School Science Lessons
2016-07-30 SP MF
Please send comments to: J.Elfick@uq.edu.au

36. Astronomy

Websites: Astronomy,

Table of contents

36.50.0 Astrology

3.0 Astronomy, (Primary)

36.36.0 Earth's motion

36.10.0 Gravitational attraction

36.1.0 Instruments

36.30.0 Measue distance

36.35.0 Measure time

36.44.0 Models

36.20.0 The Moon

36.10.0 The Sun

36.14.0 Stars & planets


36.40.0 Sundials

36.36.0 Earth, effect of the earth's motion
36.41.1 Circumference of the Earth using Polaris
36.42.3.1 Leap second

Experiments
36.41 Circumference of the Earth, Eratosthenes
36.21 Earth's axis of rotation, apparent daily rotation of the sky
36.39 Photograph star trails
36.38 Seasonal change of position of the Sun, solstice

36.1.0 Instruments for astronomy, telescopes
Telescopes, (Commercial websites)
Experiments
36.3.1 Astrolabe, simple theodolite, sextant
36.2.0 Simple reflecting telescope
36.1.0 Simple refracting telescope

36.30.0 Measuring distance
36.12.2 Great circles
36.42.2 Latitude, nautical mile, knots, log, logbook
36.71 Radio waves
Experiments
36.17 Azimuth, altitude, zenith and horizon, the horizontal system of co-ordinates
36.20 Equatorial system of co-ordinates, latitude and longitude

36.35.0 Measuring time, latitude and longitude
36.14.2 Light year, parsec
36.8.1 Equation of time
36.42.0 Equinox, precession of the equinoxes
36.42.1 Celestial equator, equatorial system, latitude and longitude
36.42.2 Latitude, nautical mile, knots, log, logbook
Longitude
Nautical mile, knot
Shackle
Fathom
36.42.3.1 Leap second
36.42.3 Longitude, Greenwich Mean Time, (GMT), Universal Time, (UT, UTC)
36.12.04 Meridians, Greenwich meridian
36.12.05 Period of rotation
36.12.4 Revolution and rotation
36.12.3 Ship's watches
36.12.02 Sidereal time
36.42.4 Time zones, Greenwich time, (GMT), Universal Time, (UT)
36.12.1 Tropical year

36.44.0 Models and demonstrations
Experiments
36.6.1 Find north with a watch compass, (clock compass)
36.6.2 Find north by the length of a shadow during the day
36.43 Find the north-south line from the Sun, Moon and stars
36.10.2 Make a model Earth with a balloon
36.10.1 Make a range finder
36.10.3 Make action-reaction engines
36.25 Make models of the solar system
36.47 The cause of the seasons

36.10.0 Observing the Sun
36.4.1 Declination of the Sun, angle of elevation of the sun
36.23 Ecliptic, Obliquity of the ecliptic, precession and nutation
36.3.02 Elements in the Sun, abundance of elements
36.35.1 Joshua's long day

Experiments
36.22 Ecliptic, apparent yearly path of the Sun
36.25 Make models of the solar system
36.33 Solar eclipse, eclipse of the sun
36.7.0 Sunrise and suns
36.14.0 Stars and planets
36.14.01 Stars and planets
36.16 Albedo
36.74 Aldebaran, Alpha Tauri
36.72 Alpha Centauri, (Rigil Kentaurus)
36.75 Arcturus, arctic, the Great bear
36.14.1 Diurnal aberration of a star
36.15 Magnitude
36.23 Ecliptic, obliquity of the ecliptic, precession and nutation
36.23a Observe planets
36.24 Pluto, Is Pluto a planet?
36.37 Pulsars
36.76 Supernova
36.73 The universe

Experiments
36.26.1 Falling stars, shooting stars, meteors, air resistance
36.14.0 Find constellations
36.18 Find constellations from north of the equator, Northern hemisphere
36.19 Find constellations from south of the equator, Southern Hemisphere
36.26 Morning Star and Evening Star, Venus
36.27 Planet movements in a jar

36.1.0 Simple refracting telescope
See diagram 36.65: Refracting telescope
Use two cardboard tubes, one fitting inside the other.
Fix a lens of focal length 2 cm as an eyepiece, mounted in a cork with a hole in it.
Fix a lens of focal length 25 cm in the wider cardboard tube.
Adjust both lenses to the same optical axis.
Focus by sliding the tube.
You can probably observe Jupiter's Moons, but not Saturn's rings.

36.2.0 Simple reflecting telescope
| See diagram 36.66.1: Reflecting telescope
| See diagram 36.66.2: Ray diagram
Make a simple reflecting telescope with a concave mirror, e.g. a shaving mirror.
Mount the mirror in a wooden box to tilt it at different angles.
Attach a wooden upright to the box to vary its angle of inclination.
Fix two short focus lenses in corks then put them in a short length of a mailing tube as an eyepiece.
Attach this eyepiece to the wooden upright and make the necessary adjustments.

36.3.1 Astrolabe, simple theodolite, sextant
See diagram 36.67: Astrolabe
Astrolabes were used to give approximate measurements of time, terrestrial measurement of heights and angles, and for navigation.
Astrolabes were used to make astronomical measurements, e.g. the altitudes of stars.
They were also a thing of beauty and are widely represented in art and many survive in museums.
The phrase "to shoot the Sun" means to use a sextant to measure the meridian altitude of the Sun, usually at midday.

Experiment
1. Make an astrolabe by attaching a drinking straw to the base line of a protractor.
Hang a plumb line from the head of a fixing screw to show whether the support is upright.
Use it to measure the elevation of a star seen through the drinking straw.

2. Make an improved model for finding the altitude and the bearing of a star, by fix the upright to a baseboard with a screw and two
washers, leaving it free to rotate.
Fix a piece of tin to the upright as a pointer to show the angle on a horizontal scale.

36.4.1 Declination of the Sun, angle of elevation of the sun
Declination = 23.44 sin [(360 / 365.242 19) × (286 + D)] = 23.44 sin [0.986, (286 +D)]
Assume 0o = the declination at the March equinox.
The number of days from the March equinox back to December 31 of the previous year = 286.
D = the day number, starting with day 1 on 01 January.
The declination over a year rises to the highest value at the June solstice and decreases to the lowest value at the December solstice.
The angle of elevation of the Sun on the meridian near noon = 90o - the angular difference between the declination of the Sun and the
latitude of the observer.

36.6.1 Find north with a watch compass, (clock compass)
During the twenty four hours from twelve noon to twelve noon the sun makes one complete circle, but the hour hand of a watch
makes two circles, so the distance travelled by the hour hand must be halved in the following methods.

In the Southern Hemisphere:
1. Hold the watch horizontal and point the 12 towards the Sun.
Hold a small stick, e.g. a matchstick, vertically next to the 12, then turn till the shadow of the stick passes through the centre of the
watch.
Imagine a line bisecting the angle between the line through the centre of the watch face and the hour hand.
This line is the north-south line.

2. Hold the watch horizontal and point the hour hand towards the Sun.
A line from the centre of the watch through a point midway between the hour hand and the number 12 will point south.
Before twelve noon, bisect the angle formed by going counter clockwise from the number twelve to the hour hand.
After twelve noon, bisect the angle formed by going clockwise from the number twelve to the hour hand.

3. Hold the watch horizontal.
Point twelve o'clock in the direction of the sun.
Bisect the angle between the hour hand and the twelve o'clock mark to get the north-south line.
The angle between number twelve and the hour hand indicates north.
North will be the direction closer to the sun, south the other way.

36.6.2 Find north by the length of a shadow during the day
In open country, moss grows mostly on the north side of trees in the Northern Hemisphere and on the south side of trees in the Southern
Hemisphere.
See diagram 36.6: Shadows from the Sun, Brisbane, 2009-07-27
Brisbane city, 2009-07-27, Latitude: -27o28', Longitude: 153o1, Height: 0.0 m
Time zone : + 10 hours.
Table 36.6.0
Time
Azimuth
Difference
Altitude
9.00
46o59'
.
27o04'
10.00
33o51'
13o08'
35o43'
11.00
17o17'
16o34'
41o30'
12.00
358o13'
19o.04'
43o19'
13.00
339o25'
18o48'
40o43'
14.00
323o27'
15o58'
34o21'
15.00
310o53'
12o34'
25o17'

Experiment
Use a large sheet of paper and a 50 cm stick fixed vertically on the paper.
Select an open space exposed to the Sun.
Mark the position of the base of the stick.
Every 15 minutes mark the position of the end of the stick's shadow and write the time of observation next to the mark.
Use a soft pencil to draw a curve linking the positions of the ends of the shadows.
Mark where the shadow was at minimum length.
Record the date.
Draw the position of true north.

36.7.0 Sunrise and sunset
Sunrise is the time when the upper part of the Sun appears above the horizon, i.e. when the zenith distance of the Sun is 90o50' and
decreasing.
Twilight is the period when the illumination of the sky increases after sunrise and decreases after sunset caused by the air molecules and
dust scattering sunlight.
Twilight lasts longer at higher latitudes because it depends on the steepness of the apparent path of the Sun.

Experiments
1. Draw an outline diagram of the eastern horizon as seen from a convenient location.
Name the main features of the outline, e.g. a big tree, a house, a hill.
Observe the eastern horizon just before sunrise on three occasions, one week apart.
Record the date, time, place and direction on the horizon of the Sunrise on the three occasions.
Mark the position of the Sun as it first appears over the horizon.
On the first morning continue to plot the path of the Sun each hour until 10.00 a.m.
Note any differences in the position of the Sunrise from day to day.
Note whether the Sun rises due east.
Use a compass to observe the direction of sunrise from the observation point.

2. Seasonal sunrise and sunset
2.1 Record the path of the Sun from sunrise to sunset on 22 December, 30 March, 22 June and 23 September.
2.2 Record the altitude of the Sun at different times and dates using the formula:
Tan altitude angle = length of shadow stick / length of shadow, (e.g. 1 January = 20o, 1 April = 47o, 1 June = 65o, 1 September = 52o)
2.3 At noon on 5 October a vertical stake casts a shadow.
Sketch where the tip of the shadow will be on 1 January, 1 April, 1 June, and 1 September.

3. See diagram 36.7.0: Sunrise
The Sun can be seen for a short time before and after it reaches the horizon, because a ray of light entering the atmosphere from space
has a curved path in the atmosphere.
The path is curved because the density of the atmosphere decreases with the altitude.
So when an observer first sees the Sun just above the horizon, would not have seen it if the light from the Sun had travelled in a straight
line.
Similarly, at the time of observed sunset, the sun has already "set" by a diameter roughly equal to the vertical diameter of the observed
Sun.

36.8.1 Equation of time
See 36.42.3: Longitude, Greenwich Mean Time, (GMT), Universal Time, (UT, UTC)
The time between two solar noons, when the Sun is due south or due north, is not exactly 24 hours.
However, for convenience, the length of a day is fixed as mean time.
So a changing difference exists between mean time and solar time.
The difference between time on a perfect clock and the apparent time on a sundial, apparent solar time, is called the equation of time.
The difference is caused by the eccentricity of the Earth's orbit and the obliquity of the ecliptic.
In northern Europe, the greatest difference is early in November when sundial time is about 16 minutes ahead of mean clock time.
So the mornings get half an hour more daylight than the afternoons.
Similarly in February, sundial time is about 14 minutes behind mean clock time, so the afternoons get a longer period of daylight than
the mornings.
Sundial time and mean clock time coincide, (the difference is zero), on or about 15 April, 14 June, 2 September, and 25 December,
when the clock and the sundial agree.
However, this equality occurs only in places on the exact meridian for which the time zone is set.
The Sun's movement eastwards relative to the distant stars varies throughout the year because the equator is not parallel to its orbit
round the Sun, but is inclined to it by 23.5 degrees to cause the seasons.
So seasons are NOT caused by the Earth's changing distance from the Sun.
Also, the Earth's orbit around the Sun is an ellipse.
Consistent with Kepler's Second Law, the Earth moves round the Sun faster when it is at its closest point, (early in January), then when
it is at its farthest point, (early July).
So in January , the Sun's apparent Eastward movement relative to the distant background stars is greater in January than in July, with
the consequence that the length of the solar day will be longer in January than in July.
Official clock time is based on the mean length of the solar day as averaged through the year.
So when the true solar day is shorter than the mean solar day, the sundial time will very gradually gain on the clock time.
However, when the true solar day is longer than the mean solar day, the sundial time will gradually lose on clock time.
GMT stands for Greenwich Mean Time, which is the mean solar time at the meridian of Greenwich, in London, which is generally
taken as the reference point for longitude on the Earth, and thus, by definition, has zero longitude.
The path of the Earth is east to west rotation, counter clockwise.

36.10.1 Make a range finder
See diagram 36.10: Range finder
1. Cut a slit in a square piece of cardboard and attach the square to a metre rule.
Place the end of the rule to the eye and move the card on the rule until a distant object just fits into the slit height.
Measure the following:
1.1 the slit height,
1.2 the distance along rule from eye to slit,
1.3 the estimated size of the distant object,
1.4 the estimated distance to the distant object.
2. Repeat the procedure for the full Moon.
The diameter of the Moon is 3 476 km.
The only unknown is the Earth's distance from the Moon.
Calculate the distance from the Earth to the Moon at different times of the year.
The average distance is 384 000 km, depending on its position in its elliptical path and the method of calculating an average.
For the full Moon, draw the slit height and rule length to scale.
Use a protractor to measure the angle shown and find the angular size of the full Moon.

36.10.2 Make a model Earth with a balloon
See diagram 36.11: Model Earth
1. Inflate a balloon to 20 cm in diameter.
Tie a knot at the entrance and use a marker pen to mark the knot with "N" to represent the north pole.
Mark the point opposite with "S".
1. Draw lines on the model Earth to represent the following:
1.1 the Greenwich meridian,
1.2 the international dateline,
1.3 the equator, the great circle that divides the Earth into Northern Hemisphere and Southern Hemisphere.
1.4 the closest longitude to the school,
1.5 the standard meridian for the local time zone, e.g. the standard meridian for a school in Brisbane, Australia is 150o east.
The 15o longitude is equivalent to one hour and 1.0 degrees every four minutes (4 X 15 = 60).

2. Mark an Earth balloon to show:
the equator,
the standard meridian through Greenwich,
the International Date line,
the Tropics of Cancer and Capricorn.
 Longitude and latitude:
Brisbane is Latitude: -27o28', Longitude: 153o1'.

36.10.3 Make action-reaction engines
See diagram 7.52: Balloon boat and rocket
1. Make a balloon-powered boat.
Cut away one side of a cardboard box and make a hole in the bottom near the edge.
Insert a tube into the hole and attach the balloon to it.
Inflate the balloon and place the boat in water.
Note the direction the boat moves as air leaves the balloon.
Repeat the experiment with the open end of the tube under surface water.
2. Make a balloon-powered rocket.
Attach a drinking straw to the side of a long balloon with adhesive tape.
Pass a wire through the drinking straw, attach each end of the wire to fence posts and tighten the wire.
Inflate the balloon then release it.
The balloon travels along the wire.
3. Discover action-reaction on roller skates.
Put on a pair of roller skates and throw a large ball over the head to another student.
Note the direction in which the other student moves.
Repeat the experiment with both students on roller skates.

36.12.01 Zone time
Zone time is the local mean time of the standard meridian for the zone.
The standard meridian for Brisbane, Rockhampton, Mackay, Townsville and Cairns is longitude 150o E.
So all these locations have the same zone time.
However, the local mean time varies with the observer's longitude.
For example, Brisbane, Rockhampton, Mackay, Townsville and Cairns have different local mean times because they are situated at
slightly different longitudes.
Local apparent time, as kept by a sundial, differs from local mean time because the Earth's orbit is an ellipse and its linear velocity varies
during a year.
The equation of time, (EOT), is the difference between local apparent time, (LAT), and local mean time, (LMT), i.e. the difference
between mean solar time from a clock and apparent solar time from a sundial.
The difference is caused by the eccentric orbit of the Earth and the obliquity of the ecliptic, now about 23o26', but regularly changing
over a period of 40 000 years.
There is no difference between LAT and LMT on 15 April, 14 June, 1 September and 25 December,  but the difference may be as
much as 16 minutes.
Usually, each geographic time zone within a country differs by 15o of longitude, unless determined by a political decision, as in
Queensland, Australia.

36.12.02 Sidereal time
Sidereal time is time related to the movement of the Earth with respect to the stars, not the Sun.
Sidereal time is the right ascension, (RA, alpha), of an object on the meridian of the observer, i.e. the angular distance from the vernal
equinox, (spring equinox), (First Point of Aries), to where the great circle passing through both celestial poles and an object meets the
celestial equator, expressed as time or angle.
One hour of right ascension = 15o.
A sidereal day is 23 hours 56 minutes and 4.091 seconds of mean solar time, i.e. the time for each rotation of the Earth spinning on its
axis at almost a uniform rate of spin.
This is the time it takes for the distant stars to return to the same position in the sky or time taken by the Earth to complete one rotation
relative to the vernal equinox.
However, when astronomers take into account the movement of the vernal equinox that precesses westwards to complete one
revolution about every 26,000 years, the term "stellar day" is used to describe the true sidereal period of the Earth's rotation relative to
the fixed stars.
The Earth spins on its axis at an almost uniform rate, taking 23 hours, 56 minutes, and 4 seconds for each rotation.
This is known as a sidereal day, and is the time it takes for the distant, ("fixed"), stars to return to the same position in the sky.
A sidereal month, the time the Moon takes to complete one revolution around the earth with respect to the stars, is 27.322 mean solar
days.
A sidereal year, (astral year), is 365.25636 mean solar days, (365 days, 6 hours, 9 minutes, and 9.6 seconds).

36.12.04 Meridians, Greenwich meridian
See diagram 36.11: Model earth
The celestial meridian, is the great circle that passes through the north pole, south pole and the observer's zenith, cuts the horizon at the
north and south points.
The standard meridian is through Greenwich.
The International Date Line is from the north pole to the south pole along the meridian, 180o from Greenwich.

36.12.05 Period of rotation
The period of rotation of a solid astronomical object is the time taken to complete one revolution about its axis of rotation relative to the
stars.
However, it is different from a solar day, which is relative to the Sun.
The period of rotation of fluid objects, e.g. the Sun and Jupiter, varies from across the fluid object's equator to near its poles because
of the differential rotation of different parts of the fluid body.

36.12.1 Tropical year
The astronomical, equinoctial, natural, solar, tropical year is the time taken by the Sun to return to the same equinox, the length of time
between successive March equinoxes, and has mean length of 365 days 5 hours 48 minutes and 46 seconds, 365.242 199 days.
The tropical year is the basic year for the calendar, so it is the calendar year.

36.12.2 Great circles
A great circle is a line on the surface of a sphere that lies on a plane through its centre, or lies on any circle that divided the sphere into
two equal parts.
So the shortest distance between two points on the Earth's surface is on a great circle.
The equator and all lines of longitude are great circles.

36.12.3 Ship's watches
12 00 to 16 00 hours, the afternoon watch
16 00 to 18 00 hours, the first dog watch
18 00 to 20 00 hours, the second dog watch
20 00 to 24 00 hours, the middle watch
04 00 to 08 00 hours, the morning watch
08 00 to 12 00 hours, the forenoon watch

36.12.4 Revolution and rotation
Revolution describes the motion of one body around another.
For example, the Earth revolves around the Sun.
Rotation describes the spinning of a body on its axis.
For example, the earth rotates every 24 hours.

36.14.0 Find constellations
See diagram 36.92: Old 35 mm slide used for teaching about constellations
1. Find the constellations during new Moon when there is no moonlight.
Prepare a piece of brown paper with pinholes pricked through as constellations.
Hold the brown paper up to a light so the pinholes become visible and  rotate the brown paper to recognize a similar star pattern.
The stars appear to make one full revolution every 24 hours and one full revolution each year.
So the constellations cannot be seen in the same position at different times of the night and at different times of the year.
The north celestial pole and the south celestial pole are points in the sky that do not move and around which the stars appear to rotate.
 In the Northern Hemisphere, stars seem to revolve around the Pole Star, Polaris, but in the Southern Hemisphere there is no star that
the other stars seem to revolve around.
2. Record the positions of the main constellations at 8.00 pm standard time and date, e.g. Southern Cross is high in the south west,
Scorpius is very high in the east.
3. Perforate underexposed and discarded 35 mm film slides with a pinpoint as constellations then project them on a screen or view them
at the end of a cardboard tube held up to the light.

36.14.01 Stars and planets
A star is a generally spherical-shaped gaseous body, which is luminous because of its internal nuclear reactions, e.g. the Sun.
A planet may be a rocky or gaseous body that revolves in elliptical orbits around the Sun and can be seen by reflected light.
In order of increasing distance from the sun, the major planets are Mercury, Venus,  Earth, Mars,  Jupiter, Saturn, Uranus, Neptune,
(Pluto).
In astrology, the movements or relative positions of the Sun, Moon and the planets affect the lives and destinies of people in some
mysterious way.
The "Earth" may be known as "Planet Earth".
A planetarium, orrery, is a building containing a mechanical model  that describes the  movement of  plants and stars relative to the Sun.
A group of fixed stars, given a traditional name as seen from the Earth is called a constellation, e.g. the Southern Cross Constellation.
However, the stars in the constellation are in no way associated or near each other.

36.14.1 Diurnal aberration of a star
An observer at the equator can observe a movement of any star to the east at a rate of 0.32 seconds of arc per day, caused by the
rotation of the Earth on its axis.
However, that observed movement reduces to zero as the observer approaches the poles.
Diurnal aberration of a star is the direct evidence that the Earth is not fixed in space.

36.14.2 Light year, parsec
1. The light year, ly, is distance light travels in a year, 9.46 × 1012 km, (5.88 × 1012 miles).
The speed of light is 2.99792458 × 108 ms-1.
The usual value used = 3 × 108 ms-1.
2. Large distances can be measured by the time light takes to move that distance.
The velocity of light is about 300 000 km per second in a vacuum.
So the distance travelled by a "ray" of light in one year =
300 000 × 365 days, 24 hours × 60 minutes × 60 seconds = 9 460 800 000 000 km.
However, based on 365.25 Julian calendar days, each of exactly 24 hours, a light year =
9, 460, 730, 472, 580.8 km or 9.46 × 1012 km, (5.88 × 1012 miles).
The Sun is about 8 light minutes from the Earth.
The nearest star, Proxima Centauri, is about 4.3 light years from the Earth.
The Andromeda galaxy, the nearest galaxy to the Milky Way galaxy containing the Earth, is about 2.5 light years from the Earth.
Four galaxies can be seen from Earth.
Only in the Northern Hemisphere, the Milky Way galaxy and Andromeda galaxy (M31) can be seen.
Only in the Southern Hemisphere, the Large and Small Magellanic Clouds can be seen.
3. Astronomers use the parsec, pc.
It is about 3.2616 light years, i.e. 30,857,000,000,000 km.
The nearest star to Earth is the double star Alpha Centauri at distance 4.37 light years, ly, (1.34 pc).
4. An arcminute, (minute of arc, minute of angle, MOA) = 1 / 60 degree, is used in the firearms industry.
5. An arcsecond = 1 / 60 arc minute, (one degree, 1o = 3 600 arcseconds), is used by astronomers.

36.15 Magnitude
The magnitude measures the brightness of stars.
About 150 B.C. the Greek astronomer Hipparchus classified stars by their brightness with the brightest star at "magnitude 1" and the
faintest star that could just be seen at "magnitude 6".
One hundred stars together of "magnitude 6" are as bright as a single star of "magnitude 1".
For each change in level of magnitude the light energy or brightness decreases by about 2.5,
(more exactly, the fifth root of 100 = 2.512).
The faintest visible star from the Earth is about "magnitude 30".
Sirius, Venus and the Sun are so bright that they have negative magnitudes.
The "apparent magnitude" is as seen from the Earth.
The "absolute magnitude" is the brightness adjusted for the distance from the Earth.
Ancient astronomers named some stars, e.g. Sirius and Rigel.
Other star names show the constellation to which a star belongs and the order of brightness of the star in the constellation using the order
of letters of the Greek alphabet.
For example, the brightest star in the constellation Crux, (Southern Cross), is Alpha Crucis.
The "pointers", Alpha Centauri and Beta Centauri, are the brightest stars in the constellation Centaurus.
All known stars are listed in catalogues by a code number.
For example, Sirius has code number "AE41".

36.16 Albedo
Albedo is a measure of reflectivity or brightness, the reflecting power of a non-luminous body.
Albedo = 1, for a perfectly reflecting white body.
Albedo = 0, for a perfectly absorbing black body.
The average albedo of the earth's surface is about 33% and varies from about 50% for snow to about 10% for a dark forest or bitumen
road.
So a low albedo surface will get hotter in sunlight than a high albedo surface.
To calculate the percentage reflectance, (albedo), of the surface, (R%), R% = (UVReflected / UVTotal) × 100.
Albedo is also used to express the fraction of the Sun reflected by bodies in the solar system.
For example, the Moon has a low albedo, while cloud-covered Saturn has a high albedo.

36.17 Azimuth, altitude, zenith and horizon, the horizontal system of co-ordinates
See diagram 36.17: Altitude and azimuth
Zenith is a point immediately overhead an observer.
The opposite point is the nadir.
Azimuth is the clockwise horizontal angle, (in degrees, minutes and seconds), from true north to the Sun or Moon.
The azimuth is its angle measured eastwards from north in a horizontal plane, i.e. the horizontal angular distance of an arc passing
through the celestial object.
Altitude is the vertical angle, (in degrees minutes and seconds), from an ideal horizon, to the Sun / Moon.
The altitude of a celestial object is its angular elevation from the horizon from 0o on the horizon to 90o at its zenith.
Note that altitude and azimuth defines the position of a point in the sky only at a certain time.
The horizon is ideal when the surface forming the horizon is at a right angle to the vertical line passing through the observer's position on
the Earth.
If the terrain surrounding the observer was flat, and all at the same height above sea level, the horizon seen by the observer standing on
the Earth would approximate the ideal horizon.

Experiment
Point your extended arms north-south, with your extended right arm pointing due south.
Start from your extended left arm pointing due north to observe the azimuth of a celestial body, e.g. a star has an azimuth of one hand
span clockwise from north and its elevation is two hand spans above the horizon.
Show the position of this star on a sky diagram.
Measure the positions of the Sun during the day and record them on the sky diagram.
Make tables of positions from the sky diagram.
For example, 5 p.m. 11 March 2006, Sirius azimuth 10o, elevation 70o, Aldebaran azimuth 320o, elevation 30o, Rigel azimuth 330o,
elevation 60o, Betelgeuse azimuth 340o, elevation 40o.

36.18 Find constellations from north of the equator, Northern Hemisphere
See diagram 36.71.1: Northern Hemisphere constellations
For the Northern Hemisphere, the pole star, Polaris, (north star, lodestar), will be very close to the north celestial pole.
So in the Northern Hemisphere, the stars appear to revolve around it.
1. To find constellations in the October sky, turn the diagram through 90o, so that the Big Dipper is lowest.
Hold the diagram as a map above your head with its face down.
2. Find the most obvious constellation, Ursa Major, (the Big Dipper, the Plough, the Great Bear), which contains seven stars.
3. Extend a straight line through the two stars that form the front edge of the dipper cup to find the pole star, Polaris.
4. The two dippers, (two bears), are the Big Dipper, (Great Bear, Ursa Major), and the Little Dipper, (Little Bear, Ursa Minor).
The pole star is the last star in the "handle" of the Little Dipper.
The Little Dipper appears to "pour" into the Big Dipper.
5. The four stars of Pegasus, the mythological winged horse, form a box.
The north-east star belongs to the constellation Andromeda.
Find Pegasus by continuing the straight line from the two stars that form the outer edge of the Big Dipper cup through and beyond the
pole star, Polaris.
6. Find the Cassiopeia constellation opposite the Big Dipper beyond the pole star.
It forms the letter W and is known as "Cassiopeia's Chair".
7. The constellation Orion, the "great hunter" contains three bright stars in a line, the "Orion's Belt".
Below the "belt" are three fainter stars, the "sword".
8. Observe Venus, known as the "morning star", "day star" and "evening star".
Note when it rises or sets in respect to sunrise or sunset.

36.19 Find constellations from south of the equator, Southern Hemisphere
| See diagram 36.71.2: Southern Hemisphere constellations
| See diagram 36.73: Southern Cross constellation
1. To find constellations in the December sky, hold the diagram as a map above your head with its face down.
For the Southern Hemisphere, start with the Southern Cross constellation to find the south celestial pole.
Extend the longer axis × 3.5, then drop vertically to the horizon.
South of the equator, the stars appear to revolve about a point in the sky, the south celestial pole.
There is no star at the south celestial pole.

2. Find the south celestial pole from the Southern Cross constellation and the two pointers.
Imagine a perpendicular bisector of the pointers.
Where this line crosses an extension of the largest diagonal of the Southern Cross constellation is the south celestial pole.
A point on the horizon exactly below the south celestial pole is due south from you.

3. The kite-shaped Southern Cross constellation, Crux, is almost surrounded by Centaurus.
Crux is the smallest constellation.
Its stars are as follows:
Alpha, (α, Acrux,), is the brightest in the constellation, magnitude 0.77, and about 320 light years away,
Beta, (β, Mimosa, Becrux), is magnitude 1.2,
Gamma, (γ, Gacrux), is magnitude 1.6,
Delta, (δ), is magnitude 2.8,
Epsilon, (ε), is magnitude 3.6.

4. At the beginning of December, see the constellation Crux, (the Southern Cross), low down on the southern horizon at midnight.
Two "magnitude 1" bright stars, Alpha Centauri and Beta Centauri, known as the pointers, are almost in line with Gamma of the
Southern Cross towards the south-west.
Alpha centauri, (Rigel Kentaurius), is the pointer farthest away from the Southern Cross and is the brightest star system in the
constellation of Centaurus.
It is called a "star system" because it was known to be a double star, but lately a third star has been found.
It is famous because it is the nearest "star" to Earth at 7.39 light years.
The pointers to the Southern Cross constellation cannot be seen from the Northern Hemisphere.

5. Follow the milky way to the north of the Southern Cross to find the Canis Major constellation, (the great dog).
This constellation contains Sirius, (the dog star).
Sirius is the brightest star in the sky, with magnitude -1.44, distance 8.6 light years away and luminosity 22 × luminosity of the Sun.
A few stars are nearer to the Earth than Sirius.
North of Canis Major find the constellation Orion.
It can also be seen from north of the equator.

36.20 Equatorial system of co-ordinates
Latitude and longitude, declination and right ascension, zenith, star chart for the tropics
1. For the identification of stars, imagine them to be on the inside of a sphere, the celestial sphere, that is concentric with the Earth.
The pole star is about at the north pole of the celestial sphere and is almost directly above the north pole of the Earth.
The celestial equator circles the celestial sphere directly over the equator of the Earth.

2. Identify the position of a point on the surface of the Earth by its latitude and longitude.
The latitude of a point is the angular distance north or south of the equator, e.g. latitude 45o S.
The longitude, the meridian, is the line joining the north and south poles and passing through the point.
The 00 longitude, the Greenwich meridian, passes through the north pole, Greenwich in England, and the south pole.

3. Identify the position of a star on the celestial sphere by its declination and right ascension.
The declination corresponds to latitude and is measured north and south of the celestial equator.
The right ascension corresponds to longitude.

4. The zenith is a point on the celestial sphere immediately overhead an observer, 90o from the horizon.
The pole star would be at the zenith of an observer at the north pole of the Earth.
At about midday on 15 May the Sun would be at the zenith of an observer in a place of latitude 200 N.

5. The tropics are parallels of latitude 23o26' north of the equator, the tropic of Cancer or south of the equator, the tropic of Capricorn.
North of the equator, the tropic of Cancer marks the most northerly declination of the Sun at the summer solstice, about 21 June.
The declination is the angular distance of a celestial object north or south of the celestial equator.
Positive towards the north celestial pole and negative towards the south celestial pole.
South of the equator, the tropic of Capricorn marks the most southerly declination reached by the Sun, about 22 December.
A star chart for the tropics represents that part of the celestial sphere that an observer on the Earth's equator would see.
It extends from 35o N to 30o S.
Orion's belt, when visible, gives an approximate east west direction and the line joining the midpoints of the shorter sides of the Orion
quadrilateral gives a guide to the north-south direction.
The distances are measured in angular degrees and the equator is divided roughly into months.
Each date sets the chart at midnight for an observer on the equator, i.e. whose zenith is on the equator.

36.21 Earth's axis of rotation, apparent daily rotation of the sky
See diagram 15.0.4.1: Axis of rotation of the Earth
1. Choose a place where you have a clear view of the sky, including parts close to the horizon.
Find your north or south celestial pole.
Fix a plumb line so that it appears to go through the celestial pole.
Note where the lower end of the plumb line appears against the stars.
Draw a line on the star chart to represent this position of the plumb line, and note the time to the nearest minute.
Make the same type of observation two hours later.
Mark a second line on the star chart and note the time to the nearest minute.
Record the calendar date.
Note whether the sky appears to turn clockwise or anticlockwise.
Measure the angle in degrees between the two lines with a protractor.
Calculate the change in degrees per hour.
Calculate the time required for one complete rotation, 360o.
You can also do this with photographs of star trails.

2. Identify a prominent constellation and sketch its position relative to a prominent landmark, e.g. a big tree.
Note the time.
Make the same observation and sketch two hours later.
Calculate the change in degrees per hour.
Calculate the time required for one complete rotation, 360o.
3. Repeat the above observations one month later.
4. Observe the diurnal aberration of a star.
An observer at the equator can observe a movement of any star to the east at a rate of 0.32 seconds of arc per day because of the
rotation of the Earth on its axis.
However, that observed movement reduces to zero as the observer approaches the poles.
The diurnal aberration of a star is the direct evidence that the Earth is not fixed in space.

36.22 Ecliptic, apparent yearly path of the Sun
The ecliptic is the apparent yearly path of the Sun against the background of stars.
It is the great circle of the celestial sphere representing the apparent path of the Sun during a year.
The ecliptic is an imaginary line based on the Earth's motion about the sun.
The ecliptic is in the middle of the Zodiac.
The name ecliptic refers to the observation that eclipses of the Sun or the Moon can occur only when the Moon is close to this
imaginary circle.
Each day the position of the Sun moves East.
The ecliptic is a line but in practice it is thought of a narrow band each side of the ecliptic.
So the ecliptic is a circle on the celestial sphere where the celestial sphere is cut by the orbit of the Earth.
The ecliptic intersects the celestial equator at the two equinoxes.

Experiment
On consecutive days, note the position of the Sun against the stars just before the Sun rises and just after the Sun sets.

36.23 Ecliptic, obliquity of the ecliptic, precession and nutation
The obliquity of the ecliptic is the angle between the plane of the ecliptic and the celestial equator, or the angle between the axis of
rotation of the Earth and the pole of its orbit.
It is responsible for the seasons.
The "True Obliquity" on 2009.12.15 was 23o 26' 19.731', i.e. 23.438814199o, 23.44o.
It varies from 21o55' to 28o18'.
It is caused by precession and nutation.
The term "precession" comes from description of the movement of the Earth.
Precession is the rotation of the axis of a spinning body about another axis caused by a torque acting to change the direction of the
first axis.
The precession of the Earth is caused mainly by the gravitational pull of the Sun and the Moon on the equatorial bulge of the Earth, that
is 43 km diameter wider than the pole to pole diameter.
Other planets have a small effect, but in the opposite direction, so the total effect is called the general precession, with a decrease of
about 50 arc seconds per year, about 1o every 72 years.
These gravitational pulls constitute a torque so that the axis of the Earth traces a circle in the sky like a wobbling spinning top.
The axis completes a circle in about 25, 800 years.
Nutation is a periodic oscillation of the axis of the Earth caused by the relative changing positions of the Sun, Moon and Earth.
On 2009.12.15 the "Nutation in obliquity" was +02.942 = +0.000817294o.
If the Earth did not spin, the gravitational forces of the Sun and Moon would pull the Earth "upright" and the Sun would be in line with
the equator.
36.23a Observe planets
The planets visible to the unaided eye are Mercury, Venus, (Earth), Mars, Jupiter and Saturn.
Planets look like stars, but, if using telescope, Uranus and Neptune appear as tiny discs.
Stars are usually shown to magnitude 5 on star charts as a compromise between as seen in light-polluted skies of a city and dark
country skies.
In Australia, star finder charts are usually prepared for Canberra, but they are useful for elsewhere in Eastern Australia.
In Canberra, in 2016, Daylight Savings Time ends on Sunday 3 April and begins on Sunday 2 October.
The apparent close encounter between Venus and Jupiter near the end of August 2016 provides an opportunity for observing planets.
Venus and Jupiter will be about one Moon width apart (30 arc minutes) and they will be easy to see above the western horizon
without a telescope as evening twilight ends.
This movement is caused by the combined effect of the movements of the planets in their orbits and the movement of the Earth in its
orbit.
Students may not know that they can see planets in the sky without a telescope.
Also,they may not know that they can watch the planet move over a few days of observation.
The word "planet" comes from the Greek planan wander.

36.24 Is Pluto a planet?
As at 24 August 2006, the International Astronomical Union, IAU, demoted Pluto as a planet.
The IAU voted to redefine Pluto as a "dwarf planet" along with the "body, UB313" outside Pluto, (and bigger than Pluto), Pluto's
Moon Charon, and Ceres, (the biggest asteroid between Mars and Jupiter).
The IAU stated that planets must be large enough to "clear the neighbourhood" around their orbits, must be in orbit around a star while
not being a star, and must be large enough in mass for their own gravity to pull them into a nearly spherical shape.
So in the model of the solar system, you may delete Pluto as a planet and / or insert the dwarf planets, Pluto, Ceres, and Eris.
Exoplanets are planets outside the solar system.
By 2012, more than 700 exoplanets have been identified.
They are of interest to the search for a planet similar to Earth that may contain life or some form of life form.
Some school children have protested at the demotion of Pluto from its planet status!

36.25 Make models of the solar system
Make models of the solar system to understand the relative size and  distance of the planets from the Sun.
Make two separate models showing:
1. The relative size of the planets,
2. The relative distances of the planets from the Sun.
Make paper circles or balls to represent the Sun and planets using the table below.
The figures in parentheses give a scale for distances, taking the Earth's average distance from the Sun and the Earth's diameter as units.
The Sun is about 1 400.000 km in diameter (110).
Attach the models to the wall of the classroom.
An astronomical unit, AU, is the mean distance of the Earth from the Sun, about 149 597 870 km, 1.496 X 108 km,
(approximately 93 million miles).
It is used as a convenient way to measure distance in the solar system.
Table 36.25 Models of the solar system
In the table , Distance = average distance from the Sun (in millions of km) and AU = distance in Astronomical Units
Planet Average Distance from the sun Equatorial Diameter
Mercury 58 million km, (0.4) AU 4 878 km, (0.4) AU
Venus 108 million km, (0.7) AU 12 104 km, (1.0) AU
Earth 150 million km, (1.0) AU 12 756 km, (1.0) AU
Mars 228 million km, (1.5) AU 6 795 km, (0.5) AU
Jupiter 778 million km, (5.2) AU 142 985 km, (11.2) AU
Saturn 1 420 million km, (9.5) AU 120 537 km, (9.5) AU
Uranus 2 870 million km, (19.2) AU 51 119 km, (3.7) AU
Neptune 4 490 million km, (30.1) AU 50 538 km, (4.1) AU
Pluto 5 900 million km, (39.5) AU 2 320 km, (0.2) AU

36.26 Morning Star and Evening Star, Venus
See diagram 36.26: Transit of venus
Observe the planet Venus and note when it rises or sets in respect to sunrise and sunset.
Recently, a pilot of a passenger aeroplane awoke from a scheduled sleep, saw Venus, and put the aircraft into an emergency dive
because he thought Venus was an approaching aircraft on fire!

36.26.1 Falling stars, shooting stars, meteors, air resistance
Note the position, time and date of "falling stars" or "shooting stars", i.e. meteors.
A small rock in space is called an asteroid.
If it enters the Earth's atmosphere and starts to burn, it is called a meteor.
The unburned remainder of a meteor, if found on the ground, is called a meteorite.
Most meteorites contain iron-nickel minerals, but they may also be composed of carbon, iron carbides and sulfides, oxides, phosphides.
and silicates.
Particles of matter penetrating the earth's atmosphere are always moving with very high velocities.
When they enter the atmosphere, they experience a very great air resistance to cause a reduction of velocity and the kinetic energy lost\
is transformed into heat.
The temperature of the matter may rise thousands of degrees and it becomes luminous.

36.27 Planet movements in a jar
Use a tall, narrow jar, some water, S.A.E. 30 grade motor oil, 90% alcohol, and a pencil.
Half fill the jar with water.
Slowly pour alcohol on top of the water.
Do not agitate the two liquids or you will disturb the interface.
Dip a pencil into the motor oil, and let several drops of the oil fall into the liquid filled jar.
Gently rotate the jar to cause the oil drop "planets" to revolve.
Alcohol has a lower density than water, so it floats on the water.
Oil sinks in alcohol, yet floats on water.
In such a "free" state, the oil forms spheres and stays at the interface between alcohol and water.

36.33 Solar eclipse, eclipse of the sun
Solar View Glasses, (Commercial)
See diagram 36.84: Solar eclipse
An eclipse occurs when a hypothetical straight-line can be drawn through the centres of the Sun, the Earth and the Moon, i.e. they all
line up.
Solar eclipses occur when the Moon in its orbit around the Earth passes between the Sun and Earth (Sun-Moon-Earth), with the
shadow of the Moon falling on the Earth (new moon).
The Moon's orbit is inclined 5o to the ecliptic, (orbit of the Earth), so that a solar eclipse does not occur at each new moon.
However, when a new Moon is within 17o of a node, (its orbit crossing the ecliptic), a solar eclipse occurs somewhere on the Earth.
Each year two to five solar eclipses occur.
The maximum time for a total eclipse is 7.5 minutes.

Experiments
1. By observing eclipses you can learn about the shape, size, and motions of the Sun, Moon, and Earth.
The coming dates of eclipses are in newspapers and almanacs so you can plan to be outdoors when an eclipse occurs in your area.
Be careful! Do not allow students to look directly at the eclipse with the naked eye or through smoked glass or exposed photographic
film.
2. One safe method of observing an eclipse is to view it indirectly.
Punch a hole through a piece of cardboard.
Turn your back to the Sun and  hold the cardboard over one shoulder to permit the Sun's image to shine through the hole on to a second
piece of cardboard held in front of you.
Be careful! Do not look at the Sun through the hole in the cardboard.
3. The sun is represented by an opal electric bulb shining through a circular hole 5 cm in diameter in a piece of blackened cardboard.
The corona is drawn in red crayon around this hole.
The moon is a wooden ball, 2.5 cm diameter, mounted on a knitting needle.
The observer views the eclipse through any of several large pin holes in a screen on the front of the apparatus (see diagram).
The corona becomes visible only at the position of total eclipse.
The moon's position is adjusted by a stout wire bicycle spoke attached to the front of the apparatus.

36.35 Rotation period of the Sun, sunspots
See diagram 36.86: Using binoculars
Sunspots are relatively cooler regions caused by the Sun's magnetic field coming to the surface as solar activity including solar flares and
solar storms.
They usually last for less than a month and are most common every 11 years.
The solar rotation period varies with the latitude of the gaseous and at the equator is about 26.25 days.
Sunspots move from left to right across the Sun.
Sunspots are used to measure solar rotation because they turn with the Sun.

Experiments
1. Find the rotation period of the Sun and the direction of its axis by observing the position changes of sunspots.
Use a small telescope or binoculars, a large box, a clipboard, paper and pencil.
Be careful! Do not look directly at the Sun through this instrument.
2. Mount binoculars in the front end of a box.
Make a sunshade for a telescope.
Leave one long side of the box open for viewing.
Elevate the box so that the front end is perpendicular to the direction of the Sun's rays.
Put the clipboard with attached paper inside the box at the back end so that the solar image can be projected on it.
Make observations each day at noon.
Draw a circle and mark in the position of any sunspots.
Show their relative sizes and approximate shapes.
From day to day, the sunspots will appear to change position as the Sun rotates.
Measure the differences between several daily sketches to estimate the rate of motion.
After some weeks a sunspot group may return or new sunspot groups may appear.

36.35.1 Joshua's long day
In the Authorized Version, (King James Bible), the following three verses occur in Joshua Chapter 10:
" 12 Then spake Joshua to the Lord. Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon.
13 and the sun stood still, and the Moon stayed, until the people had avenged themselves upon their enemies.
So the sun stood still on the midst of heaven, and hasted not to go down about a whole day.
14 and there was no day like that before it or after it."
This event is known as "Joshua's long day" or "the day the earth stood still".
Similar long days have been reported in the ancient records of the Incas, Aztecs, Chinese kingdom of Yao and in an Egyptian temple as
reported by Herodotus.
However, no scientific evidence exists for the event occurring during the time of Joshua or any other time.
Also, NASA has not proved that the events did occur, despite rumours to the contrary.
There are only two possible explanations for the Sun to stand still in the sky for a day but there is no evidence for either explanation ever
occurring:
1. the Earth would stop spinning on its axis,
2. the Sun would start moving in the solar system in a way that it appears to us on the Earth to be standing still.

36.37 Pulsars
A pulsar is a tiny and brilliant neutron star.
It is probably like a black hole because it is the last stage of a supernova explosion.
The rotational axis and magnetic axis are misaligned causing regular pulses of energy as light and radio waves like a lighthouse flashing
beam, which can be detected as a clacking noise and act as a very accurate clock about every 0.03 seconds.

36.38 Seasonal change of position of the Sun, solstice
See diagram 36.38: Shadows
A summer solstice is when the Sun reaches the farthest point north of the equator, at about 22 December, the longest day in the
Southern Hemisphere.
A winter solstice is when the Sun reaches the farthest point south of the equator, at about 22 June, the longest day in the Northern
Hemisphere.
These two points of the ecliptic are midway between the equinoxes.
A summer solstice occurs at the time of the longest day, and reaches the highest point in the sky at noon, at about 21 June in the
Northern Hemisphere and at about 22 December in the Southern Hemisphere.
A winter solstice occurs at the time of the shortest day, and reaches the lowest point in the sky at noon, at about 22 December in the
Northern Hemisphere and at about 21 June in the Southern Hemisphere.
The Sun reaches its extreme northern and southern points on the ecliptic and appears to stand still before it reverses its apparent course.
These two points of the ecliptic are midway between the equinoxes.
The hours of light and darkness become the same a few days before the spring equinox and a few days after the autumn equinox.

Experiments
1. From a fixed location with a good view, note accurately the point where the Sun disappears behind landmarks as it sets.
Repeat the observations at intervals of a week for four weeks at least, and find the rate of change in degrees per day.
To measure degrees, a clenched fist at arm's length covers about 10 degrees of the sky, (10o), and a thumb covers about 2 degrees
of the sky, (2o).

2. Mark a line on the floor or the wall where the Sun shines in your room and makes a shadow's edge.
Note the exact month, day and hour.
At the end of each week make another line at the same hour.
Repeat this throughout the year to obtain an interesting set of observations.
The variation in position of the line from week to week and from month to month is caused by the movement of the Earth around the
Sun.

3. In an open space, drive a 150 cm vertical thin rod, the gnomon, into the ground.
Mark a north-south line on the ground from the base of the gnomon.
Record the length of the shadow of the gnomon at different times of the day and at different seasons of the year.
Note whether the noon shadow is north or south of the north-south line.
Mark the position of the end of the shadow at noon each day.
By the end of a year, join the positions to form a figure eight, an analemma.
The highest position is at the summer solstice and the lowest position is at the winter solstice, caused by the axial inclination of the Earth.
The variation across the short axis is because of the eccentricity of the orbit of the Earth.

36.39 Photograph star trails
See diagram 36.90: Star trails around the north celestial pole
Star trails at the equator are almost straight lines.
1. Photograph star trails as the Earth revolves.
Wait for a clear moonless night where you can see the horizon.
Avoid a place with extraneous light, e.g. motor car headlights.
Face the camera on a tripod at a celestial pole, i.e. pole star or south celestial pole.
Record the time.
Focus for infinity, open the diaphragm to full aperture, set the shutter for time exposure and  start the exposure.
Leave the camera with the diaphragm open for two hours.
Close the shutter for two minute without moving the camera then open the shutter again for one minute and finally close it.
The last short exposure identifies the end of the exposure.
Record the time.

2. The developed film show star trails as concentric arcs with centres at the celestial pole.
Measure the longer arcs to show how many degrees of rotation occurred and use this to calculate the period of full rotation.
Each star near the pole traces a tight circle in its movement, and as the distance from the pole increases, the radius of curvature
increases until the stars above the equator appear to travel in straight lines.
3. Record the apparent path of the Moon by taking two seconds exposures every fifteen minutes until the Moon moves out of the field
of the camera.
4. Record the apparent path of the Sun during the day with the lens stopped down.
Be careful! Do not look at the Sun through the viewfinder.

36.41 Circumference of the Earth, Eratosthenes
| See diagram 36.41: Looking down well at noon
Syrene, Angle of elevation of the Sun = 7.2o, E = centre of the Earth, A = Alexandria, S = Syrene
| See diagram 36.41a: Angles of elevation
At noon on the day of the summer solstice the Sun is directly overhead in Syrene and there is no shadow, but at Alexandria there is
a shadow.
Eratosthenes looked down a deep well at Syrene, (now Aswan), and observed that a circle of light was reflected from the surface of
the water in the well.
Here the Sun was vertical and cast no shadow.
At the same time in Alexandria, using a shadow stick, the angle between the vertical and the Sun was measured at 7.2o, (7o12').
The Sun is so far from the Earth that the rays of the Sun falling on Syrene and on Alexandria can be assumed to be parallel.
The angular difference between the two places = 7.2 / 360 = 0.02 = 1 / 50.
If distance between Syrene and Alexandria was 5000 stadia, then circumference of the Earth = 50 × 5000 = 250,000 stadia,
approximately 46,500 km.
The modern measurement of circumference of the Earth at the equator = 40,075.0167 km.
The logic of the calculation is correct, but the straight line distance between Syrene and Alexandria was not known accurately before
surveyors had invented triangulation.

Experiment
Select two schools on the north-south axis, i.e. same longitude, 500 km apart.
Both schools have a vertical flag pole five metres high.
At about noon at the time of the summer solstice, note when the flag pole at the first school has no shadow, or almost no shadow.
Immediately telephone a teacher at the second school and ask for the length of the shadow of their flag pole.
Draw a right angle triangle ABC such that angle ABC is a right angle, AB is the length of the flag pole, BC is the length of the shadow
and AC is the hypotenuse.
Angle CAB is the angle of the Sun's rays.
If the rays of the Sun through the two schools are parallel, angle a / 500 = 360o / circumference of the Earth.
Circumference of the Earth = 360 × 500 / angle CAB.

36.41.1 Circumference of the Earth using Polaris
For an observer at the equator, the Pole Star, (Polaris), appears to be on the horizon.
However, at the north pole, the Pole Star would appear to be directly overhead the observer.
The angle through which the Pole Star rises, to be confirmed with a sextant, is equal to the latitude of the observer.
So if the Pole Star rises by 10o, the observer has travelled 10o of latitude.
So the circumference of the Earth = distance travelled by observer when Pole Star as risen by 1o × 360.

36.42.0 Equinox, precession of the equinoxes
See diagram 36.42.1: Parallels of latitude for every 10 degrees of latitude, E = equator.
The location of P is latitude 45oS / 30oE
See diagram 36.42.2: Longitude, G = Greenwich Meridian.
P = The point at 30oE, so the location of P is 45oS / 30oE, W shows the direction of western longitudes, E shows the direction of
eastern longitudes
1. The equinoxes are the two events in the year when the length of the day is the same as the length of the night throughout the world
as the Sun crosses the celestial equator.
The Sun rises at 6 a.m. and sets 12 hours later.
At the equinoxes the Sun rises due east at 6 a.m. and sets due west 12 hours later.
On an equinox day, to an observer at the equator, the Sun at noon is directly overhead.
The equinoxes are the two points on the celestial sphere where the ecliptic intersects the celestial equator, i.e. where the Sun crosses
the equator.
The plane of the Earth's equator passes the centre of the Sun.
The celestial equator and the ecliptic intersect.
So on this day the Sun rises due east and sets due west.

2. The equinoxes are named for the convenience of the Northern Hemisphere.
So the vernal equinox, (start of Northern Hemisphere spring, Latin vernus: spring), occurs when the Sun crosses from south to north
on about 21 March.
It is the point in time when the sun crosses the celestial equator in a northerly direction.
This point of intersection is the vernal point.
The autumnal equinox occurs when the Sun crosses from south to north, about 23 September, (2.03 p.m. on 23 September, 2006).
It is the point in time when the sun crosses the celestial equator in a southerly direction.
In Brisbane, Queensland, Australia the "autumnal (fall) equinox" was on Wednesday, 20 March 2013 at 9:02 PM AEST (Australian
Eastern Standard Time), i.e. at 11:02 UTC, (Coordinated Universal Time), formerly Greenwich Mean Time (GMT).
The Spring Equinox occurs on Sunday, 22 September 2013.

3. Precession of the equinoxes
1. The Earth bulges at the equator such that the equatorial diameter is about 43 km longer than the north-south diameter.
The Sun pulls preferentially on the planet-wide bulge at the equator, causing the Earth's axis to gyrate slowly at one degree every
72 years.
2. The north-south diameter, (axis of rotation), is about 23.5o to the perpendicular to its orbit.
Gravitational pull from the Sun and  Moon tends to pull the Earth back to the perpendicular.
So the Earth wobbles like a spinning top.
The circular path of the wobble takes 25, 000 years and accounts for the precession of the equinoxes, the western or backwards
movement of the equinoxes of 50.27' per year.
3. As the vernal point moves through constellations, this period of time can be called the "age" of that constellation.
From about 4 000 B.C. to 2 000 B.C. the vernal point was in the constellation of Taurus, so it was "the age of Taurus", the bull.
From about 2 000 B.C. to 1 B.C. it was "the age of Aries", the lamb.
From about 1 AD to AD 2 600, it is "the age of Pisces", the fish.
The next age will be the "age of Aquarius", a constellation of the zodiac.
4. The medley "The Age of Aquarius" or "Let the Sunshine In" in the 1967 musical "Hair" expressed the hope of an imminent age of love,
quite different from the current "Age of Pisces".

36.42.1 Celestial equator, equatorial system , latitude and longitude
The celestial co-ordinate system is based on regarding the sky as an imaginary sphere with the Earth at the centre and with a north
celestial pole, south celestial pole and celestial equator.
So you can extend latitude and longitude to the sphere for identifying the location of points on the sphere.
The baseline or zero point in not based on north but the 0o Aries point on the ecliptic of the tropical zodiac, i.e. the vernal equinox.
Celestial equator is the great circle of the celestial sphere with its plane perpendicular to the Earth's axis and is equidistant from the two
celestial poles.
The celestial equator marks the distance between the the Northern Hemisphere and the Southern Hemisphere.
The equatorial system is the usual co-ordinate system using latitude and longitude to define position.
The position of an object on the Earth is defined by an ordered pair, with first co-ordinate Latitude from 0o at the equator to 90o N or
S at the poles, and second co-ordinate longitude from 0o at the prime meridian to 180o east or west on the other side of the globe.
Latitude is represented by the vertical angle above or below the celestial equator and is called the "declination".
So the celestial equator has declination = 0.
Longitude is represented by the angular distance measured eastwards along the celestial equator from the vernal equinox to the
semicircle of the declination and is called the "right ascension".
Longitude is measured in degrees up to 180o, (right ascension)
It is measured in hours, minutes and seconds..
Usually, each geographic time zone within a country differs by 15o of longitude = 1 hour.
One hour of right ascension = 15o, so 24 hours of right ascension = 360o.
So star catalogues specify locations in terms of right ascension and declination.

36.42.2 Latitude, nautical mile, knots, log, logbook
See diagram 36.42.1: Parallels of latitude
The latitude is the angular distance from the ecliptic, so the latitude of a point P is the angular distance north or south of the equator,
e.g. latitude 45o S.
All points with the same latitude are on the same circle called a parallel.
Two points with difference in latitude of 1o are about 110 km apart.
The variation is because of the shape of the Earth that is flatter at the poles, oblate.
Two points with difference in latitude of 1 minute, one sixtieth of a degree of latitude or one nautical mile, are about 110 / 60 =
1.83' km apart.
The international nautical mile is 1852 m.
The UK nautical mile is 1853.18 m (6,080 ft).
Latitude is represented by the vertical angle above or below the celestial equator and is called the declination.
Parallels of latitude, (lines of latitude), are circles measured parallel to the equator.
Lines of latitude are measured north and south of the equator and run east to west.
Latitude is the angular distance on its meridian of any place on the Earth's surface measured from the equator.
Two places may have the same or different parallel of latitude.
Brisbane, Australia, has latitude 2725'S.
Latitude of a point P is the angular distance north or south of the equator, e.g. latitude 45o S.
All points with the same latitude are on the same circle called a parallel.
Two points with difference in latitude of 1o are about 110 km apart.
The variation is because of the shape of the Earth that is flatter at the poles, oblate.
Two points with difference in latitude of 1 minute, one sixtieth of a degree of latitude or one nautical mile, are about 110 / 60 =
1.83' km apart.

Longitude is represented by the angular distance measured eastwards along the celestial equator from the vernal equinox to the
semicircle of the declination and is called the Right Ascension, measured in hours, minutes and seconds.
1 hour of right ascension = 15o. (24 hours of right ascension = 360o.)
Star catalogues specify locations in terms of right ascension and declination.

Nautical mile
The international nautical mile used by ships and aircraft is 1 852 m, 6 076 feet.
A speed of one nautical mile per hour is called "one knot", equal to one minute of latitude, about 7 / 6 land miles.
You cannot say "knots per hour".
However, if a nautical mile is one minute of arc on the meridian, then using the International Terrestrial Geoid based on the different
polar and equatorial radii, a nautical mile is 1 852.276 metres.
The UK nautical mile is 1 853.18 m, (6 080 ft), its value in latitude 48o.

Shackle
Ship's cable was measured in shackles, with 1 shackle = 12.5 fathoms, so 8 shackles, (100 fathoms) = 1 nautical mile / 10.
A log was formerly the apparatus used to measure the rate of a ships motion consisting of a thin quarter of a circle of wood, radius six
inches, weighted to float upright and fastened to a 100 fathom "log line" wound on a reel, with knots at intervals for timing the run-out
of a length of line.
As the line unravelled, the number of knots passing out per unit time could be measured.
The ship's logbook was used to record the rate of progress in knots of the distances and directions travelled, as part of the daily record
of a ships voyage with meteorological records and other observations and records of incidents.
Fathom
A fathom referred to the distance of outstretched arms, being standardized to 6 feet, 1.8288 m, is still used for sounding the depth. of
water

36.42.3 Longitude, Greenwich Mean Time, (GMT), Universal Time, (UT, UTC)
See diagram 36.42.2: Longitude
Longitude, right ascension
The longitude of a point P is the angular separation between an imaginary circle called a meridian that passes through the point P and
north and south poles, and the prime meridian that passes through Greenwich, England, north and south poles, e.g. longitude 30o East
(of Greenwich).
Another point could have longitude 25o West.
The right ascension refers to the angular distance of an object eastward along the celestial equator from prime meridian.
Differences between degrees of longitude are greater approaching the equator and lesser approaching the poles.
Longitude of a point on the surface of the Earth is sometimes called terrestrial longitude.
Lines of longitude are same size circles that pass through the North Pole and South Pole and run north to south.
Each line of longitude is broken by the equator into two meridians.
The prime meridian runs through Greenwich, near London and all the other meridians pass east or west of the prime meridian.
The longitude is the angular distance of any place on the Earth's surface east or west of the standard meridian through Greenwich.
It is measured in degrees up to 180o or in time, where 1 hour = 15o.
Greenwich Mean Time, GMT, is the mean solar time at the meridian of Greenwich, in London, the standard time zone for the Prime
Meridian, and is the reference point for longitude on the Earth, i.e. zero longitude.
It is the reference point for longitude on the Earth, i.e. zero longitude.
UTC, (Co-ordinated Universal Time), replaced Greenwich Mean Time, (GMT), as the World standard for time in 1986.
It is based on atomic measurements rather than the earth's rotation.
Brisbane, Australia, Longitude 153 9' E, UTC / GMT +10 hours, Time zone: Eastern Standard Time, EST, (Australian Eastern
Standard Time, AEST).
The 15o longitude is equivalent to one hour and 1.0 degrees every four minutes, (4 × 15 = 60).
The north pole of the earth's axis now points at Polaris, (Pole Star, North Star), in Ursa Minor, (Little Bear, Little Dipper).
In the next millennium, this star will be replaced by Alrai in the constellation Cepheus.

36.42.3.1 Leap second
One extra second is added to Universal Coordinated Time, (UTC), about every one and a half years to keep UTC close to mean solar
time.
The leap second is added because the rotation of the around its axis Earth's may become slower because of climatic and geological
changes.
However, atomic clocks used to define UTC keep almost constant speed.
Since 1972, 24 leap seconds have been added and the next leap second will be added in June 2012.
Only the days on which the leap seconds are added have 86,401 seconds instead of 86,400 seconds.
The International Earth Rotation and Reference System Service, (IERS), compares the Earth's rotation to atomic time and add a leap
second when the differences approach 0.9 seconds.
Experts at the International Telecommunication Union, (ITU), have been unable to decide whether to abolish the leap second, so have
deferred the decision until 2015.
While the US, Japan, Italy, Mexico and France have argued that leap seconds were causing problems for communication and navigation
systems, the UK, Germany and Canada, want to keep adding the leap second every few years.

36.42.4 Time zones, Greenwich time, (GMT), Universal Time, (UT)
See: Time products, "Scientrific", (commercial website)

Greenwich Mean Time, (GMT), Greenwich Time, now also known as Universal Time, (UT), is the mean time for the meridian of
Greenwich, system of time in which noon occurs at the moment of passage of the mean Sun over the meridian of Greenwich.
This was standard time in the British Isles until 18 February, 1968 when clocks were advanced one hour and Summer Time became the
standard as British Standard Time.
Greenwich is near the City of London on the bank of the Thames River.
Nearby is a tunnel under the Thames for pedestrians.
To standardize time globally, the Earth was divided into 24 adjacent, equal and equatorial perpendicular wedges called time zones, each
zone delimited by two meridians forming an hour angle of 1 hour at the poles.
The mean solar time of the central meridian of each time zone was assigned by convention to all places belonging to that time zone.
The Greenwich time zone centred on the Greenwich meridian was taken as the reference time zone.
So the time zone to the East of Greenwich is 1 hour in advance in comparison with Greenwich mean time, i.e., (UT + 01.00), and
similarly the time zone to the West of Greenwich is 1 hour later, i.e., (UT-01.00).
Although the time zones were officially adopted on 1 November 1884 at the International Meridian Conference at Washington D.C.,
USA, actual time zones are often delimited at state borders instead of at medians, e.g. the Peoples' Republic of China is one time zone.
Australian time zones, (summer):
Daylight saving  time, (DST) (advance clocks one hour), occurs in New South wales, Victoria, South Australia, Tasmania and the
Australian Capital Territory, but not in Queensland, the Northern Territory and Western Australia. DST does not necessarily occur on
the same date every year, but it always starts at 2.00 AM (clock forward) and finishes at 3.00 AM (clock backward).
Dates: 2015: 5 April (Easter Sunday), 2016: 3 April, 2017: 2 April.

36.43 Find the north-south line from the Sun, Moon and stars
1. Set a watch to the local mean solar time.
If north of the equator, point the hour hand towards the Sun.
The north-south line is given by the bisector of the angle between the hour hand and 12 o'clock.
If south of the equator, point 12 o'clock towards the Sun.
The north-south line is given by the bisector of the angle between the hour hand and 12 o'clock.
3. If you have no watch, use the shadow of a stick.
Drive a stick vertically into the ground.
As the Sun crosses the sky during the day, the shadow of the stick will turn.
It will also grow shorter in the morning and longer again in the afternoon.
When the shadow is shortest, close to noon its far end will point north or south, depending on whether you are north or south of the
equator.
3. One hour before noon, put a one metre stick vertically in the ground and mark the position of the tip of the shadow, T1.
An hour after noon, mark the position of the tip of the shadow, T2.
The line T1T2 is an east west line.
4. Put a longer and shorter stick vertically in the ground.
Crouch down at the side of the short stick and select a star along the line of sight of the tips of the two sticks.
For the Northern Hemisphere, if the star appears to rise, face east.
If the star appears to lower, face west.
If the star appears to move to the right, face south.
If appears to move to the left you are facing south.
For the Southern Hemisphere, the directions of apparent movement are opposite.
5. If the Moon rises before the Sun has set, the illuminated side will be on the west.
If the Moon rises after midnight, the illuminated side will be on the east.

36.47 The cause of the seasons
| See diagram 36.98: The cause of seasons
| See diagram 15.0.4.1: Axis of rotation of the Earth
The tilt of the Earth's axisis  23.44o
The angle between the axis of rotation and the pole of its orbit is called the obliquity of the ecliptic, about 23o26' and decreases by
about 0.47' per year.
Also it is defined as the angle between the plane of the ecliptic and the celestial equator.
For half the year the Sun is in the Northern Hemisphere in the sky and half the year in the Southern Hemisphere.
The Sun travels about eight days longer in the Northern Hemisphere than in the Southern Hemisphere.

Experiment
Use a hollow rubber ball to represent the Earth.
Push a 15 cm length of wire or a knitting needle through the ball to represent the Earth's axis.
Draw a circle about 40 cm in diameter on a piece of cardboard to represent the Earth's orbit.
Hang an electric lamp about 15 cm above the centre of the cardboard to represent the Sun.
Place the ball representing the Earth successively at the four positions shown in the diagram with the axis slanted about 23.5o.
Observe how much of the ball that is always illuminated.
Observe where the direct rays of the Sun strike.
Observe which hemisphere receives the slanting rays of the Sun.
Repeat the experiment with the needle perpendicular to the table top in each of the four positions and observe what would happen if the
axis of the Earth were not inclined.

36.71 Radio waves
Radio frequency electromagnetic radiation emitted by the Sun, Jupiter, pulsars and other stellar sources, e.g. spiral galaxies, have
frequency 3 kHz to 300 GHz and very low energy, a million times less energy than light energy.
To detect radio waves you need a very accurate radio telescope consisting of a radio antenna, detector and amplifier, or any array of
steerable receivers, e.g. a dense aperture array, to simulate a telescope and determine the intensity of radio emission and its spectrum.

36.72 Alpha Centauri, (Rigil Kentaurus)
Alpha Centauri is the brightest star in the constellation of Centaurus.
It is the third brightest "star", but it is really three stars because it is a visual binary star, Alpha Centauri AB, that orbits each other
every 80 years + the red dwarf star Proxima Centauri.
Proxima Centauri is the closest star to the Sun.
The Alpha Centauri system is the closest star system to the Solar System.
Alpha Centauri AB is about 4.35 light years from Earth.
Proxima Centauri is about 4.22 light years from earth.

36.73 The universe
The substances in the universe consist of 1 / 10 stars and 9 / 10 gases.
The total "contents" of the universe = 0.4 % stars, 3.6 % intergalactic gas, 23 % "dark matter", 73 % "dark energy".
The scientific theories that explain the origin of the universe suggest that the universe came into existence from a "big bang" 13.6 billion
years ago and is still expanding.

36.74 Aldebaran, Alpha Tauri
Aldebaran is a binary star.
One stars is the red giant Tauri, the bull's eye in the constellation of Taurus.
Aldebaran is the "follower" star in the Pleiades in constellation Taurus.

36.75 Arcturus, arctic, the Great bear
Arcturus is a double star and is the brightest star in the constellation Boötes and north of the celestial equator, and fourth brightest star
in the sky.
In the Bible "Arcturus" is used for the Great Bear constellation, Ursa Major, (Job 38:32), (Greek: arktos, bear), also the "arctic"
that is under the Great Bear.

36.76 Supernova
A supernova occurs when a huge star collapses when its hydrogen and helium fuel is exhausted or when a white dwarf star in a binary
star picks up mass from the twin star in the binary.
The supernova releases a huge amount of energy and an expanding gas cloud of stardust.
The last supernova explosion, SN1987A, was seen in 1987.