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 (c) (d) 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 (c) (d) 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 (c) (d) 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 i t u s Aldebaran a e t l o e r C 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 (c) (d) r C to e a le u s q t E ia l l a ti E s q e u l a e C Aquila to r Capricornus Sagittarius 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.