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Astronomy 1
Positional Astronomy
Dr Ross K Galloway
Room 505
[email protected]
Overview:
We will consider the position in the sky and the apparent motion
of celestial objects.
Topics:
• Apparent nature of the sky for a terrestrial observer.
• The celestial sphere.
• Definitions of celestial co-ordinate systems.
• Converting between different co-ordinate systems.
• Apparent motion of the planets.
• Apparent motion of the Sun.
Textbooks:
• Chapter 1 of Carroll & Ostlie.
• “Astronomy: Principles and Practice” by Roy & Clarke
(copies in the Kelvin Building student library, room 332,
and also in the main university library).
Software:
Stellarium, very nice – free – computer planetarium software.
Download from www.stellarium.org
A1 Positional Astronomy
Page 1
Lecture 1
1. Observational Phenomena
Consider an observer in Scotland at sunrise in winter.
The Sun rises in the east, follows a curved path through the sky,
and sets in the west. The stars then become visible. Like the
Sun, these also follow circular arcs from east to west.
The apparent movement of objects through the sky over the
course of a day is caused by the rotation of the Earth on its axis,
and is called diurnal motion.
The circular arcs are centred on a point called the north
celestial pole. The star Polaris is situated (coincidentally) very
close to the north celestial pole.
Some stars rise and set like the Sun. Other stars close to the
pole are above the horizon at all times, and never rise or set.
These stars are called circumpolar.
circumpolar star
non-circumpolar star
Polaris
horizon
N
The diurnal motion preserves the relative patterns of the stars.
These patterns remain unchanged over extremely long periods
of time (millions of years): therefore, reference is often made to
the ‘fixed stars’. Some patterns have been formalised and
named – these are the constellations.
Some well-known constellations include Orion, Taurus, Ursa
Major, Gemini, Cygnus, etc. The northern hemisphere
constellations in general use today date from ancient Greece,
and are mostly based on Greek mythology.
A1 Positional Astronomy
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Lecture 1
The southern hemisphere constellations mostly date from the
16th century, and many have names influenced by scientific
trends of the time, e.g. Microscopium (microscope), Horologium
(clock), Norma (set-square), etc. There are 88 modern
constellations, as recognised by the International Astronomical
Union. (Other cultures had their own distinct constellations, e.g.
Chinese, Indian, Polynesian, Viking, etc.)
Image credit: Jodrell Bank Observatory
Stars are identified by various means. The brightest stars may
have names, often Arabic in origin, such as Betelgeuse and
Rigel in the constellation Orion. Stars may also be labelled
using the Bayer designation, where they are given a Greek or
Latin letter followed by the Latin possessive form of their
constellation name. Frequently (but not always), α is the
brightest star in the constellation, β the next brightest, and so on.
For example, Betelgeuse is α Orionis, Rigel is β Orionis, etc.
A1 Positional Astronomy
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Lecture 1
Stars may also be identified using the Flamsteed designation,
which is similar to the Bayer designation but uses numbers
rather than letters, e.g. 51 Pegasi. Certain variable stars have
names beginning with Latin letters subsequent to Q in the
alphabet, e.g. RR Lyrae, W Virginis.
These systems have been superseded by various modern star
catalogues, but are still in widespread colloquial use in
astronomy.
Consider now an observer at the same place in Scotland, but in
summer rather than winter.
Some of the winter constellations are now no longer visible at
night, and new ones have taken their place. The circumpolar
constellations are still visible at night, but appear at different
angular positions on their diurnal paths.
summer
winter
E
S
W
During the day, the Sun still follows a diurnal path, but
compared to the winter it reaches a higher altitude in the sky, it
spends longer above the horizon (i.e. more hours of daylight),
and it rises and sets at different locations on the horizon.
The position and motion of the Sun depends on the time of year:
it exhibits annual variation in addition to its diurnal motion.
The Sun moves eastward relative to the ‘fixed’ background
stars, making one complete circuit each year. The path on
which it moves through the constellations of stars is called the
ecliptic. The constellations through which the ecliptic passes
are the zodiacal constellations (plus Ophiuchus).
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Lecture 1
The other solar system objects also exhibit annual motion in
addition to diurnal motion (which is exhibited by all objects in
the sky).
The Moon, Mercury, Venus, Mars, Jupiter and Saturn are all
visible to the naked eye. With telescopes, Uranus, Neptune and
the minor and dwarf planets (asteroids and Kuiper Belt objects
such as Pluto) become visible. As the year progresses, these
objects all move relative to the ‘fixed’ background stars. Mostly
this motion is direct, i.e. in the same direction as the Sun’s
annual motion. However, at times the solar system objects
appear to move in the opposite direction relative to the
background stars, i.e. their motion is retrograde. The paths of
the planets all lie approximately on the ecliptic.
The apparent motion of Mars
direct
retrograde
direct
Image credit: Tunc Tezel
Mercury and Venus show properties which are distinct from the
other planets: Mercury is never seen more than ~ 28° and
Venus never more than ~ 48° away from the Sun, whereas the
other planets can be found anywhere along the ecliptic.
Mercury and Venus also show the full range of phases (like the
Moon), whereas the other planets never show less than a
gibbous phase.
In this course, we will seek to investigate, explain, quantify and
predict all of these observational phenomena.
A1 Positional Astronomy
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Lecture 1
2. Solar and Sidereal Days
Starting from due south, the average time taken for the Sun to
appear to travel right around the sky and return to exactly due
south is 24 hours. This is the Mean Solar Day.
Starting from due south, the time taken for a star to appear to
travel right around the sky and return to exactly due south is 23
hours, 56 minutes and 4 seconds. This is the Sidereal Day.
The sidereal day is the length of time it takes the Earth to rotate
relative to some distant, ‘fixed’ reference – it is the true rotation
period of the Earth. The mean solar day is slightly longer than
the sidereal day since during one diurnal rotation the Earth has
moved slightly along its orbital path round the Sun, so must
complete slightly more than one full rotation for the Sun to
appear back in the same place in the observer’s sky.
NOT TO
SCALE
‘night’
constellation
orbital motion
diurnal
rotation
‘day’
constellations
The motion of the Earth along its orbital path causes the Sun to
appear in front of a progressively different ‘background’ of
fixed stars. Equivalently, the Sun appears to be moving relative
to the constellations, taking 1 orbital period (1 year, or 365.25
mean solar days) to complete the cycle. ‘Day’ and ‘night’
constellations vary on this annual period.
A1 Positional Astronomy
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Lecture 1