UNPh36

School Science Lessons
36. Astronomy, Earth's motion, instruments, sundials, Sun and Moon, stars, planets, telescopes
2012-01-28 SP
Please send comments to: J.Elfick@uq.edu.au

See: Interesting websites, Part 2, Astronomy, space sciences

Table of contents
36.0.0 Astronomy experiments
36.40 Astrology and the zodiac
36.36.0 Effects of the Earth's motion
2.0.3 Greek alphabet
History
36.113 Inservice training - The Sun and the Earth, Equipment
36.1.0 Instruments for astronomy, telescopes
36.113.3 Measurements using the Earth
36.113.2 Measurements using the Sun
36.44.0 Models and demonstrations
36.113.4 Preparation for the Total Solar Eclipse in 2012
36.51.0 Space science
36.113.1 Sun, Our Sun is a star
36.4.0 Sundials
36.14.0 Stars and planets
36.28.0 Sun and the Moon

36.36.0 Effects of the Earth's motion
36.40 Astrology and the zodiac
36.41 Circumference of the Earth, the method of Eratosthenes, 250 BC
36.41.1 Circumference of the Earth using Polaris
36.111 Earth rotation and wind farms
36.42.0 Equinox, celestial co-ordinate system, right ascension
36.43 Find the north-south line from the Sun, Moon and stars
36.36 Foucault pendulum
36.42.2 Latitude, nautical mile, knots, log, logbook
36.42.3 Longitude, Greenwich time (GMT), Universal Time (UT)
36.12.03 Lunar month, synodic month
36.12.04 Meridians
26.12.05 Period of rotation
36.39 Photograph star trails
36.42.1 Precession of the equinoxes
36.38 Seasonal change of position of the Sun, solstice
36.12.02 Sidereal time
36.42.4 Time zones, Greenwich time (GMT), Universal Time (UT)
36.12.01 Zone time

36.113 Inservice training: The Sun and the Earth
36.113.1 Sun, Our Sun is a star
36.113.2 Measurements using the Sun
36.113.3 Measurements using the Earth
36.113.4 Preparation for the Total Solar Eclipse in 2012

36.1.0 Instruments for astronomy, telescopes
36.3 Commercial telescopes
4.129 Magnifying power of a lens
36.2 Simple reflecting telescope
36.1 Simple refracting telescope
36.4.0 Simple theodolite or astrolabe, sextant

36.14.0 Stars and planets
36.16 Albedo
36.74 Aldebaran, Alpha Tauri
36.72 Alpha Centauri (Rigil Kentaurus)
6.3.3.2 Angle, degree, arc minute, arc second, radian
36.21 Apparent daily rotation of the sky, the axis of rotation of the Earth
36.75 Arcturus, arctic, the Great bear
3.3.2.0 Astronomical unit
36.17 Azimuth, altitude, zenith and horizon, the horizontal system of co-ordinates
36.76 Constellarium
36.76.1 Constellarium, Umbrella constellarium
36.112 Constellations, List of constellations
36.4.1 Declination calculation
36.14.1 Diurnal aberration of a star
36.22 Ecliptic
36.23 Ecliptic, Obliquity of the ecliptic, precession and nutation
3.8.0 Ellipse
36.8.1 Equation of time
36.20 Equatorial system of co-ordinates
36.26a Falling stars, shooting stars, meteors
36.14 Find the main constellations
36.18 Find constellations from north of the equator, Northern hemisphere
36.19 Find constellations from south of the equator, Southern hemisphere
36.12.2 Great circles
36.11 Greenwich Mean Time, GMT, UTC
36.112 List of constellations
36.14.2 Light year, parsec
36.12.03 Lunar month, synodic month
36.15 Magnitude
36.10 Make a range finder
36.11 Make a model Earth
36.12.04 Meridians, celestial meridian, standard meridian
36.26 Morning Star and Evening Star, Venus
36.13 North, Find due north
26.12.05 Period of rotation
36.92 Photograph constellations
36.93 Photograph satellites
36.39 Photograph star trails
36.91 Photograph star trails in colour
36.27 Planet movements in a jar
36.24 Pluto, Is Pluto a planet?
36.108C Satellite in stable orbit, geostationary orbit
36.106 Satellite launcher
36.77 Seasonal shift of the sky
36.12.3 Ship's watches
36.12.02 Sidereal time
36.25 Solar system model
36.78.1 Star calendar
36.78.2 Star clock
6.20 Southern Cross constellation (Primary)
36.7.0 Sunrise and sunset
36.76 Supernova
36.73 The universe
36.78 Time and date using the stars
36.12.1 Tropical year
36.94 "Twinkle, twinkle little star"

36.28.0 Sun and the Moon
36.49 Angle of the Sun's rays on the Earth
36.35.1 Joshua's long day
36.34 Lunar eclipse
36.9 Measure the altitude of the Moon and the Sun
6.19 Moon and tides (Primary)
36.32.1 Moon illusion
36.29 Moon watch, observe the Moon for four weeks
36.70.1 Parallel rays of the sun
36.28 Phases of the Moon and its apparent position in the sky
36.30 Positions of the Moon
36.32 Rising and setting Moon
36.35 Rotation period of the Sun
36.38 Seasonal change of position of the Sun, solstice
36.33 Solar eclipse
18.3.6.7 Tides simulation, spinning glass of water
36.32.2 Sun and moon diameter illusion
36.35 Sunspots
36.31 "The man in the Moon"

36.1 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 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 Commercial telescopes
" Celestron Astromaster 70Q telescope. Includes 2 eyepieces and an equatorial mount for easy tracking of objects in the sky."
"Celestron Sky Prodigy 130 telescope. Combines computer technology with an on-board camera to automatically align the telescope with no input from the user."

36.4.0 Simple theodolite or astrolabe, sextant
See diagram 36.67: Astrolabe
The astrolabe is perhaps the most iconic of all scientific instruments. Used by astronomers, astrologers, mariners and those with pretensions, it flourished for the first half of the second millennium as a calculation tool and a thing of beauty. They are widely represented in art and many survive in museums. Use an astrolabe to show the appearance of the celestial sphere and then estimate the altitude of celestial bodies. Astrolabes were used to give approximate measurements of time and terrestrial measurements of heights and angles, and for navigation. Make a simple theodolite or astrolabe by fixing a drinking straw to the base line of a protractor with adhesive tape. Hang a plumb line from the head of a fixing screw to show whether the support is upright. Also use it to measure the elevation of a star seen through the drinking straw. To make an improved model for finding the altitude and the bearing of a star, 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. The phrase " to shoot the sun" means to use a sextant to measure the meridian altitude of the sun, usually at mid day.

36.4.1 Declination calculation
Declination = 23.44 sin [(360 / 365.242 19) X (286 + D)] = 23.44 sin [0.986 (286 +D)]
Assume 0^o = 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 = 90^o - the angular difference between the declination of the Sun and the latitude of the observer.

36.7.0 Sunrise and sunset
Order online: Sun Tracker Kit, photovoltaic, follows arc of the sun
1. 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 90^o50' 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.
2. 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.
1. Seasonal sunrise and sunset
1.1 Record the path of the Sun from sunrise to sunset on 22 December, 30 March, 22 June and 23 September.
1.2 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 = 20^o, 1 April = 47^o, 1 June = 65^o, 1 September = 52^o)
1.3 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 refracted by the atmosphere having a density that decreases with altitude. So when an observer who first sees the sun above the horizon would not have seen it if the light from the sun had travelled in a straight line.

36.8.1 Equation of time
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 the northern Europe, the greatest difference is early in November when sundial time is about 16 minutes ahead of mean clock, 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, and 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 furthest 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. Since official clock time is based on the mean length of the solar day as averaged through the year, when the true solar day is shorter than the mean solar day, the sun-dial time will very gradually gain on the clock time; whereas when the true solar day is longer than the mean solar day, the sun-dial 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.

36.9 Measure the altitude of the Moon and the Sun
See diagram 36.9: Simple astrolabe, (sextant)
1. Cut out a rectangular piece of cardboard slightly larger than a protractor. Trace the shape of the protractor on the cardboard and mark the main points of a scale at 10 degree intervals. Start with zero degrees at the bottom of the scale. Punch a small hole through the cardboard at the point corresponding to the position of the cross hairs of the protractor. Attach a drinking straw to the edge of the cardboard closest to the hole. Attach a washer as a plumb bob to one end of a piece of string. Thread the other end of the string through the hole in the cardboard and tie a knot at the end. The plumb bob should swing freely from the cross hairs. Sight through the drinking straw at any object, e.g. top of a tree, and measure the angle showing the altitude of the object above the ground. At night, use the simple astrolabe to measure the altitude of the Moon.
2. Measure the altitude of the Sun during the day. Cut out a 4 cm X 4 cm piece of cardboard. Punch a hole in the middle to form a tight fit over the drinking straw. Attach the cardboard to one end of the drinking straw. With the back to the Sun, adjust the alignment of the astrolabe so that the shade forms a shadow on a screen. When you can observe a point of light in the middle of the shade patch, you can read the altitude of the Sun.

36.10 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.

36.11 Make a model Earth
See diagram 36.11: Model Earth
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". Draw lines on the model Earth to represent the following: 1. the Greenwich meridian, 2. the international dateline, 3. the equator, 4. the closest longitude to the school, 5. the standard meridian for the local time zone, e.g. the standard meridian for a school in Brisbane, Australia, 150^o east.

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 150^o 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 23^o26' 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 15^o 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 = 15^o.
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 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 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. However the
A sidereal year (astral year) is 365.25636 mean solar days (365 days, 6 hours, 9 minutes, and 9.6 seconds).

36.12.03 Lunar month, synodic month
Earth is moving in its orbit about the Sun so the Moon has to travel more than 360^o to get to the next new moon so the lunar month or synodic month is 29.531 days.

36.12.04 Meridians
The celestial meridian, is the great circle that passes through the north pole, south pole and the observer zenith, cuts the horizon at the north and south points. The standard meridian is through Greenwich. The International Date Line is from north pole to south pole along the meridian, 180^o 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 but it is not the same as a solar day that 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.

36.12.2 Great circles
A great circle is a line on the surface of a sphere which 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, e.g. the Earth revolves around the Sun.
Rotation describes the spinning of a body on its axis, e.g. the earth rotates every 24 hours.

36.13 Find due north
See diagram 36.13: North-south meridian
1. Find due north to align the gnomon of the sundial along the north-south meridian. Draw a circle on a cardboard base. Attach a shadow stick to the base at the centre of the circle and put the apparatus in a sunny location. Use a plumb bob to check that the shadow stick is vertical. Mark Point M where the shadow just touches the circle in the morning. Mark Point A where the shadow just touches the circle in the afternoon. The line drawn from the shadow stick to the midpoint of MA represents due north-south.
2. Use a shadow stick to find the shortest shadow of the day. The direction of the shortest shadow is due north-south.
3. Set up the sundial so that the shadow is aligned with local apparent time of 10 h 15 m at exactly 10 h 30 m zone time, so that the gnomon is pointed due north-south. Use a shadow stick to find the direction of the Earth's daily rotation.

36.14 Find the main 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.
2. Record the positions of the main constellations at 8 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.

36.14.1 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 due to 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 X 10¹² km, (5.88 X 10¹² miles).
The speed of light is 2.99792458 X 10⁸ ms^-1, usual value used = 3 X 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 X 365 days, 24 hours X 60 minutes X 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 X 10¹² km (5.88 X 10¹² miles). For example, the Sun is about 8 light minutes from the Earth, the nearest star, Proxima Centauri, is about 4.3 light years from the Earth, and the Andromeda galaxy, the nearest galaxy to the Milky Way galaxy containing the Earth, is about 2.5 light years from the Earth.
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 4.385 ly (1.338 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, 1^o = 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. Apparent magnitude is as seen from the Earth. Absolute magnitude is the brightness adjusted for the distance from the Earth. Ancient astronomers named some stars, e.g. Sirius, 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 are the brightest stars in the constellation Centaurus, Alpha Centauri and Beta Centauri. All known stars are listed in catalogues by a code number. For example, Sirius has code number AE41.

36.16 Albedo
The albedo is a measure of reflectivity or brightness, the reflecting power of a non-luminous body. Albedo = 1 for a perfectly reflecting white body and albedo = 0 for 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) X 100. Albedo is also used to express the fraction of the Sun reflected by bodies in the solar system, e.g. 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
Azimuth is the clockwise horizontal angle (in degrees, minutes and seconds) from true north to the Sun or Moon.
Altitude is the vertical angle (in degrees minutes and seconds) from an ideal horizon, to the Sun / Moon.
Zenith is the point immediately over the head of the observer. The opposite point is the nadir.
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.
The altitude of a celestial object is its angular elevation from the horizon from 0^oon the horizon to 90^o at its zenith. 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. Note that altitude and azimuth defines the position of a point in the sky only at a certain time. 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 10^o, elevation 70^o, Aldebaran azimuth 320^o, elevation 30^o, Rigel azimuth 330^o, elevation 60^o, Betelgeuse azimuth 340^o, elevation 40^o.

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 90^o 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, known as the Big Dipper, the Plough. the Great Bear, contains 7 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", and record 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 X 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 Southern Cross constellation, Crux, is kite-shaped, almost surrounded by Centaurus. Crux is the smallest constellation. Its stars are as follows: Alpha (Acrux), the brightest in the constellation, magnitude 0.77, about 320 light-years away, Beta (Mimosa, Becrux) magnitude 1.2, Gamma (Gacrux) magnitude 1.6, Delta magnitude 2.8, Epsilon 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, also known as Rigel Kentaurius, is the pointer farthest away from the Southern Cross and is the brightest star system in the constellation of Centaurus. It is 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" 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 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 X 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 45^o 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, 90^o 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 23^o26^' north of the equator, the tropic of Cancer or south of the equator, the tropic of Capricorn. 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 35^oN to 30^oS. 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 Apparent daily rotation of the sky, axis of rotation of the Earth
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, 360^o. 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, 360^o.
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. Diurnal aberration of a star is the direct evidence that the Earth is not fixed in space.

36.22 Ecliptic
The ecliptic is the apparent yearly path of the Sun against the background of stars. It 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.
On consecutive days, note the position of the Sun against the stars just before the Sun rises and just after the Sun sets. 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.

36.23 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 23^o 26' 19.731', i.e. 23.438814199^o, 23.44^o. It varies from 21^o55' to 28^o18'. It is caused by precession and nutation. The precession is caused mainly by the gravitational pull of the Sun and the Moon on the equatorial bulge of the Earth, 43 km diameter than pole to pole. 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 1^o 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 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 = +0.000817294^o.
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.

36.24 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 7.79 Model of the Solar System, you may delete Pluto as a planet and / or insert the dwarf planets, Pluto, Ceres, and Eris.

36.25 Solar system model
Make models of the solar system to understand the relative size and distance of the planets from the Sun. Make two separate models:
1. showing the relative size of the planets, 2. showing their 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 between the Earth and the Sun, about 149 598 000 km (92 956 000 miles). It is used as a convenient way to measure distance in the solar system.
The planets (Greek: planētēs, wanderer) revolve around the Sun in approximately circular orbits. The planets listed below are called the primary planets. Secondary planets are satellites or Moons. The asteroids between the orbits of Mars and Jupiter are called the minor planets.

Planet	Distance (A	Diameter
Mercury	58 (0.4)	4 800 (0.4)
Venus	108 (0.7)	12 000 (1.0)
Earth	150 (1.0)	13 000 (1.0)
Mars	228 (1.5)	6 800 (0.5)
Jupiter	778 (5.2)	140 000 (11.2)
Saturn	1 420 (9.5)	120 000 (9.5)
Uranus	2 870 (19.2)	50 000 (3.7)
Neptune	4 490 (30.1)	53 000 (7.1)
Pluto	5 900 (39.5	2 700 (0.2)

36.26 Morning Star and Evening Star, Venus
Observe the planet Venus and note when it rises or sets in respect to sunrise and sunset.

36.26a Falling stars, shooting stars, meteors
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 remains 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.

36.28 Phases of the Moon and its apparent position in the sky
See diagram 36.28: Phases of the Moon | See diagram 36.28.1: Phases of the moon in a classroom
1. The phases of the Moon are visible because different portions of the illuminated and non-illuminated parts of the Moon are facing towards Earth at different times. The Moon shines because it reflects light from the Sun. At any particular time, half the Moon is illuminated by the Sun. the Moon takes 27 days 7 hours and 43 minutes to travel around the Earth. As it orbits the Earth, it takes the same length of time to rotate once on its axis so the same side of the Moon is always facing the Earth. So from the Earth we cannot see the other side of the Moon. On 2006-09-22 the Moon was farthest from Earth, apogee, at 406 498 km. On 2006-09-08 the Moon was closest to Earth, perigee, at 357 174 km. Phase refers to the illuminated part of a celestial body. The different relative positions of the Moon and Sun cause the phases of the Moon (new, crescent, half, gibbous, full Moon). When the Moon and Sun are on opposite sides of the Earth, you can see the sunlight reflected from all of the face of the Moon, a full Moon. When the Sun is on the same side of the Earth as the Sun, little light is reflected back towards the Earth, a new Moon. When the angle made by the Sun and the Moon at the Earth is between 0^o and 180^o you see the light from only a part of the Moon, a crescent Moon. From just after the new Moon, the crescent shape changes into a quarter Moon then a gibbous Moon and finally into a full Moon. Then the changes reverse.
2. A "blue Moon" means a second full Moon in the same calendar month that occurs about seven times in each nineteen years, i.e. "once in a blue Moon". The Moon has no atmosphere so you see a clear separation between the lit and unlit portions of its surface, the terminator. It is an arc of an ellipse. A lune or crescent is the area enclosed by the terminator and the nearer edge of the Moon.
3. A "harvest Moon" is the full Moon nearest to the autumnal equinox (autumn equinox) during 22 September, 2008, in the Northern hemisphere and during 20 March, 2008. in the Southern hemisphere.
4. From the Southern hemisphere, the Moon appears to move around the Earth in a clockwise direction, while from the Northern hemisphere, the Moon appears to move around the Earth in an anticlockwise direction. The Moon rises about 50 minutes later each day. For a few days after the new Moon to a few days before the full Moon, the Moon appears to move clockwise from west to east and can be seen in the morning during school time. The best time to observe the Moon is 7.00 p.m. The waxing crescent Moon is visible low in the western sky, the first quarter is visible high in the Northern sky and the full Moon is visible low in the eastern sky.
5. Lunation is the mean time between successive new moons, i.e. for one lunar cycle, 29.530589 days.
6. Simulate the phases of the moon in the classroom. In the Southern hemisphere, assume that one end of the classroom is approximately north. Use a ball to simulate the Moon and a big electric torch (flashlight) to simulate the Sun. One student will carry the "Moon" around the class with the torch always pointing at the "Moon" in a north to south direction. The rest of the class remains in the centre of the classroom on the "Earth". Starting from the north end of the classroom, with the torch pointing south behind the moon, the students can only see a weak rim of light illuminating the periphery of the "Moon", a new Moon. Moving to the right hand side of the classroom, east, with the torch still pointing south at the "Moon", the students see half the "Moon", first quarter. Moving to the south end of the classroom with the torch still pointing south at the moon, students see the whole moon illuminated by the torch, full moon. Moving to the west side of the classroom with the torch still pointing south, students see half the "Moon", third quarter.
7. Instead of using a torch the ball representing the "Moon" could be painted half white, i.e. illuminated by the sun, and half black, i.e. not illuminated by the sun. The student taking the moon around the class always keeps the white half facing north and the black half facing south.
8. Early researchers deduced that the moon has no atmosphere based on the sharpness with which it occults starlight at its edge.
9. The whole hemisphere of the moon can be see even when it is in its first or last quarter because the part of the moon that does not receive any light directly from the sun does receive sunlight reflected from the earth and some of this light is again reflected from the moon to the earth to make the dark part faintly visible.

36.29 Moon watch, observe the Moon for four weeks
At the same time each evening, e.g. 8.00 p.m. record the date, time, apparent shape (full, gibbous, half, crescent, new, crescent, half, gibbous, full), azimuth and altitude. Draw a Moon each night so that the lunge remains white and the rest of the Moon is shaded black. When the Moon is a gibbous Moon, use circles to represent the Moon and show the orientation of the terminator of the gibbous Moon through the night, i.e. when the Moon is in the east, north and west. Record the dates of the phases. Make these observations during four weeks. Always observe from the same place. Consult an almanac so you can begin the observation on the date when the crescent Moon is just visible in the evening, two or three days after a new phase. The horns of the crescent Moon are turned away from the sun. A lunar month is from new Moon to new Moon, about 29.5 days, i.e. the time taken for the Moon to revolve around the Earth., however, most people think of the lunar month as being a period of 28 days.
(Waxing, Old English weaxan: to increase), (Waning, Old English wanian: to lessen)

Phase	First quarter	Waxing gibbous	Full Moon	Waning gibbous	Last quarter	Waning crescent	New Moon	Waxing crescent	First quarter
Date	Jul. 29	.	Aug. 6	.	Aug. 14	.	Aug. 20	.	Aug. 27
Rise	.	.	.	.	.	.	.	.	.
Set	.	.	.	.	.	.	.	.	.

36.30 Positions of the Moon
1. On the first night, draw the position of the Moon relative to prominent landmarks, e.g. above a tower or church steeple. Measure its height above the horizon in degrees, using your fist or your fingers extended, e.g. a fist at arm's length = 100, a span of a thumb and little finger = 200. Record these measurements and the time on a sketch. Also, record the direction of the horns of the Moon, and the shape of the crescent. Two hours later, repeat the observations and note the time.
2. Make repeated observations in the same way every night for two weeks.
Record the following observations:
2.1 how the shape of the Moon's illumination changes from night to night, 2.2 how its apparent location changes, 2.3 how its horns, or cut-off edge, are oriented relative to the position of the Sun below the western horizon
2.4. how the Moon changes position during one night.
A drawing of an "impossible Moon" shows horns pointing down!

36.31 "The man in the Moon"
1. Observe the craters and flatter areas, "seas" (Mare) and oceans (Oceanus). The space craft Apollo 12 was launched 14 November 1969 and landed on the Oceanus Procellarum on 19 November 1969. Then the astronauts walked to the remains of previous lunar probe Surveyor 3 and retrieved some pieces of it. The arrangement of craters, sea oceans and other features allow different people and cultures to see figures in the Moon. Although "the man in the Moon" in the Northern hemisphere looks like an old man walking away carrying sticks or leaning on a fork, some people can see different faces and figures, even a frog. In China and Japan they see a large rabbit stretched across the Moon with the ears pointing down from the upper right and the legs crossed at the lower left. The rabbit is making something in a box. Most figures can be seen only at or near a full Moon. Some of these figures appear differently in the Northern and Southern hemisphere. Stare at the Moon at different phases until you can see figures. Record the figures on a Moon diagram and note the time and date of the observations.
2. Measure the diameter of the Moon, 31 minutes 4 seconds. So 347 full Moons side by side would fill a circle across the sky from horizon to horizon.

36.32 Rising and setting Moon
During the last quarter phase of the Moon, make the above observations during the morning and compare them with the same observations during the evening.

Phase	Rising time	Time in eastern sky	Time highest in sky	Time in western sky	Setting time
New Moon	Sunrise	Morning	Noon	Afternoon	Sunset
Waxing crescent	Just after sunrise	Morning	Just after noon	Afternoon	Just after sunset
First quarter	Noon	Afternoon	Sunset	Evening	Midnight
Waxing gibbous	Afternoon	Sunset	Night, before midnight	Midnight	Night, after midnight
Full Moon	Sunset	Night, before midnight	Midnight	Night, after midnight	Sunrise
Waning gibbous	Night, before midnight	Midnight	Night, after midnight	Sunrise	Morning
Third quarter	Midnight	Night, after midnight	Sunrise	Morning	Noon
Waning crescent	Just before sunrise	Morning	Just before noon	Afternoon	Just before sunset

36.32.1 Moon illusion
See diagram 36.32.1: Rising moon illusion | See diagram 36.32.2: Ebbinghaus illusion
The rising moon appears to be much bigger on the horizon than the moon high in the sky, but if you photograph both moons they are the same size in the photograph. The rising moon optical illusion is caused by the adjacent buildings and trees that appear to be close to it. This illusion may be called the angular size illusion and optical scientists are still discussing the best explanation for this common illusion. It may be partly explained by the Ebbinghaus illusion where for most people black circle "A" looks bigger than "B".

36.32.2 Sun and moon diameter illusion
The sun and the moon appear to be greater in diameter at sunrise and sunset than when vertically overhead. The appearance of the size of an object depends on the angle subtended by the object, α, and the distance from the object, d. The distance may be known or may be estimated from the size of other familiar objects. However, if there are no other objects in view the distance is usually under-estimated. We estimate that the sky is a saucer-shaped covering so when the sun or moon is at its zenith we estimate that it is closer than when at the horizon. So its size is estimated as being greater that at the horizon.

36.33 Solar eclipse
See diagram 36.84: Solar eclipse
The Moon's orbit is inclined 5^o 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 17^o of a node, (its orbit crossing the ecliptic), a solar eclipse occurs somewhere on the Earth. Each year 2 to 5 solar eclipses occur. The maximum time for a total eclipse is 7.5 minutes.
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.

36.34 Lunar eclipse
See diagram 36.85: Eclipse of the moon | See diagram 36.95: The moon in the sky
Direct observation of a lunar eclipse is safe. Observe the shape of the Earth's shadow as its edge crosses the Moon as evidence that the Earth is spherical. However the effect could be caused by a disc-shaped Earth.

36.35 Rotation period of the Sun
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 is about 26.25 days. Sunspots move from left to right across the Sun. As sunspots turn with the Sun they are used to measure solar rotation
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 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
s. Show their relative sizes and approximate shapes. From day to day, the spots 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 spot group may return or new spot groups may appear.

36.35.1 Joshua's long day
In the authorized King James’ version of the 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:
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.
There is no evidence for either explanation ever occurring.

36.36 Foucault pendulum
See diagram 36.87: G-clamp support to allow pendulum to swing in any direction
In 1851, Jean-Bernard Foucault hung a 137 kg brass ball from a 70 metre long wire attached to the inside of the dome of the Pantheon in Paris and set it in motion in one direction as a pendulum.. He showed that the earth rotates once each day because while the direction of swing of the pendulum does not change the surroundings do change their position due to the rotation of the earth.
1. Use a G-clamp with a ball bearing soldered to the inside of the jaw to makes a good support for the pendulum. Hang the pendulum indoors with the ball bearing resting on a razor blade or another hard surface. Use nylon fishing line to suspend the bob. It can be a solid rubber ball, but best results are obtained if the bob is at least 5 kg.. For a pointer, use a short knitting needle pushed into the bob and continuous with the suspending fishing line. The pointer should just touch a reference line drawn in fine sand in a tray on the floor. The length of the pendulum at least 6 m long. The pendulum must be allowed to swing freely so that it swings backwards and forwards in the same plane. However it appears to change its path during the day.
2. To set the pendulum in motion, attach a long cotton thread to a drawing pin pushed into the bob. Align the thread along the direction of the reference line, then burn the thread near the drawing pin. After the pendulum is set in motion note that the plane of the swing has changed after a few hours compared with the reference line. If the ceiling-mounted pendulum swings freely, note the change in the path of the pendulum after one hour. Then note the plane of swing at try six X ten minute intervals. A pendulum releasing ink can mark a clear pattern. Getting good quantitative results without many refinements is not easy, but observing the effect is not difficult.
3. Note the variation of rotation of the Foucault pendulum with latitude. The Earth rotating beneath the bob causes the change. The precession period for an ideal pendulum is 23.93 hours / sine of the latitude. For example, at Sydney, Australia, at latitude 34^o S, the period is about 43 hours, i.e. about one degree every seven minutes. At the south pole the pendulum precesses through 360^o in a day. At the equator the pendulum does not precess.
4. Make a miniature Foucault pendulum. Mount a small Foucault pendulum from a stand set upon a turntable or office chair that can be rotated. Observe the behaviour of the pendulum when the turntable is rotated slowly.

36.37 Pulsars
A pulsar is a tiny and brilliant neutron star, probably like a black hole because it is the 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, that 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 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.
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 equals about 100.
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
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, the method of Eratosthenes, 250 B.C.
See diagram 36.41: Looking down the well
36.41.2 A Alexandria S Syrene, E centre of the Earth, 1. To zenith at A, 2. To Sun at noon, 3. To Sun at Syrene
1. At noon on the day of the summer solstice the Sun is directly ahead in Syrene and there is no shadow but at Alexandria there is a shadow. He 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. 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 7.2^o. The Sun is far from the Earth so the rays of the Sun falling on Syrene and Alexandria are parallel. The angular difference between the two places 800 km apart = 7.2 / 360 = 0.02 = 1 / 50. So the circumference of the Earth = 50 X 8000 = 40 000 km.
2. 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 = 360^o / circumference of the Earth. Circumference of the Earth = 360 X 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 10^o, the observer has travelled 10^o of latitude. So the circumference of the Earth = distance travelled by observer when Pole Star as risen by 1^o X 360.

36.42.0 Equinox, celestial co-ordinate system, right ascension
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 am and sets 12 hours later. At the equinoxes the sun rises due east at 6 am and sets due west 12 hours later. On an equinox day an observer at the equator the Sun at noon appear to be 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 equinoxes are named for the convenience of the Northern hemisphere. The vernal equinox (start of autumn) is when the Sun crosses from south to north, about 20 March. The autumnal equinox is when the Sun crosses from north to south, about 23 September (2.03 p.m. on 23 September, 2006). The vernal equinox is the base point of the celestial co-ordinate system. On this day, the Sun rises due east and sets due west.

36.42.1 Precession of the equinoxes
The Earth bulges at the equator such that the equatorial diameter is about 43 km longer than the north-south diameter. Also, the north-south diameter or axis of rotation is about 23.5^o to the perpendicular to its orbit. Gravitational pull from the Sun and Moon tend to pull the Earth back to the perpendicular, so the Earth wobbles like a spinning top. The circular path of the wobble takes 25 800 years and accounts for the precession of the equinoxes, the western or backwards movement of the equinoxes of 50.27' per year. 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, the age of Taurus. From about 2 000 B.C. to 1 B.C. was the age of Aries, the lamb. From about 1 AD to AD 2 600 is the age of Pisces, the fish. The next age will be the "age of Aquarius", a constellation of the zodiac.
The celestial co-ordinate system is based on regarding the sky as an imaginary sphere with the Earth at the centre with North celestial pole, South celestial pole and celestial equator, 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 0^o Aries point on the ecliptic of the tropical zodiac, i.e. the vernal equinox.
Latitude is represented by the vertical angle above or below the celestial equator and is called the declination. 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 = 15^o.(24 hours of right ascension = 360^o.) 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 position of an object on the Earth is defined by an ordered pair, with first co-ordinate Latitude from 0^o at the equator to 90^o N or S at the poles, and second co-ordinate longitude from 0^o at the prime meridian to 180^o east or west on the other side of the globe. 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 27°25'S. Latitude of a point P is the angular distance north or south of the equator, e.g. latitude 45^o S. All points with the same latitude are on the same circle called a parallel. Two points with difference in latitude of 1^o 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 used by ships and aircraft is 1 852 m. 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 48^o.
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 runout 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.

36.42.3 Longitude, Greenwich Mean Time, GMT, UTC
See diagram 36.42.2: 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 180^o or in time, where 1 hour = 15^o. 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)
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 30^o East (of Greenwich). Another point could have longitude 25^o West. 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.
The 15^o longitude is equivalent to one hour and 1.0 degrees every four minutes (4 X 15 = 60).

36.42.4 Time zones, Greenwich time (GMT), Universal Time (UT)
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 equatorially 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. Also, the time in the State of Queensland, Australia, is one hour different from time in the State of New South Wales when that state adopts "daily saving", Eastern Australian summer time, but otherwise the times are the same.
Australian time zones (summer)
NSW, ACT, Victoria, Tasmania, EDT, (Eastern Daylight Saving Time) = EST + 1 hour, 9.00 pm
Queensland, EST (Eastern Standard Time), 8.00 pm
South Australia, CST (Central Standard Time), EST + 1/2 hour, 8.30 pm
Western Australia, WST (Western Standard Time) = EST -2 hours, 6.00 pm
NorthernTerritory, CST (Central Standard Time) = EST + 1/2 hour, 7.30 pm

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.
2. Watch compass (clock compass)
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.
3. If you have no watch, you can use the shadow of a stick instead. 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.
4. 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.
5. 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. In the northern hemisphere, if the star appears to rise you face east, if appears to lower you face west, if appears to move to the right you face south, if appears to move to the left you are facing south. For the southern hemisphere, the directions of apparent movement are opposite.
6. 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.

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

36.72 Alpha centauri (Rigil Kentaurus)
Alpha centauri is the brightest star in constellation Centaurus, third brightest star in the sky, is really 3 stars. It is a visual binary that orbits each other every 80 years + Proxima Centauri. The latter is a red dwarf star and the nearest star to the Sun. Its distance from the Earth is 40 petametres, 4.3 light years.

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 universe came into existence from a "big bang" 13.6 billion years ago and is still expanding.

36.74 Aldebaran, Alpha Tauri
Binary star, one of the stars is a red giant, Tauri, the bull's eye in the constellation of Taurus, 65 light years distant. Aldebaran the "follower" star is 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.