of the Earth's equator and the Earth's axis to vary slowly in time.

      This motion causes slow continuous change of equatorial coordinates and catalogs have to be updated every 10 years or less to account for it.

      You may ask why NOT have a coordinate system that does NOT have an intrinsic variation like equatorial coordinates.

      There are such coordinate systems, but having a coordinate system tied to the Earth's equator and the Earth's axis is useful. It allows to us easily comprehend the motions of objects as the Earth rotates daily and to relate longitude and latitude to what can be seen in sky and when it can be seen.

      So with we stick with equatorial coordinates for most ordinary astronomical work.

      We describe axial precession below in section Axial Precession.

    6. Conversion Between Equatorial Coordinates and Horizontal Coordinates: NOT a Required Reading:

      Given that you know the right ascension (RA), it is easy to find the transformation formulae between horizontal coordinates and equatorial coordinates for altitude measurements made along the meridian---which occur for astronomical objects transiting the meridian.

      We derive these formulae in a figure above (local link / general link: declination_altitude.html).

      But we leave these derivations just as a reading. They are too mathematically intricate for classroom presentation.

  5. The Sun on the Celestial Sphere

    6. Now the extra-solar-system astro-bodies do slowly change relative positions on the celestial sphere (not just their equatorial coordinates) over time because of their own and the Sun's motion through space.

    But those changes arn't easily noticed in a human lifetime.

    What is obvious is that the Solar System bodies (i.e., Sun, Moon, planets, asteroids, comets, spacecraft, etc.) do change position on the celestial sphere relative to the fixed stars over a human lifetime and often much shorter time scales.

    In this section, we consider the Sun's motion on the celestial sphere.

    The motion other Solar System bodies, we consider in section The Moon, Planets, Asteroids, and Comets on the Celestial Sphere.

    1. The Earth's Orbit and the Ecliptic Plane:

      We usually say that the Earth physically orbits the Sun or it orbits the Sun relative to the fixed stars and these statements are correct. But recall the statements are shorthands. More exactly, the Earth orbits the Solar-system barycenter (i.e., center of mass of the Solar System which is nearly at the Sun) in the inertial frame of the Solar-system barycenter. Also recall all inertial frames do NOT rotate relative to the bulk mass-energy of the observable universe (except maybe near black holes???), and so there is an absolute rotation for the observable universe even though there is NO absolute space as theorized by Isaac Newton (1643--1727). And so the Earth orbits the Solar-system barycenter in an absolute rotation.

      For an illustration of the Earth physically orbiting the Sun, see figure below (local link / general link: ecliptic_plane.html).

      The plane of the Earth's orbit is called the ecliptic plane

      The perpendicular to the ecliptic plane and the Earth's axis (and therefore the celestial axis) is tilted with respect to the ecliptic axis.

    2. The Ecliptic:

      Because of the Earth's axial tilt, from the Earth's PERSPECTIVE, the ecliptic plane is also tilted by 23.4° from the Earth's equator and therefore by 23.4° from the celestial equator.

      The ecliptic plane cuts the celestial sphere in a great circle which we call the ecliptic.

      The ecliptic is the path of the Sun on the celestial sphere as it geometrically orbits Earth in a year---for which kind of year, see subsection Years: Solar, Sidereal, Common, Leap, Julian below.

      Note the path of the Sun on the celestial sphere is a great circle since the ecliptic plane passes through the Earth which is at the center of celestial sphere.

      The ecliptic plane is explicated in the figure below (local link / general link: season_001_ecliptic.html).

      Also explicated are four special points on the ecliptic: two equinoxes and two solstices.

      The yearly motion of the       Sun on the celestial sphere is mostly eastward on ecliptic, and so slightly opposes the westward daily rotation of the celestial sphere which is parallel

      The TWO MOTIONS are added---but in a slightly complicated way since they are NOT along the same great circle---you need spherical trigonometry to do the "addition"---but let's NOT go there today.

      The TWO MOTIONS do result in a difference between solar day and sidereal day which we explicate the subsection Solar Day and Sidereal Day below.

      The motion of the Sun on the ecliptic is illustrated in the video Constellations of the zodiac | 1:45 in Constellation videos below (local link / general link: constellation_videos.html).

    3. Solar Day and Sidereal Day:

      The fact of the TWO MOTIONS of the Sun on the celestial sphere (discussed in the subsection The Ecliptic above) is the cause of the distinction between solar day (solar noon to solar noon) and sidereal day (rotation period relative to the observable universe or to good approximation the fixed stars).

      The distinction is explicated in the figure below (local link / general link: sidereal_solar_time.html) from the Earth orbiting the fixed Sun perspective.

    4. The Stars Rise Earlier Every Day:

      The eastward motion of the Sun on the ecliptic also explains the solar time daily advance of the day sky and night sky, and of celestial phenomena like rising, setting, and transiting the meridian for objects that are moving relatively slowly on the celestial sphere compared to the Sun.

      All extrasolar object (i.e., astronomical objects outside of the Solar System) are relatively unmoving and so are many solar-system astronomical objects.

      Now the Sun continuously moves eastward relative to the relatively unmoving bodies.

      But relative to the Sun, they are moving westward.

      This means that every day the relatively unmoving objects will rise earlier, transit the meridian earlier, and set earlier than the day before according to solar time which is approximately standard time.

      After a year, almost all the Sun-related recurring events beyond the Solar System have cycled back to the solar times they had a year earlier. Solar System Sun-related recurring events are different since the Solar System astro-bodies move relatively rapidly on the celestial sphere. So they do NOT cycle back in general.

      The figure below (local link / general link: zodiac_ecliptic.html) and the applet in figure below that (local link / general link: naap_zodiac.html) make the solar time advance clear.

    5. Years: Solar, Sidereal, Common, Leap, Julian:

      There are actually two kinds of astronomical year for the Earth to orbit Sun: the sidereal year = 365.256363004 days (J2000) and the solar year = 365.2421897 days (J2000) (AKA the tropical year) which differ in their decimal fractions:

      1. The physical year (i.e., relative to the observable universe or to good approximation the fixed stars) is called the sidereal year = 365.256363004 days (J2000). Traditionally "sidereal" meant relative to the fixed stars, but in modern times it means relative to the observable universe.

        Note J2000 means value as of the year 2000. Due to astronomical perturbations, all Solar System quantities vary slowly with time, and so values cited to a large number of significant figures are only exactly valid at one time. The year 2000 is the standard reference time for the 21st century.

        To be a bit more precise J2000 means 2000 Jan01, noon Terrestrial Time (TT)). Terrestrial Time is pretty darn close to Coordinated Universal Time which is pretty nearly Greenwich Mean Time which is nearly solar time in Greenwich, England (which is near London).

        For exact astronomy, one has to be exact about one's time system.

      2. The solar year = 365.2421897 days (J2000) (AKA the tropical year). This is the time for the Sun to cross the celestial equator twice: once going north (called the vernal equinox (c.Mar21)) once going south (called the fall equinox (c.Sep21). It usually defined as the time vernal equinox to vernal equinox. We discuss the equinoxes in the subsection The Ecliptic above and the subsection Equinoxes and Solstices below.

        The difference between the sidereal year and the solar year is due to the Earth's axial precession (AKA precession of the equinoxes) which we explicate below in section Axial Precession.

      As everyone can understand for calendrical purposes having years with decimal fractions is inconvenient and no one has ever, ever thought of using the astronomical years calendrically.

      They have thought of using everything else. There are lots of other kinds of years, in fact. See, e.g., Wikipedia: Year: Astronomical years and Wikipedia: List of calendars.

      The modern civil Gregorian calendar uses the common year = 365 days exactly and the leap year = 366 days exactly.

      Another year is the Julian year = 365.25 days (exact by definition) which is the approximate time-weighted average year of the Gregorian calendar years and the exact time-weighted average year of the Julian Calendar.

      For a discussion of the Julian Calendar and its correction the Gregorian calendar, see the explication in the figure below (local link / general link: julius_caesar_tusculum_like.html).

  6. The Seasons

    7. To understand, Earth's seasons, we will largely use the Sun-centered perspective.

    1. The Main Idea Via an Animation:

      Recall the Earth's axis maintains the nearly same direction relative to the fixed stars over relatively short time periods like a year and a human lifetime.

      This illustrated in the animation in the figure below (local link / general link: earth_seasons_animation.html).

      The       video Earth Sun Relations | 1:11 in Earth season videos below (local link / general link: earth_season_videos.html).

        EOF

    2. Solar Intensity and the Solar Year Cycle:

      Let's now expand the explanation of the seasons in tedious detail.

      First, the solstice seasons as explicated in the figure below (local link / general link: season_solstices.html).

      In general, the amount of energy received per unit area per unit time on a surface is called       intensity.

      In this subsection to be brief, we will just say solar intensity to mean the intensity of solar light received by the ground.

        There is a special term, insolation, for the amount of solar energy received per unit area in some specified time.

        I find this term a bit klutzy since one has to add "per unit time" in order make it an intensity.

      In general, intensity of light depends on the orientation of the surface to the incoming light rays. The amount is higher, the more directly the light rays strike the surface.

      The orientation effect is illustrated in the two figures below (local link / general link: power_flux_area.html; local link / general link: naap_intensity_orientation.html).

      The upshot of the orientation effect is that when the       Sun is above the celestial equator, you have the following situation: the Northern Hemisphere receives light more directly, days are longer, the north polar region is always in daylight, and the Northern Hemisphere tends to be warmer.

      This is illustrated in the figure below (local link / general link: season_003_summer.html).

      When the       Sun is below the celestial equator, you have the reverse situation: the Northern Hemisphere receives light less directly, days are shorter, the north polar region is always in darkness, and the Northern Hemisphere tends to be colder.

      This is illustrated in the figure below (local link / general link: season_004_winter.html).

      The above remarks are the essential explanation of why in the       Northern Hemisphere summer occurs near the summer solstice (as we call it north of the equator) and winter occurs near the winter solstice (as we call it north of the equator).

      For the Southern Hemisphere, one has the same case as for the Northern Hemisphere, mutatis mutandis.

      The orientation effect on solar intensity is the main reason for the seasons.

    3. At the Equinoxes:

      The figure below (local link / general link: season_equinox.html) illustrates the Earth's situation at an equinox.

    4. How Does the Sun Traverse the Sky as the Seasons Change?

      For some mid northern latitude the two figures below show how: from the perspective of (1) the horizontal coordinates (local link / general link: sunpath_equinox.html) and (2) the equatorial coordinates (local link / general link: celestial_sphere_004_day.html).

    5. The Seasons Summarized:

      The seasons are summarized in the applet in the figure below (local link / general link: naap_seasons.html). The reader should play around with it and push all the buttons.

    6. What About the Elliptical Orbit of the Earth?

      Actually, the Earth's orbit is NOT exactly a circular orbit. It is an elliptical orbit with the Sun at one focus.

      The eccentricity e = 0.0167 = 1.67 % which means that the Earth's distance from the Sun varies up and down from the mean orbital radius by 1.67 %.

      The perihelion is actually in the first week of January (on about January 3) and the aphelion in the early July (on about July 4).

      This distance variation has some modulating effect on the seasons, but the dominant cause of the seasons is overwhelmingly the Earth's axial tilt.

        Question: If the eccentricity of the Earth's orbit were significantly larger than e = 0.0167, would the eccentricity have a more significant effect on the Earth's climate?

        1. Yes
        2. No.
        3. Maybe.











        Answer 1 is right.

        Unless you also invoked some wild compensating effect, I think answer 1 is the only valid answer.

    7. Terrestial Heat Energy and the Earth's Energy Budget:

      1. The Main Source:

        The light energy from the Sun is the MAIN SOURCE OF TERRESTRIAL HEAT ENERGY at ground level as explicated in the figure below.

          The heat sources at the Earth's surface

          Caption: The heat sources at the Earth surface. The 700 W/m**2 should be 170 W/m**2.

          About 170 W/m**2 on average---an average over the whole Earth surface including both day and night sides---comes from the Sun and only 8*10**(-2) W/m**2 from geothermal heat flux (CW-46).

          The 170 W/m**2 on average is what solar power has to rely on.

          There is lots of solar power since there is lots of land, but the energy density (energy per square meter) is low.

          That low density is a problem for solar power.

          Credit/Permission: © David Jeffery, 2003 / Own work.
          Image link: Itself.

      2. Why Don't We Fry?

        Of course, there is no net build up of heat energy---if there were, we'd just get hotter and hotter until we fried.

        The Earth's surface is approximately in a steady state---a time independent state---NOT counting little variations like weather, seasons, global warming, etc.

        All the heat energy to the Earth's surface we get mostly in the form of visible light (high temperature light) gets re-radiated back to space eventually as infrared light (low temperature light).

        The situation is analogous to a house heated by a furnace in winter.

        The figure below (local link / general link: heat_flow.html) explicates the heated house case.

      3. The Greenhouse Effect in Brief:

        In the case of the Earth, the Earth's atmosphere constitutes the Earth's thermal insulation. Without the atmosphere the Earth's temperature would be lower than it is.

        So the greenhouse effect---which is the thermal insulation effect of the Earth's atmosphere---is good---but only in the right amount.

        We will return to the greenhouse effect in IAL 11: The Earth.

        However, as a preview, the Earth's energy budget is illustrated in the figure below (local link / general link: earth_energy_budget_2.html).

      4. Seasonal Lag:

        The equinoxes and solstices mark the astronomical start dates for their respective seasons: spring, summer, fall, winter.

        Now judging from the heating effect of the Sun, one would at first glance think that the astronomical start dates would be about the middle of the climatic seasons. However, seasonal lag (mainly due the time it takes large bodies of water to heat and cool) is of order a month. This makes the astronomical start dates reasonablly appropriate for the start dates of the climatic seasons.

        For example, the hottest period (i.e., July) is typically about a month after the summer solstice and the coldest period (i.e., January) is typically about a month after the winter solstice.

  7. Axial Precession

    8. The Earth's axis exhibits an axial precession.

    A precession is the sweeping out of a cone or a double cone by a body's rotation axis. A double cone is illustrated in the figure below (local link / general link: double_cone.html).

    In older     astro jargon, the Earth's axial precession was called the precession of the equinoxes. The Earth's axial precession causes the whole equatorial coordinate system to shift westward. In particular, the celestial equator, shifts westward and thus equinoxes shift westward along the ecliptic: i.e., there's a precession of the equinoxes.

    1. The Kinematics of the Earth's Axial Precession:

      Kinematics is the description of motion without reference to causes.

      The kinematics of the Earth's axial precession is explicated by the figure below (local link / general link: axial_precession_animation.html).

    2. The Cause of the Axial Precession:

      What is the cause of the axial precession?

      An explication is given in the figure below (local link / general link: axial_precession_physics.html).

    3. The Axial Precession and the Equatorial Coordinates:

      The axial precession is the main reason why the equatorial coordinates of extra-solar astro-bodies have to be updated continually for high accuracy/precision.

      Equatorial coordinates are defined using the Earth's axis and the Earth's equator.

        This is the good way to define the equatorial coordinates.

        The rotating Earth is our platform for observations.

        Having coordinate system tied to that platform makes location and precise measurement of astronomical objects relatively straightforward.

      Thus, the equatorial coordinates of extra-solar astro-bodies continuously---but slowly---shift all the time due to the axial precession.

      The shift is small over a human lifetime, but precise astrometry requires updates at least every 10 years.

      There are also shifts due to the motion of the motion of the astronomical objects and the Solar System in space, but these shifts are usually much smaller than those due to the axial precession.

    4. The Solar Year and the Sidereal Year:

      The difference between the solar year and the sidereal year is due to the axial precession as explicated in the figure below (local link / general link: axial_precession_year.html).

    5. The Variation the Earth's Axial Tilt:

      As well as the axial precession (which is a change direction without necessarily a change in Earth's axial tilt size), the Earth's axial tilt size does vary in time too as shown in the figure below (local link / general link: axial_tilt.html).

  8. The Moon, Planets, Asteroids, and Comets on the Celestial Sphere

    9. The Moon moves on a great circle on the celestial sphere near the ecliptic and its direction is EASTWARD relative to the fixed stars like the Sun.

    The planets and asteroids move on great circles on the celestial sphere near the ecliptic and their direction is EASTWARD MOST OF THE TIME relative to the fixed stars like the Sun.

    These facts, of course, are because the orbital planes of the Moon, planets, and asteroids are NEARLY aligned with the Earth's orbital plane (i.e., the ecliptic plane) and because they all circle the Sun counterclockwise when viewed from the NCP side of the ecliptic plane.

    The near alignment of planet and Moon orbits is due to the formation history of the Solar System which is discussed in IAL 10: Solar System Formation.

    1. The Alignment of the Orbital Planes is Not Nearly Perfect:

      The alignment of the orbital planes of the Solar System is NOT nearly perfect.

      For example, the Moon's orbital plane is tilted by 5°, 9' from the ecliptic (Se-33). This tilt is illustrated in the figure below (local link / general link: earth_moon_system.html).






      The tilts (i.e.,       orbital inclinations) of the planets etc. are shown below in Table: Solar-System Planets.

      The figure below (      local link / general link: orbital_inclinations.html) gives a schematic illustration of the orbital inclinations of Mercury and ex-planet Pluto: these astro-bodies have the largest orbital inclinations among the planets---they are the outliers.

      You can see the near alignment of the       Moon and planets on the ecliptic on the sky or from space as is shown the figure below (local link / general link: moon_clementine.html).

      The       orbital inclinations are further illustrated below in the video Simulation solar system | 0:36 in Solar System videos below (local link / general link: videos_solar_system.html).

        EOF

    2. Planetary Configurations:

      There is some recognized special arrangements of Earth, Sun, and planets.

      These arrangements are called planetary configurations.

      The figure below (local link / general link: planetary_configurations.html) illustrates the common planetary configurations.

      As well as its meaning as a       planetary configuration, conjunction can mean the alignment or near alignment of any astro-bodies on the sky.

      For example, Moon and Venus are in near conjunction in the figure below.

      Planetary configurations are dynamically illustrated by the applet in the figure below (local link / general link: naap_planetary_configurations.html).

    3. Apparent Retrograde Motion:

      The planets as stated above, move EASTWARD MOST OF THE TIME on the celestial sphere, but they can move WESTWARD on it for relatively short times near opposition for superior planets or inferior conjunction for inferior planets.

      This WESTWARD MOTION is called apparent retrograde motion---which is often abbreviated to "retrograde motion", especially when speaking historically of the Copernican Revolution (c.1543--c.1700) and earlier times when apparent retrograde motion was usually thought of as a motion in 3-dimensional outer space.

      To explicate apparent retrograde motion, "apparent" as used in astro jargon, and retrograde motion in the modern sense, see the apparent retrograde motion on the celestial sphere of Mars in the figure below (local link / general link: apparent_retrograde_motion_mars.html).

      Apparent retrograde motion is a consequence of observing other Sun-orbiting planets from a Sun-orbiting Earth.

      To over-simplify for a moment, apparent retrograde motion is like observing a car move backward relative to the landscape when you are passing it.

      When the car is far ahead or far behind it appears moving forward relative to the nearby landscape at least: i.e., curbs and shoulders and bushes by the roadside.

      It is most easy to understand apparent retrograde motion from a top view of the Solar System (i.e., looking down from the NCP side of the ecliptic plane).

      Apparent retrograde motion for both superior planets and inferior planets is explicated in the figure below (local link general link: apparent_retrograde_motion.html).

      Yours truly leaves it as an exercise to the students to understand why inner planets retrograde near inferior conjunction. HINT: Just consider motions in the figure above (local link general link: apparent_retrograde_motion.html) from the point of view of Mars.

      The Apparent retrograde motion videos below further illustrate apparent retrograde motion.

      Retrograde motion was a great puzzle to the ancient Greek astronomers since they almost all accepted geocentric models of the Solar System. The most prominent of these geocentric models are Aristotelian cosmology and the Ptolemaic system---which had epicycles (little circular motions) superimposed on the geocentric planetary orbits (AKA deferents).

      When the heliocentric solar system of Nicolaus Copernicus (1473--1543) (see figure below: local link / general link: copernicus_portrait.html) was introduced, the puzzle of retrograde motion vanished for those who accepted the heliocentric solar system which was almost everyone eventually.

      The historical issues are discussed IAL 4: The History of Astronomy to Newton: Nicolaus Copernicus (1473--1543) and Heliocentrism.

    4. Asteroids:

      The asteroids mostly behave like small planets as objects on the sky: but they are unresolvable in ordinary observations and look star-like: hence the name asteroid which means star-like.

      They mostly have orbits near the ecliptic plane and move counterclockwise as seen from above and have apparent retrograde motion when in opposition or inferior conjunction.

      There are a few oddballs among the asteroids---a few with true retrograde motion (i.e., they orbit clockwise when viewed from the NCP (see Wikipedia: Retrograde motion: Asteroids, comets, and Kuiper belt objects) and probably a few with very high tilts to their orbital planes relative to the ecliptic plane.

      We will discuss asteroids later in IAL 16: Minor Planets, Asteroids, Icy Bodies, Meteoroids, and Target Earth.

      Besides asteroids, there are icy-rocky bodies in various resevoirs of the outer Solar System most famously trans-Neptunian objects that dwell beyond about the orbit of Neptune.

      Our remarks about asteroids apply generally to these outer-solar-system bodies too, but they are a more diverse population in orbital behavior.

      For images and videos on asteroids, see the figure below (local link / general link: asteroid_collage.html).

    5. Comets:

      What of comets?

      First, see the great comet film in the figure below (local link / general link: coronal_mass_ejection_comet.html).

      Now what of       comet orbits?

      Well, comets have rather different orbits from the astro-bodies we've discussed above.

      Comets have highly elliptical orbits with huge eccentricities. They come in two broad classes: short-period comets and long-period comets (Se-569).

      The short-period comets have orbital periods less than about 200 YEARS, have orbital inclinations that are usually less than 30°, and mostly orbit counterclockwise about the Sun (looking down from the north ecliptic axis direction).

      Long-period comets can have orbital periods from 200 years to millions and sometimes to infinity (i.e., they escape the Solar System). Their orbits have random orientations and can be clockwise or counterclockwise for any pole direction you choose.

      The figure below (local link / general link: comet_orbits.html) shows a cartoon of the orbits of comets including long-period comets.

      From the above discussion, it is clear that       comets can appear anywhere on the celestial sphere: they are NOT confined to the region near the ecliptic: for example, they can go near or over the NCP and SCP.

      Maybe one day a bad comet will thwack us.

      The long-haired stars have always been considered portentous, ominous. See Halley's comet figure below (local link / general link: bayeux_tapestry.html).

      More about comets is given in IAL 10: Solar System Formation and IAL 17: Pluto, Icy Bodies, Kuiper Belt, Oort Cloud, and Comets.

    6. See Comet Videos:

      See Comet videos below (local link / general link: videos_comets.html).

        EOF

  9. Constellations: Reading Only

    10. Here, we only give a brief discussion of constellations which complements the discussion given above in subsection Constellations as Skymarks.

    1. Naked-Eye Astronomy:

      But to discuss constellations, we need to discuss what class of stars they are made of---that class is the set of stars that are those visible to the naked eye: see the figure below.

      The number of stars that one can see with the naked eye under ordinary good observing conditions is estimated to be only about 5600 (Wikipedia: Naked eye astronomy)---they are NOT infinite---but maybe uncountable. Under exceptional conditions many more could be seen. Under Las Vegas maybe 10 at a first glance.

      Of course, everyone's scotopic vision is a bit different, and so some people can see more than others. Also extraordinary good observing conditions allow you to see more stars.

        Question: Can the naked-eye stars be seen all at once?

        1. Yes.
        2. No. Sky conditions can hide stars: daylight, clouds, etc.
        3. No. Half the celestial sphere is occulted (i.e., hidden) by the Earth.











        Answers 2 and 3 are right.

        Just as a guess maybe you can see of order 1000 on a clear night.

        Of course, when you use telescope or binoculars, you see vastly more stars.

      The naked-eye stars are in a small local region of the Milky Way: mostly they are between a few and a few hundreds of parsecs away (FK-A-7).

        For comparison, the diameter of the disk of the Milky Way is about 30 kpc as it is usually defined (CK-379).

    2. Grouping Stars:

      On the size scale of our local region in the Milky Way, stars are rather RANDOMLY located in 3-dimensional space.

      Thus, these local stars are rather RANDOMLY located on the 2-dimensional celestial sphere when they are projected onto that remote imaginary sphere from the center of the Earth.

        Only rather RANDOMLY because the local stars have some overall ordering because of the local structure of the spiral arms of the Milky Way.

      The local       stars are often called the fixed stars.

        They are NOT really fixed since they and the Sun are orbiting the Galactic center with periods of order 200 Myr: the Sun's period is 220 Myr (FK-565).

        The orbits, by the way, are NOT fixed either. The stars are subject to constant small gravitational perturbations, and so their motions are a bit randomized.

      But over a human lifetime and even some millennia, the fixed stars are relatively fixed---except for the daily rotation of the celestial sphere of course.

      Because the fixed stars are relatively fixed and relatively RANDOMLY located on the sky, they can be grouped into relatively fixed, relatively arbitrary groupings.

        At least mostly ARBITRARY groupings. The fixed stars in such groupings usually have no strong gravitational interaction with each other and are often far apart in 3-dimensional space. They may be just close in angular position on the celestial sphere.

        Of course, some actual physical groupings do occur: i.e., groups of gravitationally bound stars which are called star clusters if there are many stars or multiple star systems if there are few stars (i.e., 2 or 3 or a few).

      The usually-arbitrary groupings that have become acknowledged by tradition, we call constellations.

    3. Finding Six Constellations:

      Consider the sky map below with constellations labeled on.

      The sky map is about what one would see in winter from a mid-northern latitude.

      We will learn how to find 6 constellations using the sky map.

      One can easily pick out the       circumpolar constellations:

      1. Ursa Major with recognizable asterism the Big Dipper.
      2. Ursa Minor with identifiable star Polaris easily found using the POINTER STARS of the Big Dipper.
      3. Cassiopeia which has a very recognizable W SHAPE.

      These circumpolar constellations can be seen at any time of the year from mid-northern latitude. They are always above the horizon---you just can't see them in the daylight. They, of course, circle the celestial axis that runs nearly through Polaris every day. Where they are relative to the ground on their circular paths at night depends on the time of the year.

      Another easily found constellation is old man Orion---lord of the winter sky---he's always looming over you when your out freezing in the night.

      Orion is NOT circumpolar since it is too near celestial equator---actually Orion straddles the celestial equator.

      So Orion is above the horizon for only about half the day---nearly exactly half a day on the equator.

      In summer (in the Northern Hemisphere), the day side of Earth faces Orion and it's NOT seen.

      In winter (in the Northern Hemisphere), the night side of Earth faces Orion and Orion lords it over the winter night.

      To the lower left of Orion is Canis Major (the greater dog) which is traditionally one of Orion's hunting dogs.

      As a constellation, Canis Major is NOT very obvious, but its brightest star Sirius (the Dog Star) is the brightest star in the sky and on average the brightest object in the sky after the Sun, the Moon, Venus, and Jupiter.

      If you follow a somewhat curvy line from Sirius through the belt of Orion, you find the bright reddish star Aldebaran, the eye of Taurus---the bull's eye.

      To the northwest of Aldebaran and above the ecliptic is a tight little group of stars called the Pleiades---just a small grouping on the sky map.

      Only 6 Pleiades are visible to the naked eye under moderate conditions, but up to 14 have been claimed for great conditions by what were probably very sharp-eyed observers (see SEDS: Pleiades (AKA Messier 45)).

      The Pleiades are actually a gravitationally bound open star cluster of which most members are NOT visible to the naked eye. The total number of stars is more than 1000 NOT counting unresolved binaries (see Wikipedia: Pleiades: Composition).

      Well, that's all the       constellation finding we will do.

      But you can see all the constellation on the all-sky sky map in the figure below (local link / general link: sky_map_all_sky.html). These, of course, are the modern IAU-defined 88 constellations (which we discuss below in section The Modern Astronomical Constellations) and only their abbreviated names are shown: see Wikipedia: 88 modern constellations: Modern constellations for the names and abbreviations.

    4. When Can You See Specific Constellations?

      Well, the circumpolar constellations above your local horizon you can always see on clear nights: e.g., at mid-northern latitudes Cassiopeia, Ursa Major, and Ursa Minor.

      The circumpolar constellations below your local horizon you can never see. For mid-northern latitudes, those are all the far south constellations.

      The other constellations are above the local horizon for part of the day, but if that part of the day is daylight, then you don't see them.

      If a star or constellations star rises at sunrise, it will set at sunset and you will never see it---except possibly just at sunrise and sunset if you can make it out.

      But the non-circumpolar fixed stars rise earlier every day due to the Earth's motion around the Sun as we discussed in section The Sun on the Celestial Sphere.

      So every non-circumpolar star and constellation cycles through all rising times in the course of a year.

      The figure below (local link / general link: zodiac_ecliptic.html) illustrates this for the zodiac constellations.

    5. Heliacal Rising: Reading Only:

      In olden days when people used pay more attention to the sky, the rising of particular stars with sunrise---the heliacal rising---was sometimes taken as marking particular times of the year.

        Before its heliacal rising, a star rises in the daytime and can't be seen usually.

        But as it keeps rising earlier, eventually it rises with the Sun or a bit earlier and can be seen---this is its heliacal rising.

      For example, the heliacal rising of Sirius (the Dog Star) marked the beginng of the Dog Days of summer: in Latin, the caniculares dies. For more on the heliacal rising of Sirius, see the figure below (local link / general link: hesiod.html).

    6. Why Do We Have the Constellations We Do:

      We CANNOT know for sure how ANCIENT CONSTELLATIONS were settled on or why. But for some of the folklore, see the Stars And Constellations | 3:11 and Carl Sagan's Cosmos - Constellations | 3:57 videos in Constellation videos (see below (local link / general link: constellation_videos.html).

      Probably the process was somewhat RANDOM itself and the name assigned to a       constellation in many cases may have been just mnemonic without implying anything intrinsic about the nature of the constellation.

      The Big Dipper was certainly so called because it looks like a set of dots outlining a dipper (a cup with a long handle)---but certainly it was NOT so identified by all cultures: e.g., in the Hiberno-British Isles, it is sometimes called THE PLOUGH or THE WAIN (the Wagon) or variations thereof (see Wikipedia: Big Dipper: Europe).

      Even with connecting lines (which, of course, arn't on the sky) most       constellations look like the object they are named for ONLY in an abstract-in-eye-of-the-beholder way.

      Without connecting lines---except for the Big Dipper and the Little Dipper---the shapes of constellations have no/almost no relation to the names assigned to them.

      The names of constellations names were no doubt often assigned to honor a god or a myth.

      For example, Taurus (the Bull) goes back at least to the Babylonian astronomers of the 7th century BCE and, perhaps, much earlier (Wikipedia: Taurus history) and may honor a bull god or a sacred bull. The ancient Greeks associated Taurus with Zeus in his bull disguise---you recall Europa and all that sorry history.

      Then there is Orion again: see the figure below (local link / general link: betelgeuse.html).

      Different human cultures have come up with different sets of traditional       constellations---but nowadays they are often a bit obscure.

      And also individual astronomers making sky maps often made up new constellations to please themselves.

      The upshot is that before circa 1900, sky maps often contained a mixture of traditional constellations and ones made up by the astronomer making the sky map.

      The following sky map from Chinese astronomy probably exhibits both kinds of constellations.

      At least some of ANCIENT CONSTELLATIONS that have found their way into the modern list of       constellations (see section The Modern Astronomical Constellations) may go back to the ancient Mesopotamians of 2000 BCE or earlier: see constellation facts.

      The       ancient Greeks had close contacts with Babylonian astronomy after Alexander the Great's conquest of the Persian empire (circa 330 BCE) (No-17,35,39,93) and probably acquired the Babylonian constellations sometime after 330 BCE.

      Greek astronomer Ptolemy (c.100--c.170 CE) in his star catalogue groups 1022 fixed stars in 48 constellations many (most???) following Babylonian constellations (No-113).

      Ptolemy's constellations are the basic set of classical constellations from which modern constellations of the Northern Hemisphere sky are derived.

    7. The Zodiac Constellations:

      These classical constellations include the zodiac constellations.

      The path of the Sun through the zodiac constellations is illustrated in the applet in the figure below (local link / general link: naap_zodiac.html)

      Yours truly once had some fun with the zodiac: see the images in the figure below (local link / general link: alien_zodiac.html).

    8. Southern Constellations:

      When Europeans first visited the Southern Hemisphere 15th century, they saw stars they'd never seen before and they eventually started inventing new constellations---the idea of asking the native southern hemispherians for what constellations were already there probably never occurred to the Europeans.

      Who sanctioned the inventions?

      The authors themselves essentially. If you make a book of sky maps, you could choose your own constellations. A book of sky maps was a major production and authors were authoritative. The authors mostly used traditional constellations, but felt free to invent new ones, particularly for the Southern Hemisphere.

      The first European southern constellations seem to have been introduced by Johann Bayer (1572--1625) in his Uranometria (Augsburg 1603).

      He made up 12 new southern constellations including Tucana (Toucan), Grus (the Crane), and Phoenix (see the adjacent figure).

      In the 17th and 18th centuries, there was a lot of making up of new constellations to fill in gaps between the ancient ones. Many of these didn't survive at all.

      For examples of 16th century--18th century images of constellations see Constellations from the Great Celestial Atlases downloaded from the Linda Hall Library exhibit Out of This World: The Golden Age of the Celestial Atlas.

      For more on constellations, see Constellation videos below (local link / general link: constellation_videos.html).

  10. The Modern Astronomical Constellations: Reading Only

    11. In 1922, the International Astronomical Union (IAU) at its first meeting decided---perhaps arrogating to itself the right to decide---on a fixed set of IAU-defined 88 constellations (see the figure below).

    These officially recognized     IAU-defined 88 constellations, as mentioned in the above figure, are NOT just the star groupings in modern usage, but also the regions on the sky that surround the star groupings. These regions cover the sky without overlap---they tile it.

    So every equatorial coordinate location is in some constellation and only in that constellation.

    Modern constellations are illustrated in the figure below (local link / general link: iau_pisces.html).

    The modern     constellations include many of the traditional constellations of Ptolemy and some of the modern inventions particularly for Southern Hemisphere sky.

    There are many listings of IAU-defined 88 constellations: Wikipedia: 88 modern constellations: Modern constellations and Munich Astro Archive: Constellations.

    Munich Astro Archive: Constellations gives the astronomical details and the mythical background if there is one.

    All of the IAU-defined 88 constellations can be seen on the sky map in the figure below (local link / general link: sky_map_all_sky.html).

    In addition to the     IAU-defined 88 constellations, there are OBSOLETE and UNOFFICIAL CONSTELLATIONS and other recognized angular groupings of stars.

    As noted above, any of these unofficial groupings, is an asterism.

    In modern usage, the term asterism is NOT used for IAU-defined 88 constellations. But in older usage an asterism could be a synonym for constellation. In IAL, I will use asterism only in the modern sense.

    The most famous asterism is the Big Dipper which is still often called a constellation in its own right, but it is NOT in the IAU-defined 88 constellations: it is just part of Ursa Major (the Great Bear).

    The Big Dipper and Ursa Major are show in the two figures below. (local link / general link: jeffery_big_dipper.html; local link / general link: polaris_ursa_minor_major.html).

    Similarly the     Little Dipper (part of Ursa Minor [the Small Bear]) is an asterism. Polaris (the North Star or the Pole Star) is at the end of the handle of the Little Dipper: in year 2000 epoch coordinates it is only 44 arcminutes, 9 arcseconds from the NCP.

    Other well known asterisms are presented by Wikipedia: Asterism: Large or bright asterisms and Wikipedia: Former Constellation: List of former constellations.

  11. Why does Astronomy Still Bother with Constellations? Reading Only

    12. Why does astronomy still bother with constellations? As we argued above, we now understand that for the most part they have no real physical significance---just arbitrary groupings of stars rather randomly distributed on the celestial sphere.

    Partially, it is just that astronomers and folks in general are FOND of their constellations---they're traditional and part of the romance of astronomy---so we should keep them in an orderly fashion---for example, the Alien (see the figure below (local link / general link: alien_constellation_2.html).

    There is also a practical use for both professional and amateur astronomers.

    The modern astronomical constellations (the regions on the sky) provide a useful rough and easily memorized location system---the constellations (the actual stars) act as SKYMARKS for the constellations (the regions on the sky). This was discussed above in subsection Constellations as Skymarks.

    One can always locate an astronomical object precisely using equatorial coordinates, but just for a rough position one can say the object is in such or such a constellation: i.e., in that region on the sky that is labeled by that constellation.

    For example, Aldebaran is in Taurus---as indeed it always is.

    For another example, one can say there is a bright supernova in Virgo. This is a relatively frequent occurrence since there is a large nearby galaxy cluster in Virgo called the Virgo cluster. Supernovae occur in galaxies, and so are relatively frequently found in the Virgo cluster, and hence in Virgo.

    The locution object x is in constellation y, although perfectly natural given the modern definition of constellation, does have astrological suggestiveness as if there was a magic sympathy between object and constellation---Venus is Virgo or Venus is in Taurus---but this is just a vestige of where we've come from.