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Astr 1101, FALL 2011
Observations of the Sun and the stars over a day (apparent DIURNAL motions) and over several
1. apparent diurnal motion of the Sun (as seen from Calgary)
The description below is long, and therefore looks complicated.
- The Sun appears on one horizon, seems to rise into the sky, travel through the sky,
and disappear somewhere along the “other” horizon.
- When the Sun reaches its highest altitude above, we say that the Sun has reached its
zenith. You can keep a record of the Sun’s zenith with a sundial (actually, just a
vertical stick in the ground – a GNOMON. You will do this in the last observing
exercise.) The stick casts a shadow; mark the end of the shadow. As the Sun gets
higher in the sky, the shadow 1) changes direction, and 2) gets shorter, and shorter.
Eventually the Sun gets lower in the sky, and the shadow gets longer and longer.
Mark all the shadows. OBSERVATION: the direction of the shortest shadow is the
same every day, and every year.
If nothing else, this observation DEFINES two directions for us: first, north is
the direction of the shortest shadow; second, south is the direction 180 from
north (halfway round the circle formed by the horizon; the Sun’s direction when
the short shadow is produced) .
There is another way to define directions, using stars: see below. It turns out
that the definitions are identical!
You can then DEFINE east and west. Imagine facing south, where the Sun
always reaches its zenith. Clockwise around the horizon from south, halfway
between south and north, is the direction we call west. Similarly, counter-
clockwise around the horizon from south, halfway between south and north, is
the direction we call east.
The reason that we have constructed clocks so that the hands move in a
particular sense (i.e. clockwise!) is that this is the sense in which the shadow
cast by a sundial (gnomon) moves.)
We can now say that the Sun rises somewhere along the Eastern horizon, and
sets somewhere along the western horizon. The exact positions of sunrise sunset
varies throughout the year, but repeats from year to year The Sun leaves the
eastern-ish horizon in a direction partly inclined to the south. The particular
combination of the sun-rise POSITION, and the direction of the sun-rise means,
among other things, that the Sun, as seen from Calgary, is NEVER directly
overhead. Page 2 of 31
Multiple-exposure photo of the setting sun, showing that it follows the same diagonal path that a star
would, as seen from a mid-northern latitude. This photo was made on June 21, when the sun set
considerably north of due west.
2. apparent daily motions of the stars
- A particular star rises somewhere on the eastern horizon, passes thru the sky, then
sets somewhere on the western horizon. (Some stars neither rise nor set. These are
called CIRCUMPOLAR stars; see below.)
- The exact location of the star at star-rise (NE, E, SE) depends on the particular star.
- Each star reaches its own zenith (highest altitude above the horizon). The Sun’s
zenith, and all the stars’ zeniths, fall on an imaginary line the runs across “the bowl
of the sky”, from north to south. The zeniths of the Sun, and all non-circumpolar
stars fall on the SAME line.
How do you know that the particular star you watched last week is the same as
the star you watched last night?
The stars SEEM to form patterns; these patterns DO change, but so slowly that
changes are not noticeable over a single lifetime. You can recognize a particular
star by its position in a particular pattern.
Strictly speaking, these apparent patterns are called asterisms. The more familiar
word “constellation” means a particular region in the sky. In this course we will
not distinguish between these two concepts.
The human brain is very good at finding patterns, whether or not patterns
actually exist. You can imagine (make up) an evolutionary reason for this. It is
better to see a tiger in the bushes when there is no tiger, than to fail to see a
tiger in the bushes when there really is a tiger. Those animals that occasionally
run from a non-existent tiger will live to make other animals; on the other hand,
an animal that doesn’t run from the real tiger won’t make any more animals.
After “a while”, only pattern-finders are left. Page 3 of 31
Three examples of “constellations” (asterisms, really…)
This is a late-fall/winter constellation seen in the Northern Hemisphere.
Face southeast/south/southwest to see Orion, fairly high in Calgary’s sky.
E S W
We have lost the reasons for the names of many constellations, but you
can imagine (make up) a plausible story. In a pre-literate society, one way to
remember which constellation is which is to tell a story, and point rhythmically
to parts of the sky as you reach different parts of your story. For instance, the
ancient Greek civilization called this group of stars (and a few other nearby stars)
the hunter – Orion. The two stars at the bottom are the hunter’s knees (or feet?) Page 4 of 31
The three stars in the middle are the hunter’s belt, and the fuzzy patch is the
hunter’s sword. The top two stars are the hunter’s shoulders – unless they are the
armpits. (The top-left star is called Betelgeuse [pronounced beetle juice]. This
has an Arabic root; the history is a little hazy, but name may mean the armpit of
The pattern you MAKE UP depends on your particular culture; for
instance, Aborigines of Northern Australia called the three central stars three
fishermen in a canoe, and the Chemehuevi natives of the Californian desert saw
three mountain sheep.
The star Betelgeuse is slightly red, and the star on the bottom right
(Rigel) is slightly blue. (When you go outside to observe, let your eyes
accommodate to the dark for about half an hour. Your pupil will dilate slightly,
to let in more light. A photo, with a long-ish exposure time, shows the colours.)
You can use the constellation Orion to find the brightest star in the sky –
in EITHER hemisphere - Sirius. (Sirius is not IN Orion, but in a neighbouring
constellation – Sirius the dog, in Greek mythology.)
I have talked about Orion, and how to find it, BECAUSE you can use it to find
the brightest star
This is a summer constellation, again seen in the Northern Hemisphere.
Face southeast/south/southwest: Sagittarius is fairly low in Calgary’s sky.
(Actually, I only show the brightest stars in the constellation.) Page 5 of 31
With a slightly over-active imagination, you might be able to see a teapot.
Milky Way center
E S W
“teapot”: handle spout
To the right (i.e. west) of the teapot, you can see a reasonably bright, red-ish star:
Antares (part of the constellation Scorpius).
I have mentioned the constellation Sagittarius because (it turns out that) you can
use it to point to the center of our galaxy – The Milky Way. Page 6 of 31
This is a squished panoramic view of Sagittarius, after it has risen in the east. (Astronomy Picture of the
Day; APOD, June 27, 2009)
“teapot”: handle spout Anatares
Saharan Starry Night
Credit & Copyright: Babak Tafreshi (TWAN)
Explanation: This panoramic image of a starry night looks across a dry, desolate landscape. The magnificent view was recorded
from Tassili National Park, in the heart of the Sahara desert in southern Algeria. Rising above eroded sandstone cliffs, the celestial
menagerie of constellations includes Draco the Dragon, Cygnus the Swan, Aquila the Eagle, and Scorpius the Scorpion. Ruling
planet Jupiter shines through clouds very close to the horizon near picture center, while star clouds of the Milky Way arc through
Sagittarius above the rocks at the far right. Bright blue stars Deneb, in Cygnus, and Altair, in Aquila, also shine in the starry night
along with Scorpius' bright yellowish star Antares, the rival of Mars. Prehistoric skygazers surely witnessed a similar sky. In
addition to dramatic sandstone formations, the Tassili region is noted for rock art and archaeological sites dating to Neolithic times
when the local climate was wetter. Page 7 of 31
c) The Big Dipper
(The Big Dipper, and a few other nearby stars form Ursa Major –
The Great Bear.)
The Big Dipper can be seen in any season, in the Northern Hemisphere.
Look north; depending on the time of night, and the season, you could
see one of the following two orientations.
Polaris Page 8 of 31
the Little Dipper
“end stars” of the Little Dipper”
the Big Dipper visible from a city like Calgary
the “pointer stars”
Over the course of a night, The Big Dipper seems to pivot around a
particular direction in the northern sky. (We call this direction the North
Celestial Pole.) If you imagine drawing a line through the end stars (the
pointer stars) on the Big Dipper, away from the bowl, you will encounter
the same star no matter the orientation of The Big Dipper. This star lies
(almost!) on the line joining the north and south directions defined by the
Sun’s diurnal motion (see above); consequently, this star is called the
North Star (or the Northern Star).
The stars in the Big Dipper neither rise nor set (as seen from Calgary):
they are examples of circumpolar stars.
Imagine walking north, in the direction of the North Star. You will
notice at least two things: first, your environment gets colder, until you
are jumping from ice flow to ice flow; second, the North Star gets higher
and higher in your sky.
Eventually, the North Star is (ALMOST) directly overhead. If you buy
the idea that the Earth rotates, you are now standing on the rotational axis
(or, rather, the rotational axis goes through you): you are standing at the
Earth’s North Pole. On the other hand, if you buy the idea that the stars
move around the Earth, you are standing under the Celestial North Pole.
Either way, we also call the Northern Star “Polaris” (the Pole Star).
Polaris is NOT the brightest star in the sky (recall that Sirius is the
brightest star in the sky.) Neither is Polaris completely stationary in the
sky: ovor the course of a complete day, Polaris traces out a tiny circle
about 1 in diameter. (This value varies noticeably over centuries; see
“long-term apparent motions”, later.)
Polaris is part of a constellation called (in North America)
“the Little Dipper”. In suburban Calgary (i.e. not downtown), you can see
Polaris, and the “end stars” of the Little Dipper; the other stars in the
“little Dipper” are relatively faint. Page 9 of 31
(I can’t post a photo, because photos posted on the internet are now copyrighted.
I can only TELL you to look at, for instance, the “astronomy picture of the day”
website (use Google to find APOD (which stands for Astronomy Picture Of the
Day), then search the archives for “Polaris”, and find a time-lapse photo of Page 10 of 31
northern stars. An example: the posting of December 24, 2010, taken from
Sweden. In such a photo, you would see that the star (almost) at the centre
actually (i.e. Polaris) is a very short streak. [Copyright P.-M.Heden′ ])
If you were to look at APOD, July 15, 2000, you would see a time-lapse photo of
stars apparently travelling around the South Celestial Pole. In the Southern
Hemisphere, there is no Southern Star. The photo is taken from central New
South Wales, in Australia. [Photo Credit: David Malin; copyright Anglo-
Why do the Sun and the stars apparently travel around the Earth? A particular group of
observations can often be explained in more than one way! Just because you have made
some observations doesn’t mean that you have THE explanation.
a) The Sun and the stars appear to be travelling around the Earth because they ARE
travelling around the Earth
b) The Earth is spinning, while the Sun and the stars are (almost) stationary. The
Sun and the stars only appear to move, because we are spinning.
The second explanation is counter-intuitive (at least it was to Greek
philosophers 2000 or so years ago).
For example, if the Earth were spinning, you would feel as if you were going in
circles. (A modern example: do you know what you feel when you are on a
If the Earth were spinning, we would “spin away” from the birds in the sky, or
anything else not attached to the ground. Page 11 of 31
If the Earth were spinning, a ball dropped from the tall mast of a ship would
appear to fall behind the mast, as the ship and its mast spun forward with the Earth.
Since the Sun travels around the Earth in one day, the circumference of the Sun’s path
cannot be “too large”, else the Sun would need to be very fast. A star cannot be a ball
like the Sun else it would have to be very, very far away in order to look like a point.
And a very distant star would have to travel very fast (MUCH faster than the Sun) to
travel around the Earth in one day.
Using this sort of reasoning, Greek philosophers were uncomfortable with the idea of a
spinning Earth, and concluded that the Earth was not spinning, and that the Sun and the
stars really travel around the Earth.
We did not have direct evidence that the Earth rotates until 1851. Leon Foucault (French
physicist) demonstrated what is now called “Foucault’s pendulum”.
How did we learn the Earth is round?
Greek philosophers (like Aristotle) knew that when you walk south (away from
Polaris) new constellations appear on the southern horizon.
When a ship sails away from land, it appears to sink (to “fall over the edge?”);
when the ship comes back, it appears to rise from below the horizon.
During a lunar eclipse when the Earth is between the Sun and the Moon, and
when Earth’s shadow passes over the Moon, the shadow is ALWAYS part of a
circle. See astronomy picture of the day website (APOD), August 20 2008 for a
GORGEOUS composite picture of the Moon passing through the Earth’s shadow!
(Takes your breath away, doesn’t it?) (photo credit and copyright: Anthony
Ayiomamitis) Page 12 of 31
How and when did we discover how big the Earth is (i.e. its circumference, in meters for
instance)? The Greek philosopher Eratosthenes was the first to determine Earth’s
circumference, in about 240 B. C. E.
1) He knew (apparently) that, in the city of Syene (now called Aswan, Egypt), on
the summer solstice (the day on which the Sun rises and sets as far to the north
as it ever rises) the Sun stood directly overhead at its zenith. In particular, when
the Sun shone down a well, its reflection could be seen in the bottom of the
well, and the well’s walls cast no shadows.
2) In his city of Alexandria (which is north and a bit west of Syene), the Sun did
not stand directly overhead on the summer solstice. In particular, a vertical
stick-in-the-ground (a gnomon) cast a shadow. Page 13 of 31
stick-in-the ground casting a shadow
1 of a complete circle
The ratio of the shadow’s length to the gnomon’s height tells you the angle between the Sun’s
direction and the overhead direction. Eratosthenes measured this to be about 50 of a complete circle
(about 7 in modern units). This means that the distance between Syene and Alexandria (about 5,000
of the Greek units for distance - stadia) is about 50of the Earth’s circumference. We do not know
exactly how large a stadium (one stadium, two or more stadia) is in kilometres, but based on the sizes
of actual Greek stadia, one stadium and km are about the same distance. (Imagine McMahon
Stadium!) Consequently, had Eratosthenes used kilometres, he would have calculated a circumference
of about 40,000 km (which IS the Earth’s circumference.) Page 14 of 31
Syene to Alexandria
1 × circumference = 5,000 stadia (multiply both sides by 50)
1 circumference = 250,000 stadia (1 stadium = 6km )
= 250,000 1km
1 circumference ≈ 40,000 km
(The symbol “=” means equal; what could be more equal than two parallel lines of equal length?
That is literally why we use this symbol! And the symbol “ ” means “approximately equal to”.)
Circumference and diameter
You can measure the circumference of a circle (e.g. the cross-sectional shape of a beer can) by
wrapping a string around the circle, and measuring the required string-length. You can measure the
circle’s diameter by finding the biggest distance across the circle. Divide the (measured) circumference
by the (measured) diameter: the answer is approximately 3 for ALL circles. (In other words, you can fit
approximately 3 diameters around the outside of a circle.) Give this particular ratio a NAME: pi
(pronounced “pie”); it is given the Greek letteas a symbol.
π ≡ circumference , or
circumference = π × diameter ), or
circumference ≈ 3 × diameter )
The distance from the center of the Earth to its surface is half the diameter, o(or
about 1 of) the circumference).
The Earth’s radius is about 6400 km, or abou6.4×10 6 m. Page 15 of 31
Summary a) What does the expression “diurnal motion of the Sun and the
b) How can you use the diurnal motion of the Sun to define north and