The #motions of the #Sun 101
The motions of the Sun 101
by Alberto Vecchiato
The sun rises in the east and sets in the west; a simple statement that nobody would deny. But why does it move in this way? Basically, as I already wrote in a previous post, this is due to the spin of the Earth, that is the rotation of our planet around an ideal axis that defines the positions of the north and south poles where it "pierces" the surface of our planet.
Let us imagine to lift ourselves up over the north pole; we would see the Earth spinning counterclockwise, as in Figure 1.
The bottom half of our planet, on the same side of the sun, enjoys the daylight, while the other half is in the darkness of the night. In the same figure we can see Joe looking to the North, and we all know that his right and left hands are thus pointing to the east and the west respectively. Clearly, Joe's watch shows midnight in A and noon in C. Moreover, it is sunrise in B, when our friend is passing from the dark to the lighted side, and it is sunset in D. And guess where is the sun in these two cases? In B Joe sees the sun on his right, namely to the east, in D he has to look to the left, i.e. the west.
So everything set now (pun intended) isn't it? Not yet.
In the previous figure every point on the Earth has 12 hours of light and 12 hours of dark, and that is because the plane separating night and day contains the north and south poles, but this happens only in two special days that, exactly for this reason, are called "equinoxes". Were the rotation axis orthogonal to the orbital plane, these two days would not be special at all. But the rotation axis makes an angle of about 23.5° with the perpendicular to the orbital plane, and while the Earth is orbiting around the sun, it keeps a constant orientation, as in Figure 2.
The sun always illuminates half of the planet but, except for the days of the equinoxes, one of the poles lies on the lighted side and the other one is in the dark. This means that the length of the day and of the night depends on the position along the orbit. Why? Because Joe continues to move along circles parallel to the equator of the Earth, completing one turn every 24 hours, but the portion of such circles lying on the lighted part of the sphere, that is the length of the day, varies depending on the position of our planet in its orbit. This varies also the path followed by the sun in the sky.
We can easily grasp its essential features by analyzing what happens to the path of the sun when, in any given orbital position, we vary the latitude of the observer (Figure 3). Similarly to the previous case, the length of the day is different at different latitudes. In general it is longer at latitudes closer to the lighted pole, and shorter otherwise. There are always (again, always but at the equinoxes) some latitudes whose circles lie entirely in the lighted side, and conversely, those close to the other pole lie entirely in the dark.
Those points have the remarkable experience of a 24-hours long day or night, respectively, and here the sun cannot "rise" or "set". It simply circles around the horizon varying its altitude above this line, reaching a minimum at midnight. Moreover, at midday Joe has to look opposite to the pole to see the sun (to the South if he is in the northern hemisphere) while the contrary happens at midnight. In other words, close to the north pole the sun culminates to the south and reaches the minimum altitude to the north, and the opposite happens in the other hemisphere. At the boundary of the zone of the 24-hours long days such minimum is just zero, i.e. the sun touches the horizon.
Moving even farther from the pole we cross the separation between light and dark. A tiny part of the parallel circle around the pole is in the dark, and the farther we move the longer is this part. This means that in this situation the sun starts to rise and set, as usual, but where? Simply by extrapolating the above reasoning, in the northern hemisphere it rises in the northeast and sets in the northwest. The exact position varies with the latitude of the observer, and continuing our extrapolation and remembering that in the southern hemisphere the sun point South and North at its lowest and highest points respectively, there will be a latitude at which our star rise exactly at East and set at West. Going to further southern latitudes sunrise will be in the south-east and sunset in the south-west.
Thus, fixing the latitude and letting the Earth move along its orbit, produces a cyclic variation of the solar path during the year similar to the one we would have by varying the latitude of the observer within a given range. From an equinox, day after day the sun rises farther and farther from the east and sets farther and farther from the west. Whether the direction of this movement is toward south or north, it depends on the hemisphere and on the season. If we are in the northern hemisphere it goes north when the day lengthens and south when it shortens, whereas the opposite happens in the southern hemisphere. Only for latitudes above 90°-23.5° or below -90°+23.5° we can see the sun at midnight. In all the other cases it reaches a maximum or minimum distance from the north or the south, in which the day is the longest or the shortest of the year. This happens when the plane separating the light and the dark is perpendicular to the one containing the Earth's rotation axis. As for the equinoxes, this happens twice per year, at the so-called "solstices". The name comes from the Latin words "sol" and "sistere" which mean "sun" and "to stop". At these points, in fact, the sun stops and reverts its motion along the horizon.
by Alberto Vecchiato
The sun rises in the east and sets in the west; a simple statement that nobody would deny. But why does it move in this way? Basically, as I already wrote in a previous post, this is due to the spin of the Earth, that is the rotation of our planet around an ideal axis that defines the positions of the north and south poles where it "pierces" the surface of our planet.
Let us imagine to lift ourselves up over the north pole; we would see the Earth spinning counterclockwise, as in Figure 1.
 |
| Figure 1 |
So everything set now (pun intended) isn't it? Not yet.
 |
| Figure 2 |
The sun always illuminates half of the planet but, except for the days of the equinoxes, one of the poles lies on the lighted side and the other one is in the dark. This means that the length of the day and of the night depends on the position along the orbit. Why? Because Joe continues to move along circles parallel to the equator of the Earth, completing one turn every 24 hours, but the portion of such circles lying on the lighted part of the sphere, that is the length of the day, varies depending on the position of our planet in its orbit. This varies also the path followed by the sun in the sky.
 |
| Figure 3 |
Those points have the remarkable experience of a 24-hours long day or night, respectively, and here the sun cannot "rise" or "set". It simply circles around the horizon varying its altitude above this line, reaching a minimum at midnight. Moreover, at midday Joe has to look opposite to the pole to see the sun (to the South if he is in the northern hemisphere) while the contrary happens at midnight. In other words, close to the north pole the sun culminates to the south and reaches the minimum altitude to the north, and the opposite happens in the other hemisphere. At the boundary of the zone of the 24-hours long days such minimum is just zero, i.e. the sun touches the horizon.
Moving even farther from the pole we cross the separation between light and dark. A tiny part of the parallel circle around the pole is in the dark, and the farther we move the longer is this part. This means that in this situation the sun starts to rise and set, as usual, but where? Simply by extrapolating the above reasoning, in the northern hemisphere it rises in the northeast and sets in the northwest. The exact position varies with the latitude of the observer, and continuing our extrapolation and remembering that in the southern hemisphere the sun point South and North at its lowest and highest points respectively, there will be a latitude at which our star rise exactly at East and set at West. Going to further southern latitudes sunrise will be in the south-east and sunset in the south-west.
Thus, fixing the latitude and letting the Earth move along its orbit, produces a cyclic variation of the solar path during the year similar to the one we would have by varying the latitude of the observer within a given range. From an equinox, day after day the sun rises farther and farther from the east and sets farther and farther from the west. Whether the direction of this movement is toward south or north, it depends on the hemisphere and on the season. If we are in the northern hemisphere it goes north when the day lengthens and south when it shortens, whereas the opposite happens in the southern hemisphere. Only for latitudes above 90°-23.5° or below -90°+23.5° we can see the sun at midnight. In all the other cases it reaches a maximum or minimum distance from the north or the south, in which the day is the longest or the shortest of the year. This happens when the plane separating the light and the dark is perpendicular to the one containing the Earth's rotation axis. As for the equinoxes, this happens twice per year, at the so-called "solstices". The name comes from the Latin words "sol" and "sistere" which mean "sun" and "to stop". At these points, in fact, the sun stops and reverts its motion along the horizon.
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