All three of the above are angles measured along the celestial equator. Hour Angle is measured westward, while Right Ascension is measured eastward. For any particular celestial object the three are related.The relation that connects them is:
Civil time is determined by the hour angle of the Sun. This is the case because our activities are for the most part determined by the position of the Sun. Astronomers are more interested in the stars and wish to know what stars are above the horizon. As a result they use celestial time or Siderial Time.
Definition of Siderial Time:
Siderial Time equals the Hour Angle of the Vernal Equinox.
If you know your siderial time, it will be equal to the right ascension of the stars on your local celestial meridian. As you can see that is very useful, since as long as you know the siderial time it tells you what stars are most visible.
How do you determine siderial time?
The time it takes for the Earth to rotate once relative to the stars is less than that to rotate once relative to the Sun. The reason for this is explained in Chapter 1 of Chaisson (p 10). During one revolution relatiive to the stars, the Earth has moved about 1 degree along in its orbit and as a result must rotate this additional amount to have rotated once relative to the Sun. This is illustrated in Figure 1.9 in Chaisson. As a result the siderial day is approximately 4 minutes shorter than a solar day. (1 degree of rotation = 4 minutes of time)
Solar Day = 86400 seconds
Siderial Day = 86164.1 seconds
Every solar day, the siderial time advances 3.94 minutes and throughout the year there will be one more siderial day in the year than solar days. Astronomers do not keep track of the number of the Siderial Day but are only interested in the Siderial Time of day.
When the Sun is at the vernal equinox (approx. March 21), siderial and solar hour angle are equal. However, since the day starts when the solar hour angle is 12 hours (midnight), the siderial day and solar day are out of step by 12 hours. When the Sun is at the autumnal equinox (approx. September 22), then the siderial and solar times are in step.
The Observer's Handbook (1996) provides a table of siderial times for the beginning of each month in the year on page 26. In addition, it provides a formula for calculating the siderial time at any time during that month.
EXAMPLE: What is the Sidereial Time (ST) at 10 pm Central Daylight Time, on August 12, 1996?
Note: We have assumed that the observer is located on the standard meridian for the central standard time zone. If not then there is a correction for the difference in longitude. We will not go into that here.
All three of the above are angles measured along the celestial equator. Hour Angle is measured westward, while Right Ascension is measured eastward. For any particular celestial object the three are related.
The relation that connects them is:
Calculating Sideral time with the method shown above is what you should do if you want an accurate Siderial Time. With another method , you look up the Right Ascension of the Sun and use the ST = HA + RA
Method:
Determine the H.A. and the R.A. of the object and add them to get the siderial time.
This is close to the previously determined value, but here we did not correct for the fact that the RA of the Sun was for 0h UT on the 13th - but for a quick estimate, this is OK.
Once you have the ST, you can determine the Hour Angle of an object given its Right Ascension.
EXAMPLE: