Sundials and the Celestial Sphere Katie Hausknecht
What is a sundial? A sundial is a device that uses the shadow cast by the sun to indicate what time of day it is, often by hours.
The Celestial Sphere Before the mechanisms of a sundial can be understood, there must be an understanding of the Celestial Sphere. The Celestial Sphere is an imaginary sphere with a gigantic radius and the Earth as its centre. The poles of this imaginary sphere are aligned with the poles of the Earth and the equator of the Celestial Sphere is aligned with the equator of the Earth as well. It is important to note that although it is called the Celestial Sphere, only half of the sphere is visible from the vantage of Earth.
The Celestial Sphere Visualized North and South Celestial Polesimply the North and South poles of the Earth extended into space. Zenith- the point directly overhead of the observer. Meridian- an imaginary line that runs through the North Celestial Pole, Zenith, and through the South Celestial Pole. In the morning the sun is East of the meridian, and in the afternoon it is to the meridian s West.
The Sun and the Celestial Sphere The image to the right shows what a full Celestial Sphere looks like, not as one would see standing on Earth like the previous, but as one viewing from space. There are two important ellipses on the Celestial Sphere; the Ecliptic and the Celestial Equator. Ecliptic- (in blue) this is the path the sun takes over a year. Celestial Equator- (in pink) the same plane as Earth s equator, this ellipse runs directly West and East. Notice that the angle between the Ecliptic and the Celestial Equator is 23.5 degrees. This is because the Earth is tilted on an axis and does not rotate straight up and down. This is an important concept to remember.
The Seasons Notice that the Ecliptic and the Celestial Equator intersect at two points, the Autumnal Equinox and the Vernal (or Spring) Equinox. These two points correspond to the first day of Fall and the first day of Spring. On the first day of Spring and Fall the Earth experiences exactly twelve hours of night and twelve hours or daytime (hence, equinox, meaning equal). This is because the sun rises directly in the East and sets directly in the West.
Winter and Summer The farthest point North on the Ecliptic corresponds to the June (Summer) Solstice. This is when the sun takes a long, high path that rises in the Northeast and sets in the Northwest. Because of this, the days are longer in the Summertime. The farthest point South on the Ecliptic corresponds to the December (Winter) Solstice, when the sun takes a short, low path that rises in the Southeast and sets in the Southwest. Because of this, the nights are longer in the Wintertime.
Back to Sundials: Sundials and Their Parts Dial Plate- the plane the gnomon rests and the part with the hour lines. Gnomon- a rod or wedge on the sundial that casts a shadow over the Dial Plate Style- the hypotenuse of a wedge-shaped Gnomon. Hour Lines- mark where a shadow would fall for a certain hour.
The Gnomon and Its Position For the sundial made- the Equatorial Sundial- it is important to have the Gnomon point the the North Celestial Pole, and to ensure that it is parallel to the Earth Axis, otherwise, the sundial will not be accurate. If it was placed differently, than the shadows cast would change in different seasons even if the time of day was the same. In addition to this, the angle the shadow covered would change too. The differences can be shown in this animation.
Why does this happen? In addition to the sun changing its position over the course a day, the sun also changes position in a year (relative to an observer on Earth). This position is not linear like often expected, but its shape is called an annalema.
The Analemma Analemmas occur because of two factors: 1. 2. The Earth does not orbit around the sun in a circle, rather it orbits in the shape of an ellipse. The Earth, as mentioned before, is tiled on an axis 23.5 degrees compared to the Ecliptic (the sun s path).
Consequences of Orbiting In An Ellipse Since the Earth moves around the sun in the shape of an ellipse, it changes the speed of the Earth as it travels throughout space, making it vary with the seasons. This is because of the relationship the Earth has with the gravity of the sun. If the Earth moved in a circular motion, its speed would be constant. Since this is not the case, however, and as a result the Earth moves faster in January and slower in July. This can be demonstrated in the animation here.
Viewed From Earth How does this change the perception of the sun from Earth? Even though time is based off of a 24-hour schedule, in reality the Earth only takes 23 hours 56 minutes to spin 360 degrees on its axis. So when the Earth hits hour 24, it has has four minutes to make an additional degree turn. This means that in a day, the Earth spins 361 degrees. This is what makes the sun appear to move East and West throughout the year. If you were to look up at the sky at noon, the sun would be East of where it would be expected because the Earth has had that extra one degree. Imagine again that the sun moved linear because its orbit around the sun was circular. This would make our time correct and at twenty-four hours, the sun would be directly overhead because the Earth has moved exactly 360 degrees.
Consequences of the Earth s Tilt As discussed, the Earth is tilted compared to the sun. If the observer from the Earth were to make a model of the sun and its position throughout the year, it would look like this animation here. The blue sun represents a sun s movements if it were circular and it the Earth was not on an exis. The red sun is our sun, the one that moves in an ellipse and it tilted compared to an observer on Earth. Where the blue sun is always equidistant from the planet, the ellipse changes in distance and angle. This is because a circle has a fixed radius and a true centre, where the boundaries of an ellipse changes relative to the centre.
Back to the Analemma Not only does the distance change, but the angle too. Because the ellipse is tilted, the sun moves further towards and away from the Earth. This is what makes the sun seem to drift East and West in the sky, making the characteristic figure-eight shape called the Analemma. This change can be graphed, as shown on the right.
The Equation of Time What was just learned is that... 1. 2. The Earth orbits the sun in an ellipse, making it move faster or slower depending on the time of the year. The Earth is tilted, making the sun appear to move West and East in the sky during a year. This is called The Equation of Time, and can be visualized as a graph, shown on the right.
Connecting the Concepts The Analemma is the reason the Gnomon of the sundial should be parallel to the Earth s Axis and pointing to the North Celestial Equator, because otherwise, the angle and speed would make the dial inconsistent.
The Equatorial Dial
Equatorial and Armillary Dials Equatorial Dials are any dials with the previously mentioned attributes (the Gnomon parallel to Earth s axis and pointing to the North Celestial Pole). In addition to Equatorial Dials, there are Armillary Dials that show the ellipses of the Celestial Sphere. The sundial I have created is a Equatorial Dial. The picture to the right shows an Armillary Dial.
Works Cited The Celestial Sphere :. Celestial Sphere. N.p., n.d. Web. 17 Jan. 2017. Equatorial Sundials. Equatorial Sundials. N.p., n.d. Web. 17 Jan. 2017. Ling, Liew Huey, and Lim Siew Lee. The Mathematics of Sundials. The Mathematics of Sundials. N.p., 2000. Web. 17 Jan. 2017.
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