Navigation Your Dreams by the Stars

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    http://www.blueanarchy.org/celestial/index.html

    Introduction

    These days, it's possible to buy a compact GPS receiver for less than a sextant. No bulky sight

    reduction tables or nautical almanacs are required, you can determine your location instantly, and

    some will even plot your course on an electronic map. With that kind of technology available, it

    might seem like a waste of time to read a pamphlet on celestial navigation. What's the point,

    anyway?

    Of course, there are all the standard excuses that old mariners give for holding on to their

    sextants: what if the batteries in your GPS die, or what if the GPS satellites go offline? Those are

    good practical reasons, but I think there is more to the value of celestial navigation. There is

    convenience in the quick glance at a glowing GPS readout, but that convenience might only

    serve as another blow for alienation. What is that vapid stare compared to the feeling of salt

    spray on your face while measuring the declinations of celestial bodies throughout the heavens?

    What about the awareness and anticipation of that perfect moment at twilight, just right for

    taking sights, when the waning light still illuminates the horizon and the planets are becoming

    visible in the sky? What about the day to day knowledge of how the planets are moving across

    the heavens, when exactly local noon occurs, and the intrinsic feeling that you are navigatingyour dreams by the stars?

    Certainly GPS is nice to have, but for me celestial navigation is wrapped up in DIY and a

    connectedness with the world which strikes back against spectatorship and alienation. If you feel

    potential for the same, hopefully this pamphlet will help you along the way.

    First Principles

    The Sextant: A tool for measuring angles between observable objects. In the context of celestial

    navigation, those bodies are most often a celestial object (the sun, a star, a planet) and thehorizon.

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    Geographical Position (GP): The point on earth

    that a celestial body is directly above. If you draw a line from the center of the earth to a celestial

    body, the point where that line intersects the earth's surface is the geographical position. GP is

    measured by 'declination' and 'hour angle'.

    Ex: Here, 'x' is the GP of the sun.

    Declination: The declination of a celestial object is just the latitude of its GP. Declination is

    measured exactly as latitude is: in degrees north or south of the equator. The declination of the

    sun moves from 23N (Tropic of Cancer) to 23S (Tropic of Capricorn) throughout the year.

    Hour Angle: Hour angle is the 'longitude' complement to declination when measuring GP.

    Greenwich Hour Angle (GHA) is the amount of time that has elapsed since a celestial bodypassed the Greenwich meridian. If you're standing on the Greenwich meridian and the sun is

    directly south, its GHA is 0. Two hours later, its GHA will be two hours. Its GHA will continueto grow through 23 hours until noon the next day, when it will become zero again. GHA can bemeasured in degrees past the Greenwich meridian as well (up to 360). So hour angle is different

    from longitude in two ways: it can be measured in time, and when it is measured in degrees it

    goes up to 360 in the westerly direction, instead of 180 east or west.

    Local Hour Angle: Hour Angle doesn't have to be measured from the Greenwich meridian.

    When it is measured from the meridian that you (the observer) are on, it is known as the Local

    Hour Angle (LHA). Simple equations for translating GHA to LHA:

    When east of Greenwich: LHA = GHA + observer's longitude

    When west of Greenwich: LHA = GHA - observer's longitude

    The Nautical Almanac: Published annually, these need to be updated every year. They give

    GPs (in GHA and declination) of celestial bodies at every second throughout the year. They also

    hold additional information about sunrise, sunset, and the phases of the moon.

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    The Zenith:This is the point immediately above your head. It makes an angle of 90 between

    you and the horizon.

    Altitude: The angle between a celestial object, an observer, and the horizon. From your

    perspective, this is the height of a celestial object above the horizon.

    Zenith Distance: The complement to altitude. Ex:

    altitude + zenith distance will always equal 90.

    Azimuth: The bearing (true not magnetic) from an observer to a heavenly body.

    The Theory

    Zenith Distance And Latitude

    It turns out that you can learn some interesting things from zenith distance. In this diagram, two

    parallel rays from the sun hit the earth. One at an observer's position, and one at the sun's GP:

    What's interesting is that the angle between the

    zenith and the first ray at the surface of the earth is the same as the angle between the zenith and

    the second ray at the center of the earth. This means that the zenith distance which you observe is

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    the same number of degrees as the distance between the GP and you. Since 1' = 1 nautical mile,

    zenith distance * 60 = the distance between you and the GP of the object you're observing.

    If the object that you're observing happens to be directly above your meridian of longitude, that

    distance + the object's declination = your parallel of latitude. Declination is something that you

    can look up in a nautical almanac for most celestial bodies at any given moment, and the sun willpredictably cross your meridian of longitude at local noon. This means that you can easily

    determine your latitude at noon every day.

    Determining Longitude At Noon

    Now that we know how to determine our latitude at noon, it would be nice if we could also

    discover our longitude. As the sun approaches its high point in the sky, begin to take a series of

    sights, marking the time of each sight taken. The altitude you measure will get larger, hang for a

    minute or so, and then begin to get smaller. Wait until the sun falls to the altitude of your very

    first site, determine the difference in time between the last and first site, add half that to the time

    of the first site, and that was the exact moment of local noon. The sun's GP moves 15 everyhour, so look up the time of local noon at Greenwich in a nautical almanac, determine the

    number of minutes between then and now, divide that by 4 to get the number of miles between

    your longitude and Greenwich, and divide that by 60 to get your longitude in degrees. Now we

    have a method for easily determining both our latitude and longitude at local noon.

    Position Circles

    Let's say that you use a sextant to take a sight of

    the sun, and its altitude is 90 (your zenith). With absolute certainty, there is only one place on

    the earth that you could possibly be: the sun's GP. As the sun continues to move across the sky,

    however, its altitude will lessen. As this happens, your number of possible positions will grow

    into a 'position circle' with the sun's GP at its center, and a number of equidistant points around

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    it. Given an observed altitude, all you know is that you're somewhere on the position circle. The

    circle gets larger and larger the lower the observed altitude.

    Position Lines

    The trick is to narrow the number of possible

    positions on the Position Circle by plotting your azimuth to the celestial object. If the celestial

    object is to the SW of the observer, than the observer must be on the NE portion of the Position

    Circle. There is no way, however, to obtain an azimuth so accurate that you can determine your

    exact position on the circle. The best you can do is draw a line at right angles to the azimuth,

    knowing that you are somewhere on the tangent of the position circle and that line.

    Spherical Triangles

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    Drawing a position circle isn't easy. There are

    enormous distances involved, so we'd need a really big chart and a really big compass to draw

    the required circle with the celestial body's GP at the center. In order to get the Position Line thatwe want, we use spherical triangles to find what's known as an Intercept. We have a celestial

    body's observed altitude and need to know where we are. But when using spherical triangles, we

    pretend that we don't have the celestial body's altitude and do know where we are. The assumed

    latitude and longitude are called an 'assumed position' (AP).

    Here 'Z' is the observer's assumed latitude, and 'X' is the GP of the celestial body. We know the

    length of PZ = 90 - the assumed latitude. We know the length of PX = 90 - the celestial body's

    declination. We know that the angle ZPX is the Local Hour Angle. Since we know two sides and

    an angle of a triangle, we can use spherical trigonometry to solve for the length of ZX and the

    other two angles. 90 - ZX = altitude, or what's known as the Calculated Altitude. The angle PZX

    will be the azimuth. Had the assumed position been a perfect guess, the calculated altitude would

    be the same as the observed altitude. If it's not, the difference between the calculated altitude and

    observed altitude is the Intercept, as specified in nautical miles.

    Plotting An Intercept

    Drawing a position line is now as easy as plotting the calculated azimuth through the assumed

    position, walking the value of the Intercept up the azimuth line, and drawing the position line at a

    right angle. We're somewhere on that line.

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    The Fix

    This position line stuff is interesting, but it'd be a hell of a lot nicer if we could find out exactly

    where we are. The solution is to plot multiple position lines and see where they intersect. There

    are two ways to do this.

    Multiple Sights

    The best way to get a fix is to take multiple sights off multiple celestial objects. This is possible

    during the day when the moon has already risen, or at twilight when the planets are already

    visible. It is, of course, possible at night when all the stars are in the sky -- but it might bedifficult to see the horizon then.

    The Running Fix

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    If all you have is the sun, it's possible to take a Running Fix. The idea is to plot a position line off

    the sun, wait for your azimuth to the sun to change (a few hours usually), plot a second position

    line, and then advance the first position line the distance you've traveled. If you've traveled 45nm

    at a bearing of 67 between the first and second sight, draw a line at 67 through any point on the

    first position line, measure up 45nm, and re-plot the first position line at that point. Your fix is

    where the advanced and second position lines intersect.

    The Practice

    The steps for plotting a position line are:

    1. Use a sextant to observe the altitude of a celestial body.2. Using the exact time of your observation, look up the GP for that celestial body in

    the Nautical Almanac.3. Assume a position.4. Solve the spherical triangle between your assumed position, the celestial body's

    GP, and the closest pole.5. Use the results of the spherical triangle to determine the difference between the

    calculated altitude and your observed altitude.

    6. Plot that difference as an intercept on a chart.

    Using The Sextant

    Look through the sextant at the horizon and adjust the sextant's index arm until the celestial body

    is visible in the silvered portion of the view finder. Slowly adjust the index arm until the bottom

    of the celestial object is touching the horizon. Either call out to a time keeper, or quickly look at

    your watch. Record the time and altitude.

    It is now necessary to correct the observed altitude for instrument error, our height above sea-

    level, refraction, and semi-diameter.

    To account for instrument error, slide the index arm to 0 and look through the view finder. If the

    sextant has no error, the horizon should be perfectly aligned in the silvered and unsilvered

    portions of the view finder. If they are not aligned, adjust the index arm until they are. Subtract

    the number of minutes on the index arm from the observed altitude to get an observed altitude

    corrected for instrument error.

    To account for height above sea level, estimate the height of the boat and the height of thesextant above deck (approximately the height of the observer). In the Nautical Almanac, on the

    right side of the 'Altitude Correction Tables -- Moon' page, there is a table labeled 'Dip'. Lookup

    your estimated height, and subtract the value in the 'Corr' column from the observed altitude to

    get observed altitude corrected for height above sea level.

    To account for refraction and semi-diameter, look at the 'Altitude Correction Tables' page in the

    Nautical Almanac. Since you measured the lower limb against the horizon, look up the observed

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    altitude in the table and subtract the 'lower limb' column from the observed altitude to get

    observed altitude corrected for refraction and semi-diameter.

    Combining all of these corrections gets you a usable observed altitude (abbreviated Ho).

    Finding The GP Of A Celestial Object

    Each page in the body of the Nautical Almanac provides information for three days. The tables

    list the GHA and declination of Venus, Mars, Jupiter, Saturn, the Sun, and the moon for every

    hour. Find the page for the day you took the sight, then record the GHA and declination for the

    hour in which you took the sight. Also note the value of 'd' (located at the bottom of the Sun and

    planets columns, but in-line in the moon column).

    At the back of the Nautical Almanac, there are a series of pages labeled 'Increments And

    Corrections.' Each page has a table for a given minute, with each row containing values for that

    second. Find the page for the minute in which you took your observation, and add the value in

    the column for the second in which you took your observation to the previously looked-up GHA.Next, look at the right three columns on the same page. These are actually one long table. Find

    the value of 'd' on the left side, and record the value on the right side as the 'declination

    correction.' You either add or subtract this to the previously looked-up declination depending on

    whether it is in a place where the values of the column are either increasing or decreasing. You

    now have the GHA and declination which specify the GP of the celestial object in the moment

    that you observed it.

    Now you know that you're somewhere on a circle that has a radius of (90 - observed altitude) x

    60 nm with the GP at its center. But we can do better.

    Assuming A Position

    For reasons which will soon become clear, your assumed position needs to be a whole number of

    degrees in latitude, and a longitude which makes the LHA of the celestial body a whole number

    of degrees as well. Choosing your AP latitude is as easy as picking the nearest latitude degree to

    your Deduced Reckoning position. Choosing your AP longitude is as easy as picking the nearest

    longitude to your Deduced Reckoning position, which when added or subtracted to GHA will

    produce an even LHA.

    Ex: If your DR position is 2734'.4N, 0825'E and the GHA you just looked up is 33701', your

    AP Lat would be 27 and your AP Long would be 759'E, such that the LHA is an even 34500'.

    Solving The Spherical Triangle

    As it turns out, spherical trigonometry is not the kind of math that we can do on our fingers. As

    such, we use a series of tables (called Sight Reduction Tables) to help us solve the spherical

    triangle. Each row in the tables contains a previously worked out solution to a different

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    permutation of spherical triangle. This is why the LHA and AP Lat must be a whole number of

    degrees: there are only so many possible permutations that the tables can contain.

    Each page for a given AP Latitude has solutions for a range of GP declinations that are either of

    'same' or 'contrary' name. If the AP latitude and GP declination that you're looking up are in the

    same hemisphere, then you should look on the 'same name' page. Otherwise, use the 'contraryname' page. Look in the row for the degree of GP declination, under the column of your

    calculated LHA. Record the Calculated Altitude (Hc), the value of 'd', and the azimuth. In the

    back of the book, in the table labeled 'Correction To Tabulated Altitude For Minutes Of

    Declination,' look up the row containing the value of 'd' under the column containing the minutes

    of your GP declination. Add this value to the previously looked-up Calculated Altitude (Hc) to

    get the correct value for Hc.

    Plotting The Intercept

    The difference between the Calculated Altitude and Observed Altitude is the intercept. Draw a

    line through the AP on a bearing of the calculated azimuth, measure off the intercept distancealong the azimuth line, and draw a line at a right angle to the azimuth line at that point. You now

    have a position line.

    This may seem like a series very confusing operations, but really it's just 8 addition or

    subtractions and 4 table lookups. Attached is a worksheet to help you work through a sight, step-

    by-step.

    http://www.encyclopedia.com/topic/equatorial_coordinate_system.aspx

    equatorial coordinate system

    The Columbia Encyclopedia, Sixth Edition | 2008 | Copyright

    equatorial coordinate system the most commonly usedastronomical coordinate systemfor indicating the

    positions of stars or other celestial objects on thecelestial sphere. The celestial sphere is an imaginary sphere

    with the observer at its center. It represents the entire sky; all celestial objects other than the earth are

    imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the

    celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole,

    and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere

    halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator

    projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An

    equatorial coordinate system the most commonly usedastronomical coordinate systemfor indicating the

    positions of stars or other celestial objects on thecelestial sphere. The celestial sphere is an imaginary sphere

    http://www.encyclopedia.com/topic/equatorial_coordinate_system.aspxhttp://www.encyclopedia.com/topic/equatorial_coordinate_system.aspxhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-astroCoor.htmlhttp://www.encyclopedia.com/topic/equatorial_coordinate_system.aspx
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    with the observer at its center. It represents the entire sky; all celestial objects other than the earth are

    imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the

    celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole,

    and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere

    halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator

    projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. Animportant reference point on the celestial equator is the vernalequinox, the point at which the sun crosses the

    celestial equator in March.

    To designate the position of a star, the astronomer considers an imaginary great circle passing through the

    celestial poles and through the star in question. This is the star'shour circle, analogous to a meridian of

    longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where

    the hour circle intersects the celestial equator. This angle is called the star'sright ascensionand is measured in

    hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360

    degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox.

    Next the observer measures along the star's hour circle the angle between the celestial equator and the

    position of the star. This angle is called thedeclinationof the star and is measured in degrees, minutes, and

    seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and

    declination together determine the location of a star on the celestial sphere. The right ascensions and

    declinations of many stars are listed in various reference tables published for astronomers and navigators.

    Because a star's position may change slightly (seeproper motionandprecession of the equinoxes), such

    tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0h

    and declination 0.

    Another useful reference point is the sigma point, the point where the observer'scelestial meridianintersects

    the celestial equator. The right ascension of the sigma point is equal to the observer's localsidereal time. The

    angular distance from the sigma point to a star's hour circle is called itshour angle; it is equal to the star's rightascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky

    (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a

    body in the sky.

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    http://www.encyclopedia.com/topic/precession_of_the_equinoxes.aspx

    precession of the equinoxes

    The Columbia Encyclopedia, Sixth Edition | 2008 | Copyright

    precession of the equinoxes westward motion of theequinoxesalong theecliptic. This motion was first noted

    by Hipparchus c.120 BC The precession is due to the gravitational attraction of the moon and sun on the

    equatorial bulge of the earth, which causes the earth's axis to describe a cone in somewhat the same fashion

    as a spinning top. As a result, the celestial equator (seeequatorial coordinate system), which lies in the plane

    of the earth's equator, moves on thecelestial sphere, while the ecliptic, which lies in the plane of the earth's

    orbit around the sun, is not affected by this motion. The equinoxes, which lie at the intersections of the celestial

    equator and the ecliptic, thus move on the celestial sphere. Similarly, the celestial poles move in circles on the

    celestial sphere, so that there is a continual change in the star at or near one of these poles (see

    precession of the equinoxes westward motion of theequinoxesalong theecliptic. This motion was first noted

    by Hipparchus c.120 BC The precession is due to the gravitational attraction of the moon and sun on the

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    equatorial bulge of the earth, which causes the earth's axis to describe a cone in somewhat the same fashion

    as a spinning top. As a result, the celestial equator (seeequatorial coordinate system), which lies in the plane

    of the earth's equator, moves on thecelestial sphere, while the ecliptic, which lies in the plane of the earth's

    orbit around the sun, is not affected by this motion. The equinoxes, which lie at the intersections of the celestial

    equator and the ecliptic, thus move on the celestial sphere. Similarly, the celestial poles move in circles on the

    celestial sphere, so that there is a continual change in the star at or near one of these poles (seePolaris). Aftera period of about 26,000 years the equinoxes and poles lie once again at nearly the same points on the

    celestial sphere. Because the gravitational effects of the sun and moon are not always the same, there is some

    wobble in the motion of the earth's axis; this wobble, callednutation, causes the celestial poles to move, not in

    perfect circles, but in a series of S-shaped curves with a period of 18.6 years. There is some further precession

    caused by the gravitational influences of the other planets; this precession affects the earth's orbit around the

    sun and thus causes a shift of the ecliptic on the celestial sphere. The precession of the earth's orbital plane is

    sometimes called planetary precession, and that of the earth's equatorial plane (caused by the sun and moon)

    is called luni-solar precession; the combined effect of the moon, the sun, and the planets is called general

    precession. Planetary precession is much less than luni-solar precession. The precession of the equinoxes was

    first explained by Isaac Newton in 1687.

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    http://www.encyclopedia.com/topic/ecliptic.aspx#1E1-ecliptic

    ecliptic

    The Columbia Encyclopedia, Sixth Edition | 2008 | Copyright

    ecliptic , the great circle on thecelestial spherethat lies in the plane of the earth's orbit (called the plane of the

    ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey

    through the heavens with the ecliptic as its path. The ecliptic is the principal axis in theecliptic coordinate

    system. The two points at which the ecliptic crosses the celestial equator are theequinoxes. The obliquity of

    the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator, an angle of about 23

    1/2 . The constellations through which the ecliptic passes are the constellations of thezodiac.

    ecliptic , the great circle on thecelestial spherethat lies in the plane of the earth's orbit (called the plane of the

    ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey

    through the heavens with the ecliptic as its path. The ecliptic is the principal axis in theecliptic coordinate

    system. The two points at which the ecliptic crosses the celestial equator are theequinoxes. The obliquity of

    the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator, an angle of about 23

    1/2 . The constellations through which the ecliptic passes are the constellations of thezodiac.

    http://www.encyclopedia.com/doc/1E1-equatrCS.htmlhttp://www.encyclopedia.com/doc/1E1-equatrCS.htmlhttp://www.encyclopedia.com/doc/1E1-equatrCS.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-Polaris.htmlhttp://www.encyclopedia.com/doc/1E1-Polaris.htmlhttp://www.encyclopedia.com/doc/1E1-Polaris.htmlhttp://www.encyclopedia.com/doc/1E1-nutation.htmlhttp://www.encyclopedia.com/doc/1E1-nutation.htmlhttp://www.encyclopedia.com/doc/1E1-nutation.htmlhttp://www.encyclopedia.com/topic/ecliptic.aspx#1E1-ecliptichttp://www.encyclopedia.com/topic/ecliptic.aspx#1E1-ecliptichttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-zodiac.htmlhttp://www.encyclopedia.com/doc/1E1-equinox.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-ecliptic-c.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/topic/ecliptic.aspx#1E1-ecliptichttp://www.encyclopedia.com/doc/1E1-nutation.htmlhttp://www.encyclopedia.com/doc/1E1-Polaris.htmlhttp://www.encyclopedia.com/doc/1E1-celest-sph.htmlhttp://www.encyclopedia.com/doc/1E1-equatrCS.html
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    http://www.encyclopedia.com/topic/ecliptic_coordinate_system.aspx#1E1-ecliptic-c

    ecliptic coordinate system

    The Columbia Encyclopedia, Sixth Edition | 2008 | Copyright

    ecliptic coordinate system anastronomical coordinate systemin which the principal coordinate axis is the

    ecliptic, the apparent path of the sun through the heavens. The ecliptic poles are the two points at which a line

    perpendicular to the plane of the ecliptic through the center of the earth strikes the surface of thecelestial

    sphere. The north ecliptic pole lies in the constellation Draco.

    ecliptic coordinate system anastronomical coordinate systemin which the principal coordinate axis is theecliptic, the apparent path of the sun through the heavens. The ecliptic poles are the two points at which a line

    perpendicular to the plane of the ecliptic through the center of the earth strikes the surface of thecelestial

    sphere. The north ecliptic pole lies in the constellation Draco.

    http://www.encyclopedia.com/topic/ecliptic_coordinate_system.aspx#1E1-ecliptic-c

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