What is Sidereal Time

The Ra is usually measured in this mode called Sidereal Hours (360 degrees=24 hours, 360 degrees/24 hours= 15 degrees/hour of RA)

Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Usually measured in degrees (°), it is the complement of right ascension with respect to 24h.[6] It is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian.

Sidereal Time literally means star time. The time we are used to using in our everyday lives is Solar Time. The fundamental unit of Solar Time is a Day: the time it takes the Sun to travel 360 degrees around the sky, due to the rotation of the Earth. Smaller units of Solar Time are just divisions of a Day:

  • 1/24 Day = 1 Hour
  • 1/60 Hour = 1 Minute
  • 1/60 Minute = 1 Second

However, there is a problem with Solar Time. The Earth does not actually spin around 360 degrees in one Solar Day. The Earth is in orbit around the Sun, and over the course of one day, it moves about one Degree along its orbit (360 degrees/365.25 Days for a full orbit = about one Degree per Day). So, in 24 hours, the direction toward the Sun changes by about a Degree. Therefore, the Earth has to spin 361 degrees to make the Sun look like it has traveled 360 degrees around the Sky.

In astronomy, we are concerned with how long it takes the Earth to spin with respect to the fixed stars, not the Sun. So, we would like a timescale that removes the complication of Earth’s orbit around the Sun, and just focuses on how long it takes the Earth to spin 360 degrees with respect to the stars. This rotational period is called a Sidereal Day. On average, it is 4 minutes shorter than a Solar Day, because of the extra 1 degree the Earth spins in a Solar Day. Rather than defining a Sidereal Day to be 23 hours, 56 minutes, we define Sidereal Hours, Minutes and Seconds that are the same fraction of a Day as their Solar counterparts. Therefore, one Solar Second = 1.00278 Sidereal Seconds.

The Sidereal Time is useful for determining where the stars are at any given time. Sidereal Time divides one full spin of the Earth into 24 Sidereal Hours; similarly, the map of the sky is divided into 24 Hours of Right Ascension. This is no coincidence; Local Sidereal Time (LST) indicates the Right Ascension on the sky that is currently crossing the Local Meridian. So, if a star has a Right Ascension of 05h 32m 24s, it will be on your meridian at LST=05:32:24. More generally, the difference between an object’s RA and the Local Sidereal Time tells you how far from the Meridian the object is. For example, the same object at LST=06:32:24 (one Sidereal Hour later), will be one Hour of Right Ascension west of your meridian, which is 15 degrees. This angular distance from the meridian is called the object’s Hour Angle.

The Local Meridian is an imaginary Great Circle on the Celestial Sphere that is perpendicular to the local Horizon. It passes through the North point on the Horizon, through the Celestial Pole, up to the Zenith, and through the South point on the Horizon.

Because it is fixed to the local Horizon, stars will appear to drift past the Local Meridian as the Earth spins. You can use an object’s Right Ascension and the Local Sidereal Time to determine when it will cross your Local Meridian (see Hour Angle).

As explained in the Sidereal Time article, the Right Ascension of an object indicates the Sidereal Time at which it will transit across your Local Meridian. An object’s Hour Angle is defined as the difference between the current Local Sidereal Time and the Right Ascension of the object:

HAobj = LSTRAobj

Thus, the object’s Hour Angle indicates how much Sidereal Time has passed since the object was on the Local Meridian. It is also the angular distance between the object and the meridian, measured in hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it transited across the Local Meridian 2.5 hours ago, and is currently 37.5 degrees West of the Meridian. Negative Hour Angles indicate the time until the next transit across the Local Meridian. Of course, an Hour Angle of zero means the object is currently on the Local Meridian. (note 1 hr = 15 degrees of RA)

The sidereal hour angle (SHA) of a body on the celestial sphere is its angular distance west of the vernal equinox generally measured in degrees.

An alternate definition is that SHA of a celestial body is the arc of the Equinoctial or the angle at the celestial pole contained between the celestial meridian of the First point of Aries and that through the body, measured westward from Aries.

The SHA of a star changes slowly, and the SHA of a planet doesn’t change very quickly, so SHA is a convenient way to list their positions in an almanac. SHA is often used in celestial navigation and navigational astronomy.

Sidereal hour angle + right ascension = 360°

The Local Meridian is an imaginary Great Circle on the Celestial Sphere that is perpendicular to the local Horizon. It passes through the North point on the Horizon, through the Celestial Pole, up to the Zenith, and through the South point on the Horizon.

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