LOCATING THINGS IN THE SKY

Constellations are convenient groups of stars in particular parts of the sky
and provide rough locations on the CELESTIAL SPHERE
. BUT they are NOT PHYSICALLY ASSOCIATED GROUPS OF STARS
--- some in the same constellation are much farther away than others.

  • Constellations are two-dimensional projections on
    the sky of stars spread out in three-dimensions.

    Brightest stars in each constellation have names from the Greek
    alphabet: alpha Orionis (Betelgeuse), beta Orionis (Rigel), etc.

    Other very bright stars have names:
    Sirius (alpha Canis Majoris); Vega (alpha Lyrae);
    Altair (alpha Aquilae), etc.

    BUT ALL STARS (AND GALAXIES) ARE
    LOCATED IN CELESTIAL COORDINATES.

    Equivalent to LATITUDE is DECLINATION;
    degrees, minutes (') and seconds(") (of arc) from +90 deg (NCP) to -90 deg (SCP).

  • 1 circle = 360 deg
  • 1 deg = 60 arcmin
  • 1 arcmin = 60 arcsec, so
  • 1 arcsec = 1/3600 th of a degree or 1/1,296,000 th of a circle.
  • Sirius has a declination of: -16 deg, 41', 58"

    Equivalent to LONGITUDE is RIGHT ASCENSION;
    it is measured in units of time: hours, minutes and seconds,
    from 0 hours to 23 h, 59 m, 59.999 s.

  • One hour of RA = 15 deg of angle (360 degrees/24 hr/day)
  • Sirius has a right ascension of: 6 h 45 m 09 s.

    Revisit circumpolar/equatorial stars:

    At the poles, ALL stars are polar.

  • the N (or S) CP is at the ZENITH (directly overhead)
  • All the other visible stars make circles about the CPs.
  • The same stars are seen all the time that the sun is below the
    horizon (i.e. half the year) and the other half are NEVER seen.

    At the equator, ALL stars are equatorial.

  • They rise and set each night.
  • Polaris is always at the northern horizon.
  • Half of the stars with DEC = 0 will pass through the zenith during the course of a night.
  • Stars with higher RA will rise and set later in a particular night.
  • Those stars just rising at sunset (so visible all night long) now
    will be just setting at sunset in six months (thus below the horizon all night long).

    More exactly:

  • At positive latitude L, stars within L degrees of the NCP will be circumpolar,
    these stars have Declinations, D > (90-L) deg.
  • At latitude L, stars with Declinations, D, satisfying:
    (90-L) > D > (L-90) are equatorial,
  • While stars with D < (L-90) are "south-polar" and never seen.

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    PRECESSION

    The EARTH's AXIS moves SLOWLY with respect to distant stars,
    just like a TOP's axis rotates much slower than it spins.

    PRECESSION is caused by gravitational torques of the Sun and Moon
    (and other planets) on the Earth's non-spherical shape.

  • The angle between the Earth's axis and the perpendicular to the ecliptic stays around 23.5 deg.
  • The total period of precession is about 26,000 years.
  • POLARIS is the POLE STAR NOW (very close to NCP),
    but 5000 years ago it was THUBAN, and
    12,000 years in the future it will be VEGA.
  • There is no Southern Pole star right now.

    Precession implies a star's RA and DEC change about 20 arcmin per year.

    There is also ``nodding'' or NUTATION:
    the Moon changes the Earth's tilt angle by less than 20" over an 18.6 year period.

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    LUNAR MOTIONS

    The MOON shows different PHASES depending on its location
    in its orbit around the earth.

    NEW (basically between Earth and Sun), then

  • WAXING CRESCENT,
  • FIRST QUARTER,
  • WAXING GIBBOUS

    FULL (basically on other side of Earth from Sun), then

  • WANING GIBBOUS,
  • THIRD QUARTER,
  • WANING CRESCENT

    We (basically) see only one face of the Moon.

    This is because of SYNCHRONICITY between its rotational
    and orbital periods.

  • If the moon rotated faster (or slower) we could see
    all of it over the course of several months.

    (The Earth's forced the Moon into this --
    it wasn't always so.)

    One can tell the approximate time from the phase of the moon
    and its location in the sky.

  • A full moon rises around 6PM in the east, is highest
    at midnight and sets around 6AM in the west.
  • So a full moon seen about 45 deg above the western
    horizon indicates a time of roughly 3 AM.
  • But a first quarter moon, seen 45 deg above the
    western horizon indicates a time of roughly 9 PM.

    YOU'LL PROBABLY HAVE TO REPRODUCE THE DIAGRAM SHOWN
    IN CLASS TO FIGURE THESE OUT, but it's easy if you remember:

  • full moon highest at midnight, so it rises at 6 PM
  • new moon highest at noon, so it rises at 6 AM
  • first quarter highest at 6 PM, so it rises at noon
  • and third quarter highest at 6 AM, so it rises at midnight

    One SIDEREAL MONTH = 27.32 days

  • (w.r.t. fixed stars).

    One SYNODIC MONTH = 29.53 days

  • (cycle of phases -- our MONth).

    Because of the earth's motion around the Sun, the Moon
    takes an extra fraction of a sidereal orbit to go from
    new moon to new moon.

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    CALENDARS

    LUNAR CALENDARS (e.g., Hindu, Jewish, Muslim) are easier to
    keep track of, but can't stay in phase with SOLAR CALENDARS, since

    365.25/29.53 = 12.37 lunar months per year.

    Therefore, either months are forced to have 30 days instead
    (and new moon shifts from first of month, and even then still have
    5 extra days -- often a big holiday)
    or else months must have unequal numbers of days
    -- as in our Gregorian, or the earlier Julian, calendars.