Color Chap 4.Cdr

Chapter 4 - Motions of the Earth Updated 10 July 2006

Figure 4.1 This is a time-exposure photograph of the northern sky from 43° north latitude. The NCP is toward the lower right and the motion is counterclockwise. This is about a 10 minute exposure. (a) (b) Celestial Equa t or

NCP (Polaris) Big Dipper (End) Big Dipper 50º (Start) 40º Sagittarius Antares

Scorpius

NW NE SE SW North South

Betelgeuse Taurus Regulus C r Orion e Leo to le a s Aldebaran u ti q a E l l E Pleiades a q ti u s Rigel a le to e r C

50º NE 50º SE SW NW East West

Figure 4.2 The solid lines indicate star streaks created by a long term photographic exposure, where the camera is held still. For clarity, not all of the possible star streaks are shown. Note that the angle shown between the celestial equator and the horizons is true only for locations at 40° north.

(a) In the northern sky, stars like those in the Big Dipper revolve around the north celestial pole (Polaris). If these stars are close enough to Polaris that they never go below the horizon, that are called circumpolar stars. Note that the altitude of the NCP is equal to the observer’s latitude.

(b) In the southern sky, all stars rise in the southeast and set in the south west. Their arched paths are parallel to the celestial equator, which is 50° above the southern horizon. Stars whose declination is lower than the altitude of the celestial equator (d < –50°) never come above the horizon and thus, are never seen.

(c) The stars of Leo rise in the east on paths parallel to the celestial equator. At 40° north latitude, the equator rises at an angle of 50° to the horizon.

(d) The stars of Orion and Taurus set in the west along paths which parallel the celestial equator. At 40° north latitude, the equator meets the horizon at an angle of 50°. (a) (b) 64º to celestial equator

Sagittarius Antares Big Dipper (End) NCP (Polaris) Scorpius Big Dipper (Start) 26º

NW NE SE SW North South

Betelgeuse

C r Regulus e o l t e a s Taurus Leo u t i q Orion a E l

l E Aldebaran a i Rigel q t u s a e l t o e r C Pleiades

64º 64º NE SE SW NW East West

Figure 4.3 The diurnal motion of the stars as seen at 26° north latitude. Note that the angles shown between the celestial equator and the eastern and western horizons are true only for locations at 26° north, such as Miami, Florida.

(a) In the northern sky, stars in the Big Dipper are no longer circumpolar, as they are at greater latitudes. There are still some circumpolar stars, like those in the Little Dipper. However, because the NCP is closer to the northern horizon, there are fewer circumpolar stars at the lower latitudes. Note that the altitude of the NCP is equal to the observer’s latitude.

(b) In the southern sky, all stars rise in the southeast and set in the southwest. Their arched paths are parallel to the celestial equator, which is 64° above the southern horizon (higher than this field of view). Stars whose declination is lower than the altitude of the celestial equator never come above the horizon and thus, are never seen. Because the celestial equator is higher at lower latitudes, more stars are visible, compared to higher latitudes.

(c) The stars of Leo rise in the east on paths parallel to the celestial equator. At 26° north, the equator rises at an angle of 64° to the horizon.

(d) The stars of Orion and Taurus set in the west along paths which parallel the celestial equator. At 26° north, the equator meets the horizon at an angle of 64°.7 90º (Zenith) +43° Local Meridian These stars are circumpolar. +90° 43º 47º 0° Equator NCP (Polaris)

W 0º+47° N 0º -47° E S Horizon All stars with Stars within declination between this circle never get +47º and -47º above the southern must rise and set. horizon. -90° SCP -47º

Figure 4.4 At latitude 40° N, all stars below –50° declination never come above the southern horizon. All stars above +50° declination are circumpolar. All stars between these declinations must rise in the east and set in the west. These declination values are given by the altitude of the celestial equator at the given latitude (section 2.5). The altitudes of important points are shown in normal print, while their equivalent declination is shown in bold. (a) (b) 90º to celestial equator 90º to celestial equator

Big Dipper (End) Southern Cross Big Dipper Southern Cross (Start) (Start) (End)

NW NCP (Polaris) NE SE SCP SW North South

Betelgeuse C

r e

o l t

Orion e

Regulus a s

u t i

q a l E Taurus Rigel

E Leo l

a q

t u

s Aldebaran a

e t l o

e r

90º 90º NE SE SW NW East West

Figure 4.5 The diurnal motion of the stars as seen at the Equator, 0° latitude. The angles shown between the celestial equator and the eastern and western horizons are true only for locations on the Equator.

(a) In the northern sky, there are no circumpolar stars, because the NCP is located directly on the northern horizon. The celestial equator is 90° from the northern horizon because at the Equator the celestial equator passes through the zenith. Notice the Big Dipper revolves around the NCP counterclockwise.

(b) In the southern sky, there are no circumpolar stars, because the SCP is located directly on the southern horizon. The celestial equator is 90° from the southern horizon. Notice the Southern Cross revolves around the SCP clockwise. Because both celestial poles are on the horizon, all sky objects are observable at the Equator.

(c) The stars of Leo rise in the east on paths parallel to the celestial equator. At 0° latitude, the equator rises at an angle of 90° to the horizon.

(d) The stars of Orion and Taurus set in the west along paths which parallel the celestial equator. At 0° latitude, the equator sets on the horizon at an angle of 90°. 90º (Zenith) 0°

Equator Local Meridian +90° W NCP N

E -90° S Horizon SCP No stars are circumpolar. Everything rises in the east and sets in the west.

Figure 4.6 When observing from the Earth’s equator, nothing is circumpolar. Everything must rise straight up in the east and set straight down in the west. The celestial equator passes through the zenith. (See section 2.5.) The altitudes of important points are shown in normal print, while their equivalent declination is shown in bold. (a) Celestial Equator (b)

Regulus SCP

Leo 40º 50º Southern Southern Cross Cross (End) (Start)

SE SW NW North NE South

Altair Altair Aquila

NE 50º SE East SW 50º NW West Figure 4.7 The diurnal motion of the stars as seen at 40° S latitude. The angles shown between the celestial equator and the eastern and western horizons are true only for locations with latitude of 40° S.

(a) In the northern sky, the NCP is 40° below the horizon. The celestial equator is 50° above the horizon. Any object with declination above 50° (d > +50°) is never visible. Polaris and the Little Dipper are never seen.

(b) In the southern sky, the south celestial pole is 40° from the horizon. The stars of the Southern Cross are circumpolar. Notice the Southern Cross revolves around the SCP clockwise.

(c) The stars of Aquila and Capricornus rise in the east on paths parallel to the celestial equator. The left arrow is pointing to the bright star, Altair.

(d) The stars of Aquila and Sagittarius set in the west along paths which parallel the celestial equator. The arrow on the right is the path of the bright star, Altair. 90º (Zenith) -43° Local Meridian 0° -90° SCP 43º 47º tor Equa

These stars are circumpolar. W 0º+47° N

0º -47° E S Horizon All stars with Stars within declination between this circle never get +47º and -47º above the northern must rise and set. horizon. +90° NCP -43º

Figure 4.8 Apparent motion of the celestial sphere at 40° S latitude. At latitude 40° S, all stars above +50° declination never come above the northern horizon and all stars below –50° declination are circumpolar. All stars between these declinations must rise in the east and set in the west. These declination values are given by the altitude of the celestial equator at the given latitude.

(a) (b)

Pollux Canus Castor Major Gemini Pleiades Lepus Taurus Sirius

Aldebaran Betelgeuse Rigel Orion r r Horizon Celestial Equato Horizon Belt Celestial Equato South South South North North North

Figure 4.9 The diurnal motion of the stars as seen at the Earth’s poles. At either pole, the altitude of the celestial equator is 0°, that is, it matches the horizon and all motion is parallel to the horizon. Everything is circumpolar – nothing rises or sets (except the Sun, Moon and planets).

(a) At the North Pole, only the upper half of Orion is visible, moving along the horizon from left to right.

(b) At the South Pole, only the lower half of Orion is visible, moving along the horizon from right to left. Notice the rotation is the opposite of the North Pole. Upp er M er Zenith idi an L - oc U a p l M p e e r r id C Celestial Pole ia u n lm in a t P i o o la n r A s x is

Horizon

L o w e r M e A r n id tim Celestial Pole ia e n ri - di L an ow e r C ulm Nadir ina tions

Figure 4.10 This diagram shows the relationship between the local meridian, the antimeridian, the celestial poles, the upper and lower meridians, the zenith, the nadir and the upper and lower culminations. The meridian is the entire great circle. The celestial poles are not labeled with north or south so the diagram works for either hemisphere.

EQUATORIAL CHART +60° +60° Capella, +46º

+30° +30°

Altair +9º 0° 0° Sirius –17º –30° –30°

–60° –60° h h h h h 12 6 0 18 12 Figure 4.11 This drawing shows the declination of a few example objects from the Equatorial Chart. The culminations of an object is determined from its declination. Add the object’s declination to the transit altitude of the celestial equator. The transit altitude of the celestial equator depends on the observer’s latitude (figures 2.23 and 2.26). Zenith Capella ian erid al M oc Altair L 4 6 ° 8 Q 4º C NCP (Polaris) el es º tia 7 l 1 º E Sirius – 9 qu at or

º 4 9 West 0 5 º º 3 3 º 0

South North

Ho ri z o n

East

Figure 4.12 This figure shows the transit altitudes of Altair and Sirius as seen at 40° N. Note that it is not intended to imply that Altair and Sirius transit the local meridian at the same time. They transit according to their right ascension coordinate. They are shown together simply for example and comparison.

Zenith ian erid UC l M ca Lo Q C e le 7 NCP s 5º (Polaris) tia l E q u a to r

4 º 0 0 º 5 West

LC 5º South North

East

Figure 4.13 The upper (UC) and lower culmination (LC) of Mizar is shown for 40° N latitude. Below 35° N latitude, Mizar is not circumpolar and would not have a lower culmination. At latitudes higher than 40° N, the culminations move toward the zenith with the NCP. Zenith Q Altair Sirius

-17º +9º Lo ca l M er id ia n º 8 3 1 7 º

º 9 0 0 9 º

West

SCP South North NCP Celestial Equator on Horiz

East

Figure 4.14 This figure shows the transit altitudes of Altair and Sirius as seen at 0° latitude. Because Sirius has a negative declination, its altitude is measured off the southern horizon. Altair has a positive declination, so its altitude is measured off the northern horizon.

Zenith Canopus Sirius –52° Q SCP º 78 Altair + 9 -1 º 7º 6 7º 4 1 º West 5 º 0 0 º 4

r to a u q South E North l a ti s le e C on Horiz

East

Figure 4.15 This figure shows the transit altitudes of Altair and Sirius as seen at 40° S. Zenith Lo cal M UC erid ian

Q SCP r (s Octantis) to ua 8º q 6 l E tia s le e C

5 º 0 0 º 4 West LC

12º South North

on Horiz

East

Figure 4.16 The upper (UC) and lower culmination (LC) of a Centauri at 40° S latitude. At latitudes north of 38° S, a Centauri is no longer circumpolar and the lower culmination is no longer visible, leaving only the transit altitude (upper culmination) of a Centauri to think about. At greater southern latitudes, the culmination points move toward the zenith along with the SCP.

April July

NCP (Polaris)

January October

Figure 4.17 The annual motion of the Big Dipper. This is the approximate position of the Big Dipper on the first day of the months shown, at 22:00. The annual motion of the Big Dipper is caused by the Earth revolving around (orbiting) the Sun. April

July

SCP (s Octantis) January

October

Figure 4.18 The annual motion of the Southern Cross is clockwise around the south celestial pole. This is the approximate position of the Southern Cross on the first day of the months shown, at 22:00 hours.

Figure 4.19 An American penny shown actual size.

Local Meridian Local Meridian

Mean Solar Day Mean Solar Day

"Long Day" "Short Day" "Short Day" "Long Day" Sun Sun Sun Sun

East South West West North East Northern Hemisphere Horizon View Southern Hemisphere Horizon View

Figure 4.20 The Sun rises in the east and sets in the west once per day – its diurnal motion. The amount of time for successive local meridian transits is one solar day. The Earth does not have a constant speed as it orbits the Sun while its rotational speed is nearly constant. Thus, the amount of time between transits is slightly different from day to day. Scorpius

Earth's Orbit

Leo Sept 1 Sun Mar 1 Aquarius

Taurus

Figure 4.21 The annual motion of the Earth around the Sun causes the “seasonal migration” of the constellations. On 1 March, we can see Leo but not Aquarius. On 1 September, the Sun blocks our view of Leo but we can see Aquarius.

EQUATORIAL CHART +60° +60°

+30° +30° June Solstice

Ecliptic March Equinox September Equinox 0° 0° September Equinox

Direction of the Sun's –30° Annual Motion December Solstice –30° (West to East)

–60° –60° h h h h h 12 6 0 18 12

Figure 4.22 The ecliptic is the path of the Sun through the zodiac constellations. The positions of the equinoxes and solstices are shown along the ecliptic line.

Figure 4.23 The symbols for the medical sciences usually contain one or two serpents. The zodiac constellation, Ophiuchus, represents “The Serpent Handler” or “The Doctor.” Figure 4.24 These are pendulum-based transmitting clocks and chronographs operating at the time service of the United States Naval Observatory near Washington D.C., about 1915. (Courtesy of the U.S. Naval Observatory.)

Figure 4.25 This is the B-12 quartz crystal clock used by the USNO time service in the early 1960s. (Courtesy of the U.S. Naval Observatory.) Figure 4.26 The “Atomichron,” one of the earlier atomic clocks, used by the time services at the USNO in 1961. (Courtesy of the U.S. Naval Observatory.)

Due to elliptical orbit Due to obliquity of ecliptic t Clock behind sundial n Equation of time e r

a +10 p p a

s u n ) i s m e

t 0 e u n i m i t

m r (

a l e o m s i

-10 n r a a l e o M s Clock ahead of sundial

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Figure 4.27 The equation of time is the difference between apparent solar time and mean solar time. The two principal causes of the difference are the varying speed of the Earth as it orbits the Sun and the obliquity of the ecliptic. When the variations caused by these two effects are added together, the result is called the equation of time. Jun

20º

a M

A A p r 10º

A p r

p e S

Minutes +20 +10 0 -10 -20

a r

t c

O -10º

F n o e i t

b a n i l c e D

N o v -20º n a J Dec

Figure 4.28 The analemma is a plot of the equation of time against the declination of the Sun. Northern Hemisphere Southern Hemisphere To Regulus Local Meridian Local Meridian Orbital path Regulus Sun 10:10 Sun of Earth Sun Regulus Local Sidereal Clock Meridian

W 12:00 E Earth

East South West West North East Solar Clock "Horizon View" "Horizon View"

Figure 4.29 We start with the Sun and the star Regulus (in the constellation Leo) on the local meridian. Notice the relationship of the positions of Regulus, the Sun and the local meridian with the clock readings. This is the first of three drawings showing the relationship of solar and sidereal time.

Northern Hemisphere Southern Hemisphere To Regulus Local Meridian Local Meridian Orbital path Regulus Sun 10:10 Sun of Earth Sun Regulus Local Sidereal Clock Meridian W E Earth 11:56

East South West West North East Solar Clock "Horizon View" "Horizon View" Figure 4.30 This is one sidereal day later from figure 4.29. The annual motion of the Earth around the Sun causes the apparent motion of the Sun against the background stars. One sidereal day later, the Earth has rotated 360° and revolved around the Sun by approximately 1° (the angle shown here for the change in the orbital position of the Earth is exaggerated, for clarity). However, the orbital motion of the Earth causes the Sun to no longer line-up with Regulus. The Sun appears to move eastward in our sky relative to the stars. This was labeled the annual motion of the Sun in section 4.4.

Northern Hemisphere Southern Hemisphere To Regulus Local Meridian Local Meridian Orbital path Regulus Sun 10:14 of Earth Sun Sun Regulus Sidereal Clock Local Meridian W E Earth 12:00

East South West West North East Solar Clock "Horizon View" "Horizon View"

Figure 4.31 About four minutes after figure 4.30, the Earth has rotated the extra degree so the Sun is now on the local meridian, but Regulus has moved to the west. The stars appear to move westward in our sky relative to the Sun. The Earth's orbital motion is also responsible for the seasonal motion of the Big Dipper (and the other constellations) around Polaris. Refer to the discussions surrounding figures 4.2 through 4.18, the annual motion of the sky in section 4.3. n r

u Horizon o t S

a f u o

q Civil Twilight h t E

l a a P i

Nautical Twilight t l s a e n l r e Astronomical Twilight u i C D

l = 0° l = 30° l = 60°

Figure 4.32 The length of twilight depends on the observer’s latitude because the angle of the diurnal path of the Sun through the twilight altitudes (the twilight zone?) varies with latitude. At the equator (l = 0°) twilight is the minimum length of time because the path of the Sun through the twilight altitudes is as short as possible. At latitude l = 30°, the angle of the Sun’s diurnal path with the horizon causes an increase in the amount of time the Sun spends in the twilight altitudes. It is even greater at latitude 60°. North or South latitude was not specified because the effect is the same north or south of the equator. This diagram shows sunrise in the northern hemisphere or sunset in the southern hemisphere.

Axis of Precession

Precessional Motion Axis of Rotation

Rotational Motion

Figure 4.33 The motion of a toy gyroscope shows both rotation and precession. Both of these motions are circular and both have an axis of rotation. 23a5

Rotating Earth F

or Ecliptic uat plane. Eq F

Figure 4.34 The tidal force pairs of the Moon or Sun act on the Earth’s equatorial bulge producing torques that cause the Earth to precess. This figure shows only one tidal force pair (labeled, F), perhaps the Sun’s. Each object creating a tidal force on the Earth has a corresponding force pair. The oblateness of the Earth is greatly exaggerated here.

Hercules Lyra

Corona Borealis 15 000AD Vega Cygnus

Boötes

Draco

4500BC 8500AD NEP a

a Thuban 2700BC Cepheus Ursa Minor Ursa Major Polaris g NCP 2000AD Cassiopeia

Figure 4.35 The orbit of the north celestial pole through the constellations is caused by the precessional motion of the Earth. The north ecliptic pole (NEP) is found at the center of this circle. n

Tuncana Octans d b Musca b s Crux SCP g Hydrus Chamaeleon Achernar g e a Mensa

4600BC Volans 8400AD SEP

Eridanus Dorado Pictor Carina Vela

Canopus

14800AD

Puppis Pyxis Columba

Figure 4.36 The orbit of the south celestial pole through the constellations is caused by the precessional motion of the Earth. The south ecliptic pole (SEP) is found at the center of this circle.

Equinoctial Colure

Pisces Vernal Equinox E cli ptic Celestial Equator Direction of vernal equinox motion

Direction of Sun's motion

Aquarius

Figure 4.37 The Earth’s precessional motion is causing the vernal equinox to creep along the ecliptic line in the opposite direction to the annual motion of the Sun. This has repercussions in terms of defining the year and in the measurement of the equatorial coordinates of celestial objects.