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 KDE_LANG = en KDE_DOCS = AUTO
 Jason Harris The Celestial Sphere The celestial sphere is an imaginary sphere of gigantic radius, centered on the Earth. All objects which can be seen in the sky can be thought of as lying on the surface of this sphere. Of course, we know that the objects in the sky are not on the surface of a sphere centered on the Earth, so why bother with such a construct? Everything we see in the sky is so very far away, that their distances are impossible to gauge just by looking at them. Since their distances are indeterminate, you only need to know the direction toward the object to locate it in the sky. In this sense, the celestial sphere model is a very practical model for mapping the sky. The directions toward various objects in the sky can be quantified by constructing a Celestial Coordinate System.
 Jason Harris The Equinoxes Most people know the Vernal and Autumnal Equinoxes as calendar dates, signifying the beginning of the Northern hemisphere's Spring and Autumn, respectively. Did you know that the equinoxes are also positions in the sky? The Celestial Equator and the Ecliptic are two Great Circles on the Celestial Sphere, set at an angle of 23.5 degrees. The two points where they intersect are called the Equinoxes. The Vernal Equinox has coordinates RA=0.0 hours, Dec=0.0 degrees. The Autumnal Equinox has coordinates RA=12.0 hours, Dec=0.0 degrees. The Equinoxes are important for marking the seasons. Because they are on the Ecliptic, the Sun passes through each equinox every year. When the Sun passes through the Vernal Equinox (usually on March 21st), it crosses the Celestial Equator from South to North, signifying the end of Winter for the Northern hemisphere. Similarly, when the Sun passes through the Autumnal Equinox (usually on September 21st), it crosses the Celestial Equator from North to South, signifying the end of Winter for the Southern hemisphere.
 Jason Harris Geographic Coordinates Locations on Earth can be specified using a spherical coordinate system. The geographic (earth-mapping) coordinate system is aligned with the spin axis of the Earth. It defines two angles measured from the center of the Earth. One angle, called the Latitude, measures the angle between any point and the Equator. The other angle, called the Longitude, measures the angle along the Equator from an arbitrary point on the Earth (Greenwich, England is the accepted zero-longitude point in most modern societies). By combining these two angles, any location on Earth can be specified. For example, Baltimore, Maryland (USA) has a latitude of 39.3 degrees North, and a longitude of 76.6 degrees West. So, a vector drawn from the center of the Earth to a point 39.3 degrees above the Equator and 76.6 degrees west of Greenwich, England will pass through Baltimore. The Equator is obviously an important part of this coordinate system, it represents the zeropoint of the latitude angle, and the halfway point between the poles. The Equator is the Fundamental Plane of the geographic coordinate system. All Spherical Coordinate Systems define such a Fundamental Plane. Lines of constant Latitude are called Parallels. They trace circles on the surface of the Earth, but the only parallel that is a Great Circle is the Equator (Latitude=0 degrees). Lines of constant Longitude are called Meridians. The Meridian passing through Greenwich is the Prime Meridian (longitude=0 degrees). Unlike Parallels, all Meridians are great cricles, and Meridians are not parallel: they intersect at the north and south poles. Exercise: What is the longitude of the North Pole? It's latitude is 90 degrees North. It is a trick question. The Longitude is meaningless at the north pole (and the south pole too). It has all longitudes at the same time.
 Jason Harris Great Circles Consider a sphere, such as the Earth, or the Celestial Sphere. The intersection of any plane with the sphere will result in a circle on the surface of the sphere. If the plane happens to contain the center of the sphere, the intersection circle is a Great Circle. Great circles are the largest circles that can be drawn on a sphere. Also, the shortest path between any two points on a sphere is always along a great circle. Some examples of great circles on the celestial sphere include: the Horizon, the Celestial Equator, and the Ecliptic.
 Jason Harris The Horizon The Horizon is the line that separates Earth from Sky. More precisely, it is the line that divides all of the directions you can possibly look into two categories: those which intersect the Earth, and those which do not. At many locations, the Horizon is obscured by trees, buildings, mountains, etc. However, if you are on a ship at sea, the Horizon is strikingly apparent. The horizon is the Fundamental Plane of the Horizontal Coordinate System. In other words, it is the locus of points which have an Altitude of zero degrees.
 Jason Harris Hour Angle As explained in the Sidereal Time article, the Right Ascension of an object indicates the Sidereal Time at which it will transit across your Local Meridian. An object's Hour Angle is defined as the difference between the current Local Sidereal Time and the Right Ascension of the object: HAobj = LST - RAobj Thus, the object's Hour Angle indicates how much Sidereal Time has passed since the object was on the Local Meridian. It is also the angular distance between the object and the meridian, measured in hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it transited across the Local Meridian 2.5 hours ago, and is currently 37.5 degrees West of the Meridian. Negative Hour Angles indicate the time until the next transit across the Local Meridian. Of course, an Hour Angle of zero means the object is currently on the Local Meridian.
 John Cirillo Julian Day The Julian Calendar is a way of reckoning the current date by a simple count of the number of days that have passed since some remote, arbitrary date. This number of days is called the Julian Day, abbreviated as JD. The starting point, JD=0, is January 1, 4713 BC (or -4712 January 1, since there was no year '0'). Julian Days are very useful because they make it easy to determine the number of days between two events by simply subtracting their Julian Day numbers. Such a calculation is difficult for the standard (Gregorian) calendar, because days are grouped into months, which can contain a variable number of days, and there is the added complication of Leap Years. Converting from the standard (Gregorian) calendar to Julian Days and vice versa is best left to a special program written to do this, and there are many to be found on the web (and &kstars; does this too, of course!). However, for those interested, here is a simple example of a Gregorian to Julian day converter: JD = D - 32075 + 1461*( Y + 4800 * ( M - 14 ) / 12 ) / 4 + 367*( M - 2 - ( M - 14 ) / 12 * 12 ) / 12 - 3*( ( Y + 4900 + ( M - 14 ) / 12 ) / 100 ) / 4 where D is the day (1-31), M is the Month (1-12), and Y is the year (1801-2099). Note that this formula only works for dates between 1801 and 2099. More remote dates require a more complicated transformation. An example Julian Day is: JD 2440588, which corresponds to 1 Jan, 1970. Julian Days can also be used to tell time; the time of day is expressed as a fraction of a full day, with 12:00 noon (not midnight) as the zero point. So, 3:00 pm on 1 Jan 1970 is JD 2440588.125 (since 3:00 pm is 3 hours since noon, and 3/24 = 0.125 day). Note that the Julian Day is always determined from Universal Time, not Local Time. Astronomers use certain Julian Day values as important reference points, called Epochs. One widely-used epoch is called J2000; it is the Julian Day for 1 Jan, 2000 at 12:00 noon = JD 2451545.0. Much more information on Julian Days is availabel on the internet. A good starting point is the U.S. Naval Observatory. If that site is not available when you read this, try searching for Julian Day with your favorite search engine.
 Jason Harris The Local Meridian The Meridian is an imaginary Great Circle on the Celestial Sphere that is perpendicular to the local Horizon. It passes through the North point on the Horizon, through the Celestial Pole, up to the Zenith, and through the South point on the Horizon. Because it is fixed to the local Horizon, stars will appear to drift past the Local Meridian as the Earth spins. You can use an object's Right Ascension and the Local Sidereal Time to determine when it will cross your Local Meridian (see Hour Angle).
 John Cirillo Retrograde Motion Retrograde Motion is the orbital motion of a body in a direction opposite that which is normal to spatial bodies within a given system. When we observe the sky, we expect most objects to appear to move in a particular direction with the passing of time. The apparent motion of most bodies in the sky is from east to west. However it is possible to observe a body moving west to east, such as an artificial satellite or space shuttle that is orbiting eastward. This orbit is considered Retrograde Motion. Retrograde Motion is most often used in reference to the motion of the outer planets (Mars, Jupiter, Saturn, and so forth). Though these planets appear to move from east to west on a nightly basis in response to the spin of the Earth, they are actually drifting slowly eastward with respect to the stationary stars, which can be observed by noting the position of these planets for several nights in a row. This motion is normal for these planets, however, and not considered Retrograde Motion. However, since the Earth completes its orbit in a shorter period of time than these outer planets, we occassionally overtake an outer planet, like a faster car on a multiple-lane highway. When this occurs, the planet we are passing will first appear to stop its eastward drift, and it will then appear to drift back toward the west. This is Retrograde Motion, since it is in a direction opposite that which is typical for planets. Finally as the Earth swings past the the planet in its orbit, they appear to resume their normal west-to-east drift on succesive nights. This Retrograde Motion of the planets puzzled ancient Greek astronomers, and was one reason why they named these bodies planets which in Greek means wanderers.
 Jason Harris Celestial Coordinate Systems A basic requirement for studying the heavens is determining where in the sky things are. To specify sky positions, astronomers have developed several coordinate systems. Each uses a coordinate grid projected on the Celestial Sphere, in analogy to the Geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle. (the fundamental plane of the geographic system is the Earth's equator). Each coordinate system is named for its choice of fundamental plane. The Equatorial Coordinate System The Equatorial coordinate system is probably the most widely used celestial coordinate system. It is also the most closely related to the Geographic coordinate system, because they use the same fundamental plane, and the same poles. The projection of the Earth's equator onto the celestial sphere is called the Celestial Equator. Similarly, projecting the geographic Poles onto the celestial sphere defines the North and South Celestial Poles. However, there is an important difference between the equatorial and geographic coordinate systems: the geographic system is fixed to the Earth; it rotates as the Earth does. The Equatorial system is fixed to the starsactually, the equatorial coordinates are not quite fixed to the stars. See precession. Also, if Hour Angle is used in place of Right Ascension, then the Equatorial system is fixed to the Earth, not to the stars., so it appears to rotate across the sky with the stars, but of course it's really the Earth rotating under the fixed sky. The latitudinal (latitude-like) angle of the Equatorial system is called Declination (Dec for short). It measures the angle of an object above or below the Celestial Equator. The longitudinal angle is called the Right Ascension (RA for short). It measures the angle of an object East of the Vernal Equinox. Unlike longitude, Right Ascension is usually measured in hours instead of degrees, because the apparent rotation of the Equatorial coordinate system is closely related to Sidereal Time and Hour Angle. Since a full rotation of the sky takes 24 hours to complete, there are (360 degrees / 24 hours) = 15 degrees in one Hour of Right Ascension. The Horizontal Coordinate System The Horizontal coordinate system uses the observer's local horizon as the Fundamental Plane. This conveniently divides the sky into the upper hemisphere that you can see, and the lower hemisphere that you can't (because the Earth is in the way). The pole of the upper hemisphere is called the Zenith. The pole of the lower hemisphere is called the nadir. The angle of an object above or below the horizon is called the Altitude (Alt for short). The angle of an object around the horizon (measured from the North point, toward the East) is called the Azimuth. The Horizontal Coordinate System is sometimes also called the Alt/Az Coordinate System. The Horizontal Coordinate System is fixed to the Earth, not the Stars. Therefore, the Altitude and Azimuth of an object changes with time, as the object appears to drift across the sky. In addition, because the Horizontal system is defined by your local horizon, the same object viewed from different locations on Earth at the same time will have different values of Altitude and Azimuth. Horizontal coordinates are very useful for determining the Rise and Set times of an object in the sky. When an object has Altitude=0 degrees, it is either Rising (if its Azimuth is < 180 degrees) or Setting (if its Azimuth is > 180 degrees). The Ecliptic Coordinate System The Ecliptic coordinate system uses the Ecliptic for its Fundamental Plane. The Ecliptic is the path that the Sun appears to follow across the sky over the course of a year. It is also the projection of the Earth's orbital plane onto the Celestial Sphere. The latitudinal angle is called the Ecliptic Latitude, and the longitudinal angle is called the Ecliptic Longitude. Like Right Ascension in the Equatorial system, the zeropoint of the Ecliptic Longitude is the Vernal Equinox. What do you think such a coordinate system would be useful for? If you guessed charting solar system objects, you're right! Each of the planets (except Pluto) orbits the Sun in roughly the same plane, so they always appear to be somewhere near the Ecliptic (&ie;, they always have small ecliptic latitudes). The Galactic Coordinate System The Galactic coordinate system uses the Milky Way as its Fundamental Plane. The latitudinal angle is called the Galactic Latitude, and the longitudinal angle is called the Galactic Longitude. This coordinate system is useful for studying the Galaxy itself. For example, you might want to know how the density of stars changes as a function of Galactic Latitude, to how much the disk of the Milky Way is flattened.
 Jason Harris Time Zones The Earth is round, and it is always half-illuminated by the Sun. However, because the Earth is spinning, the half that is illuminated is always changing. We experience this as the passing of days wherever we are on the Earth's surface. At any given instant, there are places on the Earth passing from the dark half into the illuminated half (which is seen as dawn on the surface). At the same instant, on the opposite side of the Earth, points are passing from the illuminated half into darkness (which is seen as dusk at those locations). So, at any given time, different places on Earth are experiencing different parts of the day. Thus, Solar time is defined locally, so that the clock time at any location describes the part of the day consistently. This localization of time is accomplished by dividing the globe into 24 vertical slices called Time Zones. The Local Time is the same within any given zone, but the time in each zone is one Hour earlier than the time in the neighboring Zone to the East. Actually, this is a idealized simplification; real Time Zone boundaries are not straight vertical lines, because they often follow national boundaries and other political considerations. Note that because the Local Time always increases by an hour when moving between Zones to the East, by the time you move through all 24 Time Zones, you are a full day ahead of where you started! We deal with this paradox by defining the International Date Line, which is a Time Zone boundary in the Pacific Ocean, between Asia and North America. Points just to the East of this line are 24 hours behind the points just to the West of the line. This leads to some interesting phenomena. A direct flight from Australia to California arrives before it departs! Also, the islands of Fiji straddle the International Date Line, so if you have a bad day on the West side of Fiji, you can go over to the East side of Fiji and have a chance to live the same day all over again!
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 Jason Harris Universal Time The time on our clocks is essentially a measurement of the current position of the Sun in the sky, which is different for places at different Longitudes because the Earth is round (see Time Zones). However, it is sometimes necessary to define a global time, one that is the same for all places on Earth. One way to do this is to pick a place on the Earth, and adopt the Local Time at that place as the Universal Time, abbrteviated UT. (The name is a bit of a misnomer, since Universal Time has little to do with the Universe. It would perhaps be better to think of it as global time). The geographic location chosen to represent Universal Time is Greenwich, England. The choice is arbitrary and historical. Universal Time became an important concept when European ships began to sail the wide open seas, far from any known landmarks. A navigator could reckon the ship's longitude by comparing the Local Time (as measured from the Sun's position) to the time back at the home port (as kept by an accurate clock on board the ship). Greenwich was home to England's Royal Observatory, which was charged with keeping time very accurately, so that ships in port could re-calibrate their clocks before setting sail. Exercise: Set the geographic location to Greenwich, England using the Set Location window (&Ctrl;G). Note that the Local Time (LT)and the Universal Time (UT) are now the same. Further Reading: The history behind the construction of the first clock that was accurate and stable enough to be used on ships to keep Universal Time is a fascinating tale, and one told expertly in the book Longitude, by Dava Sobel.
 Jason Harris The Zenith The Zenith is the point in the sky where you are looking when you look straight up from the ground. More precisely, it is the point on the sky with an Altitude of +90 Degrees; it is the Pole of the Horizontal Coordinate System. Geometrically, it is the point on the Celestial Sphere intersected by a line drawn from the center of the Earth through your location on the Earth's surface. The Zenith is, by definition, a point along the Local Meridian. Exercise: You can point to the Zenith by pressing Z or by selecting Zenith from the Location menu.
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