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The analemma lies almost horizontal, so the horizon can be tangential to it at two points, one in each loop of the analemma.
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analemma and almost
Since the Earth's mean solar day is almost exactly 24 hours, an analemma can be traced by plotting the position of the Sun as viewed from a fixed position on Earth at the same clock time every day for an entire year.
analemma and horizontal
By time you got down to the equator, the analemma would be completely horizontal.
) If the analemma is drawn in a diagram, tilted at the appropriate angle for an observer's latitude ( as described above ), and if a horizontal line is drawn to pass through the position of the Sun on the analemma on any given date ( interpolating between the date markings as necessary ), then at sunrise this line represents the horizon.
analemma and so
Because of the Earth's annual revolution around the Sun in an orbit that is elliptical and tilted relative to the plane of the equator, an observer at a fixed point on the Earth sees the Sun appear to move in an analemma around a mean position, taking a year to do so.
In practice, the analemma is so nearly symmetrical that the shapes of the mirror images are not easily distinguished, but if date markings are present, they go in opposite directions.
Generally, making these estimates depends on visualizing the analemma as a rigid structure in the sky, which moves around the Earth at constant speed so it rises and sets once a day, with the Sun slowly moving around it once a year.
However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information.
* Venus: There are slightly less than two days per year, so it would take several years to accumulate a complete analemma by the usual method.
The paraboloidal dishes that are used for radio communication with geosynchronous satellites often have to move so as to follow the satellite's daily movement around its analemma.
analemma and horizon
With reference to the image of a simulated analemma in the eastern sky, the lowest point of the analemma has just risen above the horizon.
Likewise, at sunset, the earliest sunset will occur when the Sun is at its lowest point on the analemma when it is close to the western horizon, and the latest sunset when it is at the highest point.
The exact dates are those on which the Sun is at the points where the horizon is tangential to the analemma, which in turn depend on how much the analemma, or the north-south meridian passing through it, is tilted from the vertical.
The distance along the equator from the point where it intersects the horizon to the position of the origin of the analemma at sunrise is the distance the origin moves between 6 am and the time of sunrise on the given date.
If the horizon line at sunrise passes above the origin of the analemma, the Sun rises before 6 am, and vice versa.
Simply measuring the distance along the horizon between these points, in angular terms ( comparing it with the length of the analemma, as described above ), gives the angle between due east or west and the direction of sunrise or sunset.
analemma and can
With such date markings, diagrams of the analemma can be put to good use in calculating such things as the times of sunrise and sunset.
The analemma can be considered as a graph in which the Sun's declination and the equation of time are plotted against each other.
This can be used to tell which way the analemma is printed.
A date-marked diagram of the analemma, with equal scales in both north-south and east-west directions, can be used as a tool to estimate quantities such as the times of sunrise and sunset, which depend on the Sun's position.
The analemma can be used to find the dates of the earlest and latest sunrises and sunsets of the year.
Calculating these dates numerically is complex, but they can be estimated fairly accurately by placing a straight-edge, tilted at the appropriate angle, tangential to a diagram of the analemma, and reading the dates ( interpolating as necessary ) when the Sun is at the positions of contact.
A similar geometrical method, based on the analemma, can be used to find the times of sunrise and sunset at any place on the Earth ( except within or close to the Arctic or Antarctic Circle ), on any date.
It can be useful to compare it with the length of the analemma, which subtends 47 degrees.
Exact calculations of the azimuths of sunset on other dates are complex, but they can be estimated with reasonable accuracy by using the analemma.
analemma and be
After spending some time building and stocking the raft and deciding when the weather conditions will be optimal ( using an analemma he has created in his cave to monitor the time of year ), he launches, using the sail to overcome the powerful surf.
Viewed from an object with a perfectly circular orbit and no axial tilt, the Sun would always appear at the same point in the sky at the same time of day throughout the year and the analemma would be a dot.
For an object with a circular orbit but significant axial tilt, the analemma would be a figure of eight with northern and southern lobes equal in size.
For an object with an eccentric orbit but no axial tilt, the analemma would be a straight east-west line along the celestial equator.
In diagrams, the analemma is drawn as it would be seen in the sky by an observer looking upward.
At the North Pole, the analemma would be completely upright ( an 8 with the small loop at the top ), and you'd only be able to see the top half of it.
If you headed south, once you drop below the Arctic Circle, you'd be able to see the entire analemma.
This would be the latest sunrise of the year, since all other points on the analemma would rise earlier.
The measurement should, of course, be done on the diagram, but it should be expressed in terms of the angle that would be subtended at an observer on the ground by the corresponding distance in the analemma in the sky.
On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different because of the interplay between the tilt of each body's axis and the elliptical shape of its orbit.
analemma and at
Therefore if the observed position of the Sun in the sky is plotted or photographed at the same time every day, or every few days, for a year, the points trace out the analemma.
The north-south component of the analemma shows the Sun's declination, its latitude on the celestial sphere, or the latitude on the Earth at which the Sun is directly overhead.
In many diagrams of the analemma, a third dimension, that of time, is also included, shown by markings that represent the position of the Sun at various, fairly closely spaced, dates throughout the year.
If, on the other hand, you looked at the analemma in the early morning or evening, it would start to tilt to one side as you moved southward from the North Pole.
Similarly, when the Sun is at the highest point on the analemma, near its top-left end, the earliest sunrise of the year will occur.
None of these points is exactly at one of the ends of the analemma, where the Sun is at a solstice.
The " origin " of the analemma, where the solar declination and the equation of time are both zero, rises and sets at 6 am and 6 pm local mean time on every day of the year, irrespective of the latitude of the observer.
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