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The Celestial Sphere To determine the positions of stars and planets on the sky in an absolute sense, we project the Earth's spherical surface onto the sky, called the celestial sphere (Figure 1). It is useful in discussing objects in the sky to imagine them to be attached to a sphere surrounding the earth. This fictitious construction is called the celestial sphere. The point on the celestial sphere that is directly over our heads at a given time is termed the zenith, while directly below you is the nadir (both of which are points on the celestial sphere). Figure 1: The Earth and the Celestial Sphere In between is the great circle of the horizon, which is the circle on the celestial sphere cut by a plane tangent to the Earth at your feet. Everything in the sky above the horizon is visible, while everything below it is not. At any one time we see no more than half of this sphere, but we will refer loosely to the imaginary half-sphere over our heads as just the celestial sphere (see Figure 2). To make it easier to understand the motions of objects in our skies, astronomers often depict the heavens as a sphere surrounding the Earth. Everything we see in space is drawn on this celestial sphere, ignoring the fact that the Sun, Moon, and stars are really at different distances from us. The Earth appears to lie at the center of a fictional celestial sphere. You pretend that you are inside the sphere at the center looking out around you. You can even buy celestial spheres that look like globes with stars and constellations instead of countries and seas. Figure 2: Half of the Celestial Sphere Motion in the Sky It is clear after only minimal observation that objects change their position in the sky over a period of time. This motion is conveniently separated into two parts: 1. The entire sky appears to turn around imaginary points in the northern and southern sky once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours. 2. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon. Celestial Coordinate System We can define a useful coordinate system for locating objects on the celestial sphere, just as the latitude-longitude coordinate system that we use on the surface of the earth. The Earth's North and South Poles are extended out to the sphere to mark the north and south celestial poles (NCP and SCP). The earth’s equator is projected out to become the celestial equator. The imaginary circle passing through the North and South points on our horizon and through the zenith is termed the celestial meridian (the circle that runs through the zenith, nadir, North celestial pole and South celestial pole). The Earth rotates about its poles from west to east (counter-clockwise as viewed from above the north pole), which makes the sky seem to rotate in the other direction about the north and south celestial poles parallel to the celestial equator. The Ecliptic Another important imaginary object on the celestial sphere is the "ecliptic" or "Road of the Sun", which is the imaginary path that the Sun follows on the celestial sphere over the course of a year. If we plot the Sun's location in our sky for each day of the year, it will trace a circle on the celestial sphere. This circle shows the Sun's path among the stars throughout the year, and is called the ecliptic (see Figure 1). This is the same word used to describe the Earth's path around the Sun because the Earth's motion is what makes the Sun seem to move among the stars. This apparent position of the sun with respect to the background stars (as viewed from the Earth) changes continuously as the Earth moves around its orbit, and will return to its starting point when the Earth has made one revolution in its orbit. Because the rotation axis of the Earth is tilted by 23.5 degrees with respect to the plane of its orbital motion (which is also called the ecliptic), the path of the Sun on the celestial sphere is a circle tilted by 23.5 degrees with respect to the celestial equator (see Figure 3). The tilt separates the celestial and ecliptic poles by 23.5 degrees, which causes the circle of the ecliptic to be tilted relative to the celestial equator by the same angle, which as a result is called the obliquity of the ecliptic. Figure 3: The Ecliptic and the Celestial Equator Right Ascension and Declination Like the longitude and latitude system here on Earth, the celestial sphere has a system to pinpoint locations. Figure 4: Declination (marked in degrees) and Right Ascension (marked in hours) Declination tells us how far an object is north or south of the celestial equator, measured in degrees. Now imagine the Earth's Equator extended out to infinity, the corresponding point on the celestial sphere is the celestial equator. Just as the angle between the pole and the equator on Earth is a right angle, the same is true of the celestial sphere. For this reason, points on the celestial equator are said to have a declination of 0° and the celestial pole is said to have a declination of 90°. Note that declination is analogous to latitude on Earth, where the pole has latitude of 90° and the equator has latitude of 0°. Of course, we can also imagine lines in between of declination 10°, 20°, 30° etc., corresponding to latitude on Earth, and note also that lines South of the equator have negative declinations (e.g. -76° is 76° South). Parts of a degree are measured in arc minutes (60 arc minutes per degree) and seconds (60 arc seconds per arc minute). So you may see a particular declination given as -7° 27' 03", which means 7 degrees 27 minutes and 3 seconds South, which is just under 7 and a half degrees South of the celestial equator. In reality arc seconds are much too tiny for us to worry about, rounding to the nearest half-degree is usually more than accurate enough. Figure 5: Lines of Declination and Right Ascension in the Celestial Sphere Obviously we can't set points with only one coordinate, another set is needed, just as longitude was needed on Earth to be able to define a point completely. Right ascension (RA) tells us how far an object is to the east of the Vernal Equinox, that point midway between winter and summer when the ecliptic (the Sun's path) crosses the celestial equator. Right Ascension is the celestial equivalent of longitude. Just as longitude doesn't have so much of a natural significance, so was arbitrarily centred on Greenwich Observatory, London, RA was defined to be zero at the first point in Aries. Because the Earth is turning, the stars appear to turn – but since there is no movement, North-South lines of declination stay fixed – this is why they are more significant. As the stars appear to rotate East-West, lines of RA move – they complete one full turn per day (well, actually a little bit more due to the fact the Earth has moved about 1° round the sun in a day, but this is small enough to be ignored day-to-day). This means that a particular star moves through 15° per hour. So, it is convenient for us to measure Right Ascension in hours, where 15 degrees is one hour and 360 degrees is 24 hours. This is further divided up into minutes and seconds (not to be confused with arc minutes and arc seconds, which are not the same thing) in the same way that time is divided, i.e. an hour is 60 minutes, a minute is 60 seconds etc. If you were looking at a star through your telescope say at 50° declination and 0 hrs RA, in 1 hour time you would be looking at 1 hr RA, then 2 hours later at 2 hrs RA and so forth. In fact, after say, 3 hours, 56 minutes and 12 seconds, you would be looking at 3 hrs 56 mins 12 sec Right Ascension! So now we have two co-ordinates, we can plot any point on the surface of the celestial sphere. For instance the Orion Nebula has co-ordinates -5° 27' declination, 5h 35m 24s RA. The Andromeda Galaxy has coordinates 41° 16' declination, 0h 42m 42s RA Note: Declination is measured to both the east and west of its starting point, but right ascension is measured only to the east (see Figure 1 and Figure 4). Equinoxes and Solstices The ecliptic crosses the celestial equator twice a year, on the equinoxes. One the vernal equinox and the other being autumnal equinox. Figure 6: Vernal Equinox and Autumnal Equinox Twice a year, the Sun crosses the equator, on or about March 20 at a point called the Vernal Equinox (also called ‘First point of Aries’), and on September 23 at the Autumnal Equinox (the terms derived from a northern hemisphere perspective). On these dates, the Sun has a declination of 0°, rises exactly east, sets exactly west, is up for 12 hours and down for 12 hours, hence the term equinox. The equinox passages respectively announce the beginning of northern-hemisphere spring and autumn (and southern hemisphere autumn and spring). (In actual fact, the risings, settings, and 12-hour durations cannot be exact, since the Sun is continuously moving along the ecliptic and is on the equinoxes but for the moment. In addition, upward refraction by the Earth's atmosphere and the finite angular diameter of the Sun renders the equinox day a bit longer than 12 hours, night a bit shorter, all the while ignoring twilight.) Figure 7: The Sun and the seasons As the Sun moves north of the equator from the Vernal Equinox, it rises and sets progressively more to the north of east and west. Days gradually become longer than 12 hours, nights shorter. On June 21, the Sun reaches its most northerly extent (as seen in the right-hand "Earth" in Figure 7), at a declination of 23.5 degrees north at the Summer Solstice, to begin northern-hemisphere summer (southern hemisphere winter). It then rises as far north of east and sets as far north of west as possible. Northern hemisphere days are now the longest of the year, nights the shortest, the extent of the effect dependent on latitude. Conversely, following the autumnal equinox, as the Sun moves south, it rises and sets progressively farther south of east and west. Northern hemisphere days now get shorter (less than 12 hours), nights longer (greater than 12 hours). On December 22, the Sun reaches its most southerly extent (see the left-hand "Earth" in Figure 7), at a declination of 23.5 degrees south, at the Winter Solstice to begin northern-hemisphere winter (southern hemisphere summer). It then rises as far south of east and sets as far south of west as possible. Northernhemisphere day-time is now minimized, night-time maximized. All the effects are reversed in the southern hemisphere, while at the Earth's equator, days and nights are always equal at 12 hours. When at the Summer Solstice, the northern-hemisphere Sun (north of the tropics) crosses the celestial meridian as high as possible, while at the Winter Solstice it crosses as far to south as possible. In the summer, sunlight spreads itself over a smaller area of ground than it does in winter, and thereby heats the ground more efficiently, yielding more heat, so it is hot in the summer, cold in the winter. This effect is the sole cause of the Seasons. (The effect of the variation in distance between the Earth and the Sun caused by the Earth's elliptical orbit is of little consequence because of the power of the oceans to store heat.) Above the Arctic Circle at latitude 66.6° north (and below the Antarctic Circle, latitude 66.6° south), the Sun can be circumpolar in the summer, yielding 24 hours of sunlight and a midnight Sun. (The midnight sun is a natural phenomenon occurring in summer months at places north of the Arctic Circle and south of the Antarctic Circle where the sun remains visible at the local midnight). The farther north of the Arctic Circle (or the farther south of the Antarctic Circle), the more days of midnight Sun you will see. In the tropics (between latitudes 23.5°N at the Tropic of Cancer and 23.5°S at the Tropic of Capricorn) the Sun can be overhead sometime during the year (on June 21 at the former, on December 22 at the latter). Point Vernal Equinox Summer Solstice Autumnal Equinox Winter Solstice Table 1: Equinoxes and Solstices Usual Date Right Ascension March 20 0 hours June 21 6 hours September 23 12 hours December 22 18 hours Declination 0° 23.5° N 0° 23.5° S Astronomical Time and Coordinates Your location on Earth is expressed through your latitude (your north-south position; see Figure 8) and longitude, which gives your east-west position. Draw a circle called a meridian from the North Pole through your location to the South Pole, then do the same through Greenwich, England to define the prime meridian, and note where they cross the equator. Your longitude (given by lower case Greek letter lambda) is the angle between the two intersections (of the meridians and the equator). In the illustration, the latitude of Greenwich is 51° 29' North (the longitude is by definition zero); those of Buenos Aries are 34° 35' South, 58° 29' West (Figure 8). Figure 8: Illustration of the Hour angle Similar way, the angular displacement of a star to the west of the celestial meridian (as measured along the celestial equator, analogous to longitude) is called the hour angle, which is usually given in time units at a rate of 15° per hour. Apparent solar time is given by the hour angle of the Sun plus 12 hours (the 12 hours added so that the "day" starts at midnight). Because of the eccentricity of the Earth's orbit and the obliquity of the ecliptic, apparent solar time does not keep a constant pace. Corrections for their effects lead to constant mean solar time, which can differ from apparent solar time by up to 17 minutes. The hour angle of the Sun, and therefore the time of day, varies continuously with longitude, wherein longitude differences exactly equal time differences. Standard times are the mean solar times of the closest standard meridians, which are displaced in units if 15° from Greenwich. (Political boundaries cause variances.) Star time, properly called sidereal time, is the hour angle of the Vernal Equinox. Because the Sun moves to the east along the ecliptic, the Sun takes longer to make a circuit of the sky on its daily path than does a star or the equinox, so the solar day is 4 minutes longer than the sidereal day. As a result, the sidereal clock gains 4 minutes (actually 3 minutes 56 seconds) per day over the solar clock, starting from the time of solar passage across the autumnal equinox on September 23, when the two are the same. The right ascension of a star or any other celestial body is the angle the body makes with the vernal equinox as measured to the east, again along the celestial equator. It too is usually measured in time units. The right ascension and hour angle of a body always add to equal the sidereal time. Given the sidereal time and the right ascension of a body, you can compute its hour angle, which with the declination allows you to set a telescope and to find anything in the sky. Solar Time and Sidereal Time Solar Time is the time as measured by the position of the sun. It is not uniform; it speeds up and slows down, because the earth moves slower and faster in its orbit around the sun, and because of different distances from the sun. The fundamental unit of solar time is the day. The solar day is the time it takes for the sun to return to the same meridian in the sky. Two types of solar time are apparent solar time (sundial time) and mean solar time (clock time). Our clocks use Mean Solar Time, which is uniform, being averaged out over a year (365.243... days). So the sun is not where the clock says it is. Apparent solar time or true solar time is given by the daily apparent motion of the true, or observed, Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian. When the center of the sun is on an observer's meridian, the observer's local solar time is zero hours (noon). Because the earth moves with varying speed in its orbit at different times of the year and because the plane of the earth's equator is inclined to its orbital plane, the length of the solar day is different depending on the time of year. It is more convenient to define time in terms of the average of local solar time. Such time, called mean solar time, may be thought of as being measured relative to an imaginary sun (the mean sun) that lies in the earth's equatorial plane and about which the earth orbits with constant speed. Every mean solar day is of the same length. The difference between the local solar time and the mean solar time at a given location is known as the equation of time. Tables used by navigators list the equation of time for different times of year so that an observer can calculate his mean solar time from his local solar time (found by determining the sun's hour angle). Mean solar time is the basis for civil time and standard time. Figure 9: Solar day and Sidereal day Sidereal Time is time kept with respect to the distant stars. Because the Earth moves in its orbit around the Sun, the Earth must rotate more than 360 degrees in one solar day. A solar day lasts from when the Sun is on the meridian at a point on Earth until it is next on the meridian. A solar day is exactly 24 hours (of solar time). Because of the Earth's revolution, a solar day is slightly longer than a sidereal day. In everyday life, we use solar time. The Earth must rotate an extra 0.986 (approx. 1) degrees between solar crossings of the meridian. Therefore in 24 hours of solar time, the Earth rotates 360.986 (approx. 361) degrees. Because the stars are so distant from us, the motion of the Earth in its orbit makes an negligible difference in the direction to the stars. Hence, the Earth rotates 360 degrees in one sidereal day. A sidereal day lasts from when a distant star is on the meridian at a point on Earth until it is next on the meridian. A sidereal day lasts 23 hours and 56 minutes (of solar time), about 4 minutes less than a solar day. Figure 10: Sidereal time The Astronomical Unit An astronomical unit (abbreviated as AU, au, a.u., or ua) is a unit of length equal to 149,597,870,700 metres (92,955,807.273 mi) or approximately the mean Earth–Sun distance. The AU was originally defined as the length of the semi-major axis of the Earth's elliptical orbit around the Sun. The average distance is about 150 million kilometres (149.6) or 93 million miles (92.9). This is defined as 1 astronomical unit, or AU, and is equal to about 8.2 light-minutes, as light from the Sun takes about 8 minutes to reach Earth. Earth's orbit is actually not perfectly circular so the distance between the Earth and the Sun varies slightly over the course of the year, from a minimum of 147.1 million kilometres (91 million miles) to a maximum of 152.1 million kilometres (94.5 million miles). More precisely, the semi-major axis of Earth's orbit is 149,597,887.5 kilometres. When it is closest to the Sun (perihelion) it is 147,098,074 km or 0.98 AU. At farthest (aphelion) it is 152,097,701 km or 1.02 AU. We are farthest away during summer in the Northern Hemisphere (around July 4th), and closest around January 4, which is summer in the Southern Hemisphere.