The inclination of the Earth's rotation axis causes the seasons and the position of sunrise and sunset to change every day. The maximum angular distance between two sunrises or two sunsets is the angle between two solstices. This angle changes with the latitude of the place. It is minimum at the equator where it is equal to ecliptic obliquity , and after that increases according to the absolute value of the latitude until it causes the midnight Sun in the polar area.
The main objective of this workshop is to present this phenomenon through images and also to calculate the inclination of the Earth's rotation axis for each latitude. It is enough to take a set of sunset photos in different latitudes to obtain the ecliptic obliquity with an acceptable error. The secondary idea of this workshop consists of studying the relationship between the solar path, the horizon and the latitude, by means of photography.
In particular, the first objective was to take a set of photos in different latitudes to show the position changes of sunset points during the year. The photos are the result of co-operation between five different countries Latvia, Spain, Colombia, Bolivia and Argentina. The same situation appears at sunrise or sunset, so it was decided to work at sunsets because it is always more convenient.
And finally, at the pole the sun path is parallel to the horizon midnight Sun , and it is not possible to consider the angular distance x, because the Sun does not have sunset points fig 3. Cities with Northern and Southern latitudes have been included. The apparent movement of the Sun has peculiarities in each hemisphere fig 4 , but the situation of the sunset points is the same fig 5.
It was not possible to obtain the photos in each city on the first day of each season, because sometimes it was raining or cloudy. In these cases the photo was taken on the first day that it was possible. However, in each case, a pair of photographs of the first day of two consecutive seasons was obtained solstice and equinox or equinox and solstice to determine the maximum angular distance x, for each latitude.
For example, it was very difficult to take the photo of the June solstice in Riga it was necessary to wait two years, and besides that it was taken on July 4th because this period is normally very cloudy there. However the photos of the December solstice and March equinox were obtained more or less correctly December 22nd and March 20th , and this is enough to determine x from the observations fig 5.
The photos were used as observations to calculate the angular distance x. After that the obliquity of ecliptic e for each latitude was determinate. From photo 1 it is possible to measure the distance d in cm and it can be converted to x degrees with the annex. Afterwards, it is possible to obtain e using the sine theorem in figure 6,. In table 1 the results obtained of the angular distance x in each city and the obliquity of ecliptic appear. These results mean a small error justified by the process.
It was not possible to take the photo at the instant of the start of the season. The photographic observations introduce an error motivated by the image deformation produced by changing a circular horizon to a flat surface. This phenomenon is especially sensitive for cameras with short focal length. With no way to gain or lose angular momentum, they remain in their elliptical orbits arbitrarily far into the future. The Earth makes its closest approach to the Sun every January 3rd or so, while it's most distant in early July.
By itself, this wouldn't make much difference, but now we need to add in another factor: the Earth doesn't rotate once on its axis every 24 hours. During an average day, when the Earth moves at its average speed around the Sun, 24 hours is just right. But when the Earth moves more slowly near aphelion , 24 hours is too long for the Sun to return to its same position, and so the Sun appears to shift more slowly than average.
Similarly, when the Earth moves more quickly near perihelion , 24 hours isn't quite long enough for the Sun to come back to where it started, and so it shifts more quickly than average.
The effect of our orbit's elliptical nature left and our axial tilt middle on the Sun's position If we only had axial tilt to contend with, and our orbit was a perfect circle, the path the Sun traced out in the sky would be a truly perfect figure symmetryic about both the horizontal and vertical axes. This is what happens roughly on Jupiter and Venus, where the axial tilts are negligible. But here on Earth, we have both an elliptical orbit and a significant axial tilt, and so both effects are significant.
In particular, when we combine them, we can immediately see why our analemma looks like an "8" that's pinched on one narrow side. As the Earth rotates on its axis and orbits the Sun in an ellipse, the Sun's apparent position Here on Earth, perihelion occurs on January 3rd: just 2 weeks after the December solstice. All told, we can combine these effects to make an equation for where the Sun will be located at any particular time as viewed from any location on Earth.
We call this derived quantity the equation of time. The equation of time is determined by both the shape of a planet's orbit and its axial tilt, as well All told, it's only axial tilt and ellipticity that determine the shape of the Sun's path as viewed at the same time, every day, from Earth. The Earth's analemma is fixed in this particular shape. But there are two more factors at play in determining the exact orientation of the analemma.
One is your location on Earth: observers from the Northern Hemisphere will see the small analemma loop occur high in the sky and the large loop occur lower in the sky, while Southern Hemisphere observers will see the reverse. If you photograph the Sun every day at noon, your analemma will appear perfectly vertical left.
These images are further proof, for any doubters out there, that the Earth is round. And the other is at what time of day you take your photographs.
If you take your daily photograph:. Or, tree poles could replace the standing stones. Or, rock cairns could be used. How does this work? The dioramas simulate the rising and setting points of the Sun, and its tracks across the sky at summer solstice longest track , winter solstice shortest track , and the spring and fall equinoxes medium track.
A bead placed on one of the tracks simulates the Sun rising along the eastern horizon, travelong along the sky, and setting on the western horizon. Imagine a tiny version of yourself standing in the middle of the wooden disk. And imagine that the outside rim of the disk represents your horizon.
On Summer Solstice, you would see the Sun rise on your "horizon" at the eastern point of the longest track. It would follow the track high in your sky, and eventually set on the western horizon. It would be up for about 17 "hours", thus making summertime days long and warm.
On the Winter Solstice, you would observe the Sun rising at the western end of the smallest track. It wouldn't rise high in the sky, and would be up for only about 6 or 7 hours, making your days short on daylight and cold.
0コメント