Unit 4 : Activity 4 : Apparent Motions of the Sun : Sidereal Time : Unit Exam

Sidereal Time

Sidereal time is defined, technically, as "the hour angle of the vernal equinox". (Solar time is technically "the hour angle of the sun, + 12 hours"). Sidereal time shifts with respect to clock time, as we go around the sun. In other words, sidereal time and clock time do not always match.

Remember! When the Vernal Equinox is on the meridian, the sidereal time is 0 hours.

An important point to remember is that the sun appears in the direction of the vernal equinox at the date of the vernal equinox, or about March 21. We can use a diagram like the one above, or some arithmetic, to figure out the sidereal time at noon clock time. Once we get that conversion, we can derive the sidereal for any other clock time: now, midnight, or whenever.

If you are out observing, there is a quick way to discover the sidereal time. The coordinate "right ascension" has been defined in such a way that the sidereal time is always equal to the right ascension of any object that lies on the observer's meridian.

To see how this works, look at "snapshots" of the sky below.

In this picture, the vernal equinox is on the meridian. The sidereal time is thus 0^h (0 hours).

This picture shows the sky an hour after the first one. The earth has turned 15° so the sky appears to have shifted by the same amount. This puts the vernal equinox 15° or 1 hour west of the meridian. Since it is 1 hour later than 0:00, the sidereal time must be (button: 01:00). Notice that the RA that is now crossing the meridian is 1^h, so sidereal time = RA of an object that is on the meridian.

The bright constellation Orion sits on the celestial equator between 6 and 7 hours in right ascension. When Orion is on the meridian, what is the sidereal time?

Diurnal motion of the sun at various seasons

We have already considered the diurnal motions (motions over the course of a year) of objects at various declinations. We have just considered the way the sun's declination changes over the course of the year. Put these together and we have the diurnal motion of the sun at the different seasons. In the next graphic, we can see the motion of the sun in the sky as seen from Ames, Iowa.

The graphic below is the same as from the previous sub-unit. Take a look at it again and consider the complete diurnal motion.

For details on the figure 8 motion of the sun, you can visit the non-ISU web site http://www.analemma.com

Interactive Graphic 4-2-1

1) At the equinoxes, the sun rises due east, sets due west. What is the maximum altitude reached by the sun at the equinox as viewed from Ames, IA, latitude 42 degrees?

Hint: The altitude is (90deg - latitude + declination of the sun), so what is the declination of the sun at the equinox?

Dec = 0 so altitude = 90-latitude = 48 deg
Dec = 23.5 so altitude = 90-42+23.5 = 71.5 deg
At noon its altitude is 90° because it is straight up

Notice how the sunrise passes through the east point on the horizon in the interactive graphic above, and notice where the sun crosses the meridian at the equinoxes. It is important to remember that when the sun crosses the meridian at the equinoxes, day and night are equally long.

Although the we say that the day and night are equal on the equinox, in fact the sky is light longer than 12 hours. First, the Sun is not a single point; it is about half a degree across. So it takes at least 2 minutes for the sun to cross the horizon, and that adds a couple of minutes to the length of daylight. Second, the sunlight is bent - refracted - near the horizon, so the Sun appears higher in the sky and this further advances sunrise and delays sunset. This effect is actually about twice as big. Exactly how much longer the daylight lasts depends also on your latitude. Finally, the sky will also be light more than 12 hours due to the continuing twilight. The sky becomes completely, astronomically, dark only when the sun is 15 degrees below the horizon. It is still quite bright out when the sun is less than 5 degrees below the horizon.

There are two days each year when the Sun is entirely below the horizon for 12 hours and above for 12 (give or take 1 minute). At the latitude of Ames, these come about 3 days before the Vernal Equinox and 3 days after the Autumnal Equinox.


Unit 4 : Activity 4 : Apparent Motions of the Sun : Sidereal Time : Unit Exam
	Sidereal Time Sidereal time is defined, technically, as "the hour angle of the vernal equinox". (Solar time is technically "the hour angle of the sun, + 12 hours"). Sidereal time shifts with respect to clock time, as we go around the sun. In other words, sidereal time and clock time do not always match. Remember! When the Vernal Equinox is on the meridian, the sidereal time is 0 hours. An important point to remember is that the sun appears in the direction of the vernal equinox at the date of the vernal equinox, or about March 21. We can use a diagram like the one above, or some arithmetic, to figure out the sidereal time at noon clock time. Once we get that conversion, we can derive the sidereal for any other clock time: now, midnight, or whenever. If you are out observing, there is a quick way to discover the sidereal time. The coordinate "right ascension" has been defined in such a way that the sidereal time is always equal to the right ascension of any object that lies on the observer's meridian. To see how this works, look at "snapshots" of the sky below. In this picture, the vernal equinox is on the meridian. The sidereal time is thus 0^h (0 hours). This picture shows the sky an hour after the first one. The earth has turned 15° so the sky appears to have shifted by the same amount. This puts the vernal equinox 15° or 1 hour west of the meridian. Since it is 1 hour later than 0:00, the sidereal time must be (button: 01:00). Notice that the RA that is now crossing the meridian is 1^h, so sidereal time = RA of an object that is on the meridian. The bright constellation Orion sits on the celestial equator between 6 and 7 hours in right ascension. When Orion is on the meridian, what is the sidereal time? Diurnal motion of the sun at various seasons We have already considered the diurnal motions (motions over the course of a year) of objects at various declinations. We have just considered the way the sun's declination changes over the course of the year. Put these together and we have the diurnal motion of the sun at the different seasons. In the next graphic, we can see the motion of the sun in the sky as seen from Ames, Iowa. The graphic below is the same as from the previous sub-unit. Take a look at it again and consider the complete diurnal motion. For details on the figure 8 motion of the sun, you can visit the non-ISU web site http://www.analemma.com Interactive Graphic 4-2-1 1) At the equinoxes, the sun rises due east, sets due west. What is the maximum altitude reached by the sun at the equinox as viewed from Ames, IA, latitude 42 degrees? Hint: The altitude is (90deg - latitude + declination of the sun), so what is the declination of the sun at the equinox? Dec = 0 so altitude = 90-latitude = 48 deg Dec = 23.5 so altitude = 90-42+23.5 = 71.5 deg At noon its altitude is 90° because it is straight up Notice how the sunrise passes through the east point on the horizon in the interactive graphic above, and notice where the sun crosses the meridian at the equinoxes. It is important to remember that when the sun crosses the meridian at the equinoxes, day and night are equally long. Although the we say that the day and night are equal on the equinox, in fact the sky is light longer than 12 hours. First, the Sun is not a single point; it is about half a degree across. So it takes at least 2 minutes for the sun to cross the horizon, and that adds a couple of minutes to the length of daylight. Second, the sunlight is bent - refracted - near the horizon, so the Sun appears higher in the sky and this further advances sunrise and delays sunset. This effect is actually about twice as big. Exactly how much longer the daylight lasts depends also on your latitude. Finally, the sky will also be light more than 12 hours due to the continuing twilight. The sky becomes completely, astronomically, dark only when the sun is 15 degrees below the horizon. It is still quite bright out when the sun is less than 5 degrees below the horizon. There are two days each year when the Sun is entirely below the horizon for 12 hours and above for 12 (give or take 1 minute). At the latitude of Ames, these come about 3 days before the Vernal Equinox and 3 days after the Autumnal Equinox.