PHYS 1070 3.0 – Introductory Astronomy
Knowing the
Heavens
Reference: Chapter 2 ‘Universe’
text
Historical
Importance:
Positional astronomy has traditionally been essential for timekeeping and
navigation. By carefully observing celestial
patterns, the ancients could determine the length of the year, predict the
positions of the planets and even the time of eclipses.
Celestial
Sphere: The
celestial sphere (CS) is the projection
of the 3-D universe onto a 2-D surface; i.e., without regard to distance. The major features of the CS are the North and South Celestial Poles (NCP, NSP), the Celestial Equator (CE), Zenith
and Nadir, Celestial Meridian (CM) and the Horizon. When looking up at the CS or any picture/map
of the heavens, E is to the left, and W
is to the right.
Stars
are arranged into constellations
(88), which are arbitrary patterns on the sky.
The Sun passes through 12 of these annually, called the zodiac, each of which is about 30º
wide. The plane of the Sun’s (or
Earth’s) orbit on the CS is the ecliptic. The ecliptic
plane is tilted by 23.5º to Earth’s equatorial
plane.
Stars
and planets (and the Moon) appear to move on the sky from East → West
during a night or diurnally. From night to night:
Cosmology: For the ancients (Aristotle),
Earth was at rest at the centre of the universe and all the heavenly bodies
revolved about Earth daily in circular orbits.
To explain retrograde planetary orbits in a geocentric model, it was necessary to postulate “circles within
circles” (epicycles), as did Ptolemy
in the 2nd century AD. It
wasn’t until Copernicus and Kepler in the 16th and 17th centuries
respectively that the heliocentric
model was adopted, that had the Sun at the centre with the planets on elliptical rather than circular orbits.
Time: As a society we keep civil
or solar time based on the mean Sun.
(The apparent Sun doesn’t move at a
constant rate on the sky.) The solar or synodic day is defined as the time between successive transits (crossings of the CM) of the mean Sun. The day is divided into 24 hours (h);
each hour is divided into 60 minutes (m); each minute is divided
into 60 seconds (s).
Greenwich Mean Time (GMT) or equivalently, Universal Time (UT), is used
as the universal reference time. There
are 24 time zones defined loosely by
longitude on Earth (each zone being about 15º wide). We keep Eastern Standard Time (EST) which is
UT – 5h.
The
sidereal day is the time between
successive transits of a star and is about 23h 56m. This difference between the length of the
solar and sidereal days results in the steady E → W progression of the
stars/constellations; one full rotation in about 360 days (1 yr).
Year: period of Earth’s
orbit. Sidereal year is 365.2564 da;
Tropical year is 365.2425 da
Month: (synodic) period of lunar
phases; about 29.53 da.
Week: ¼ of lunar cycle; 7 da.
Day: (synodic) rotation period
of Earth; 24h.
Hour: 1/24 day.
Minute: 1/60 hour.
Second: 1/60 min, though now based
on atomic clocks and specific 133Cs-atom frequency.
Seasons: Because the ecliptic and
equatorial planes are tilted by 23.5º, the Sun appears to move not only E/W but
also N/S on the CS during the year. The spring or the vernal equinox (“equal day/night”) is defined as the point when the
(mean) Sun crosses the equator moving North (near March 21-22). Autumn is
when the Sun crosses the equator moving South (near September 21-22). The summer and winter solstices (“Sun standing still”) occur around June 21
(Tropic of Cancer) and December 21 (Tropic of Capricorn) respectively.
The
seasons are caused by a variation in solar
insolation: the energy/area/time absorbed by Earth’s surface, and not
by a change in the Earth-Sun distance. But why is February and not the end of
December our coldest month?
Because
Earth’s axis is tilted by 23.5º, it is subject to torques exerted by the Sun
and Moon that cause its axis to precess
with a period of around 26,000 yr. This
is responsible for the difference between the sidereal and tropical years (the
latter defined as the time between successive crossings by the Sun of the
vernal equinox). It is this difference
that led Pope Gregory to introduce the Gregorian
calendar in 1582, superceding the Julian
calendar of Julius Caesar.
Co-ordinate
Systems: To
locate an object on the CS, two co-ordinates are required. The most common co-ordinate system used by
amateur astronomers is the horizon or
altitude-azimuth system. Altitude is
the angle between the horizon and the star, while azimuth is the angle along
the horizon measured N through E.
Because a star’s altitude and azimuth change with time and location on
Earth, a more general system is needed.
Astronomers use the equatorial system, which is analogous to the latitude-longitude system for identifying positions on Earth. Declination
(dec or δ) is an exact analogue to latitude. Stars move along lines of
constant declination. Right ascension (RA or α) is a close analogue to longitude. (A star maintains a fixed
α,δ.) The only difference is
that stars appear to move with respect to an observer with time. Thus, the (local) sidereal time
(LST) and RA are required in order to
locate an object on the CS. The LST is
simply the RA of a star on the observer’s CM.
The zero-point for dec is the celestial equator, while the zero-point
for RA is the vernal equinox.
Declination is measured from 0˚ to +90˚ (NCP) and -90˚
(SCP). RA is measured from 0h
through 24h (or about 15º per hr).
The hour angle (HA) of an
object is the angle between the meridian on which the object is situated and
the (observer’s) celestial meridian.
Thus