LEAP DAYS account for difference between 365.2422 days per
TROPICAL YEAR (equinox to equinox) and 365.0000 days (noon to noon).
(The SIDEREAL YEAR is 365.2564 days -- Julian year has 365.25000.)

WHEN DO WE HAVE LEAP YEARS? (since Pope Gregory the system has been:)

  • Add one day to February if the year is divisible by 4 (1992, 1996, 2004, 2008)
  • Except in every year divisible by 100 (NOT 1900, 2100)
  • BUT include in every year divisible by 400 (i.e., 2000!)

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    ECLIPSES

    An ECLIPSE occurs when one astronomical object casts a shadow on another.

    LUNAR ECLIPSES

  • Moon moves into the shadow the Earth casts.
  • Only occurs at FULL MOON but NOT each month.
  • Lunar orbit around Earth is inclined by about 5.2 degrees
    from Earth's orbit around Sun (ECLIPTIC).
  • FAVORABLE FOR ECLIPSE WHEN LINE OF NODES
    (intersection of those two planes) POINTS AT THE SUN.
  • Partial eclipses occur more often than TOTAL LUNAR ECLIPSES;
    roughly only every 18 months.
  • Total lunar eclipses last no more than about 100 minutes.
  • During total lunar eclipses, moon often looks red.
    --- due to the small amount of red light refracted through
    the earth's atmosphere.

    SOLAR ECLIPSES

  • Moon casts a shadow on the Earth.
  • Can only occur at NEW MOON but NOT each month (same reason).
  • Partial shadow: PENUMBRA. Complete shadow: UMBRA.
  • PARTIAL ECLIPSE: Moon only covers up part of Sun (not perfect alignment)
  • ANNULAR ECLIPSE: Perfect alignment, but Moon too small to cover entire Sun (near apogee).
  • TOTAL ECLIPSE: Perfect alignment and Moon big enough to cover entire Sun (near perigee).
  • As Earth rotates, shadow races for 1,000s of km across surface (at 1700 km/h),
    but totality rarely more than 100 km wide and lasts < 7.5 minutes.
  • Astronomers study the CORONA --- the outermost layer of Sun's atmosphere ---
    during a total Solar eclipse.

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    DISTANCES and SIZES

    Angular diameter = Diameter/Distance (in words)
    theta = D/d (in symbols)

  • this is measured in RADIANS, with 2 pi radians = 360 degrees
  • or 1 rad = 57.296 deg

    Example: We know the distance to the Sun and the Diameter of the Sun.
    What is the angular size of the Sun?

  • theta_sun = 2 R_sun / 1 AU = 1.392 x 10^6 km / 1.496 x 10^8 km
  • = 9.305 x 10^-3 rad = 0.5331 deg = 31.99 arcmin

    If the distance to the Moon is about 400,000 km, what is its approximate diameter?

    Total solar eclipses exist and imply theta_moon ~= theta_sun

  • thus D_moon = theta_moon x distance_moon
  • D_moon = (9.3 x 10^-3 rad) x (4.0 x 10^5 km) = 3.7 x 10^3 km
  • or R_moon ~= 1.9 x 10^3 km -- more precisely, 1.738 x 10^3 km
  • (The difference comes from approximations to the distance and angular diameter.)

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    PARALLAX: A key tool in measuring distances to nearby stars.
    Apparent shift in star's position due to Earth's orbit around the Sun.

    One PARSEC (PARallax SECond) is the distance at which a star would
    subtend a 1 arcsec angle from a 1 AU baseline.
    1 pc = 3.26 ly = 3.085678 x 10^16 m.

    One can also measure distances to planets, comets, asteroids etc.
    in the solar system using two telescopes widely separated on earth to
    see shifts in apparent position w.r.t. distant stars.

    The simplest example comes from looking through your left and right eyes alternately --
    the finger held at arms' length "moves" less than one held out at half that distance.

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