Coordinates

(Wikipedia Commons)

Coordinates

On Earth:

zero of latitude is fixed by the equator,

zero of longitude is fixed by international agreement.
Latitude is measured as the number of degrees north or south of the equator. i.e. subtended angle at the centre of the earth

Longitude is measured around the surface of the earth, at the equator, from a point due south of Greenwich England.

Finding stars:

Pretend we are surrounded by a "Celestial Sphere": this is an horizon based system (ie. what the earth bound observer sees).

A meridian is a North South line in the sky.

The zenith is the point in the sky vertically above the observer.

Then we can describe the position of a star by its altitude/azimuth.

Inconvenient for star maps, since stars rise 4 minutes earlier every night, so need star based reference system. The North Celestial Pole is the point in the sky vertically above earth's North pole.

Stars above the earth's equator lie on the celestial equator, defined to have a declination δ = 00.

Declination is the angle measured from the earth's Equatorial plane (the same as latitude) so the north pole has a dec. +900. Stars which always lie to the north for observers at the equator have a δ > 00.

Longitude:

  • The origin of Longitude must be defined through an arbitrary choice.
  • The Greenwich Meridian is defined as 00 Longitude.

    Note that 3600 of longitude (once around the globe) = 24 hrs of time,

  • so 1 hr. of earth's rotation = 150.
  • Thus, roughly every 150 is a new time zone.
  • We could just as well measure angles in hours, given that the earth's rotation rate is constant.

    Finding stars:

    Right Ascension (R.A. or α) is the equivalent of Longitude.

    The first star will rise, (say) 1.5 hrs before the second. After earth has rotated for 1.5 hours, second star is on the observer's meridian

    The Hour angle = 1.5 hours. or \color{red}{\theta = 22.5^\circ } . In fact, we define hour angle as the time to cross the meridian.

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    Right Ascension:

    The origin of R.A. is also arbitrary.

    Earth's equatorial plane and the plane of the earth's orbit about the sun cross each other at any time along a line. Twice each year, the sun crosses the ecliptic. March 21 & Sept 22

    Zero of R.A. defined by position of the sun on March 21, the vernal equinox,
    Sun's Right Ascension changes from 0h in spring, through 6h in summer, 12h in fall, and 18h in winter.

    Stars in the midnight sky in midsummer have α of ~18 hours, which results from their being 180° (~12h) away from the sun's direction, and the earth's progress of about 1/4 of its way about its orbit (90° ≈ 6h).

    Stars in the midwinter midnight sky in have α ~6 hours. R.A. is measured in hours and minutes.

    Thus Sirius has R.A.= 6 hr 42.9 minutes, and δ = -16.39°.

    Finding Stars:

    The earth must rotate more than 3600 in order that the sun may appear to be in the same position in the sky.

    A solar day is the interval between two successive occurances of the sun being due south.

    A sideral day is the interval between two successive occurances of any star being in the same place in the sky.

    1 solar day = 1 sidereal day + ~1/365 sidereal day.

    1/365 day = 3.95' (minutes).

    Why are the equator and the ecliptic different?

    The earth's spin axis is tilted with respect to the orbital plane.
    Sun, planets,and the moon move approximately on the ecliptic: divided into 12 zodiacal constellations:

    Aries, Pisces, Aquarius, Capricorn, Sagittarius, Scorpius, Libra, Virgo, Leo, Cancer, Gemini, Taurus.

    The Final Catch:
    The Earth precesses, like a top. The cycle takes 26,000 yrs.
    The earth spins about its north-south axis. This axis does not stay fixed with respect to the stars in the sky, but rather it wobbles slowly like a child's spinning top. During this 26000 year period, the earth's spin axis traces out a cone in the sky.

    The effect is to move the ecliptic (really, the plane of the earth's orbit is fixed, and the equator is what is tilting).

    Note the crossing of the celestial equator and the ecliptic in Aries, as was the case for the Babylonians 3600 years ago. 26000/12 ~ 2200 yrs/Constellation

    The crossover was previously in Aries (1600 B.C.).

    It then moved into Pisces (0 A.D.)

    Now his is the dawning of the age of Aquarius.

    Summary:

    There are actually 3 sets of coordinates:
    1. Earth (equator) based altitude/azimuth, tilted 22° with respect to...
    2. Sky (ecliptic) based RA and dec, tilted 60° with respect to...
    3. Galaxy based, which is defined by the plane of the Milky Way.
    Important since we can assume that