module 3: the celestial sphere 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.

As the Earth rotates on its axis from west to east, the Sun appears to rise in the east and set in the west.

(a) Day and night & the Earth’s rotation

that is, day and night.

Locations on the Earth’s surface alternate between sunlight and darkness -

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 settingin the southwestern sky.

Star trails around the south celestial pole, towards the dome of the Anglo-Australian Telescope (AAT)

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) andthe “north celestial pole” (for northern hemisphere viewers).

(c) The celestial sphere & celestial poles

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 east south west

South CelestialPole

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 CelestialPole

north west north eastPolaris

There is no bright star at the South Celestial Pole.

south east south west

South CelestialPole

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

north celestial pole

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”

south celestial pole

north celestial pole

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

south celestial pole

north celestial pole

… which is anextension of theEarth’s equator.

We can also project the Earth’s imaginary longitude

south celestial pole

north celestial pole

and latitude lines onto the celestial sphere

The correspondingcelestial coordinatesare:

Longitude right ascension (RA)Latitude declination (dec)

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

south celestial pole

north celestial pole

An observer on the Earth’ssurface

sees the night skyabove the horizon

but not below.

observer’s horizon

So this observer cansee the North Celestial Pole and much of the sky (as the Earth rotates),but not the southern-mostsky near the South Celestial Pole

N

S

WETheir order mayseem odd, but remember thatthey apply to anobserver’s view whenlooking directly up.

Looking up, this northern hemisphere observer will see:

horizon

Polaris, at thenorth celestial

pole

Note the relativepositions of Eastand West on thissky chart.

N

S

W

horizon

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,

zenith

is called the “celestial meridian”.

S

WE

horizon

NWe can superimposelines of constant right ascension (RA)

and declination(dec)

An observer in the southern hemisphere will see: N

WE

horizonthe south

celestial pole

x

RA lines

dec lines

S

(d) Sidereal & Mean Solar TimeThe 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 returnto 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

Sun4mins

Day Zero: Sun and distant star overhead

Sidereal day: distant star overhead again(but not Sun)

Solar day: Sun overhead again (but now more than one sidereal day has passed)

Local standard time (the time we set our clocks to) is derived from mean solar time, but stars rise accordingto 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

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