Activity 1: The Rotating Earth Module 3: The Celestial Sphere Activity 1: The Rotating Earth

Summary: In this Activity, we will investigate (a) day and night & the Earth’s rotation, (b) star trails, (c) the celestial sphere & celestial poles, and (d) sidereal and mean solar time.

(a) Day and night & the Earth’s rotation As the Earth rotates on its axis from west to east, the Sun appears to rise in the east and set in the west. Locations on the Earth’s surface alternate between sunlight and darkness - that is, day and night.

Here we show four frames of the Earth rotating, showing Australia move from day to night. The Sun in on the left: Sunlight animations © Swinburne

(b) Star trails Because of the Earth’s rotation, the stars appear to slowly move across the night sky as the hours go by. (The stars also appear to slowly shift in position each night - so that you will see different stars overhead each night at, say, midnight. This is due to the changing position of the Earth in its orbit around the Sun, and means that we see different zodiacal constellations through the course of a year.)

If a camera is left outside with its shutter open for several hours on a clear night, it will photograph “star trails”, recorded on the film due to the apparent motion of stars across the night sky. Star trails photographed in the southwest, towards the dome of the Anglo-Australian Telescope (AAT)

To make this picture, David Malin of the Anglo-Australian Observatory pointed a camera towards the dome of the Anglo Australian Telescope at Siding Spring Mountain in New South Wales, Australia. Most stars rise & set in our sky - the star trails here are made by stars setting in the southwestern sky.

(c) The celestial sphere & celestial poles Some stars never set. Their trails form complete circles around points in the sky called (c) the celestial sphere & celestial poles the “south celestial pole” (for southern hemisphere viewers) and the “north celestial pole” (for northern hemisphere viewers). Star trails around the south celestial pole, towards the dome of the Anglo-Australian Telescope (AAT)

We can explain this apparent motion if we recognize that it is caused by the Earth’s daily rotation on its axis. Almost all stars appear to follow circular paths, but most are partly obscured below the horizon. South Celestial Pole south east south west

Only stars on a direct extension of the Earth’s rotation axis appear to stay stationary during the night. Observers in the northern hemisphere see Polaris, the North Star, as stationary - it happens to be located almost at the North Celestial Pole. North Celestial Pole Polaris north west north east

There is no bright star at the South Celestial Pole. south east south west

north celestial pole Although stars are actually at widely varying distances from Earth, we can picture these apparent motions as happening on an imaginary “celestial sphere”: south celestial pole

Although alt and az are easy coordinate systems Although alt and az are easy coordinate systems* to use, they depend on where the observer is (i.e. where the horizon is located). We can use the idea of the celestial sphere to define another celestial coordinate system. This one is the same for all Earth observers. *To be reminded of how altitude (alt) and azimuth (az) are defined, review the Activity on Star Patterns.

We can imagine the celestial sphere as having a “celestial equator” north celestial pole We can imagine the celestial sphere as having a “celestial equator” south celestial pole

We can imagine the celestial sphere as having a “celestial equator” north celestial pole We can imagine the celestial sphere as having a “celestial equator” … which is an extension of the Earth’s equator. south celestial pole

We can also project the Earth’s imaginary longitude north celestial pole We can also project the Earth’s imaginary longitude and latitude lines onto the celestial sphere The corresponding celestial coordinates are: Longitude  right ascension (RA) Latitude  declination (dec) south celestial pole

Declination is measured in degrees, arcminutes and arcseconds above or below the celestial equator - so, for example, stars near the north celestial pole have declinations close to +90°, and stars close to the south celestial pole have declinations close to - 90°. (1 degree = 60 arcmin, 1 arcmin = 60 arcsec)

Right ascension is measured in hours, minutes and seconds, because it takes approx. 1 day for a star to reappear at the same point in the sky.

So a star’s coordinates might look something like: 12:52:03, – 47:34:43 which means RA = 12 hours 52 min 3 sec, dec = - 47 degrees 34 arcmin 43 arcsec

An observer on the Earth’s surface north celestial pole An observer on the Earth’s surface sees the night sky above the horizon but not below. So this observer can see the North Celestial Pole and much of the sky (as the Earth rotates), but not the southern-most sky near the South Celestial Pole observer’s horizon south celestial pole

Looking up, this northern hemisphere observer will see: N Polaris, at the north celestial pole N Note the relative positions of East and West on this sky chart. E W Their order may seem odd, but remember that they apply to an observer’s view when looking directly up. horizon S

is called the “celestial meridian”. The imaginary line across the sky from the most northern point on the horizon, through the zenith, to the most southern point on the horizon, W is called the “celestial meridian”. zenith horizon S

We can superimpose lines of constant right ascension (RA) N and declination (dec) E W horizon S

RA lines dec lines An observer in the southern hemisphere will see: N x horizon the south celestial pole S

(d) Sidereal & Mean Solar Time The period of rotation of the Earth itself (the “day”) depends on whether one defines it as relative to the position of the Sun or relative to the fixed stars. The time interval between when any particular (far distant) star is on the celestial meridian, from one day to the next, is the sidereal day. The average time interval from when the Sun is at celestial meridian from one day to the next is called the mean solar day.

Because the Earth moves a small distance along its orbit during one day, the Sun shifts its position in the sky slightly eastwards each day. Because of this, it takes a little longer for the Sun to return to the meridian each day than it does for a distant star. Therefore the mean solar day is slightly longer than the sidereal day - by about 4 minutes (or, more exactly, 3m 55.51s!).

If we start counting a day when the Sun and some distant star are directly overhead, after the Earth has turned far enough for the stars to return to the same apparent position in the sky, the Earth must still move an extra 1/365 of 24 hours (or about 4mins) for the Sun to return to your meridian. distant star Sun 4mins Solar day: Sun overhead again (but now more than one sidereal day has passed) Sidereal day: distant star overhead again (but not Sun) Day Zero: Sun and distant star overhead

Local standard time (the time we set our clocks to) is derived from mean solar time, but stars rise according to sidereal time. This is why stars appear to rise about 4 minutes earlier each night. This is why astronomers prefer to use sidereal time to record their observations. If you visit the control room of a research telescope, you are likely to find clocks displaying local sidereal time, local standard time and Universal Time (otherwise known as Greenwich mean time).

Image Credits NASA: View of India and Saudi Arabia, taken by the Clementine spacecraft http://nssdc.gsfc.nasa.gov/image/planetary/earth/clem_india_saudi.jpg NASA Photo p-41508c: Image of the Earth and Moon from Galileo (cropped) http://nssdc.gsfc.nasa.gov/image/planetary/earth/gal_earth_moon.jpg AAO, David Malin: Image reference AAT 5 Star trails in the southwest (© reproduced with permission) http://www.aao.gov.au/local/www/dfm/aat005.html AAO, David Malin : Image reference AAT 6 Star trails around the south celestial pole (© reproduced with permission) http://www.aao.gov.au/local/www/dfm/aat006.html

Hit the Esc key (escape) to return to the Module 3 Home Page Now return to the Module home page, and read more about day & night and the celestial sphere in the Textbook Readings. Hit the Esc key (escape) to return to the Module 3 Home Page