# Does mean solar time and sidereal time sometimes indicate the same time?

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I'm trying to wrap my head around the different definitions of time. Since mean solar time depends on the Sun, and sidereal time depends on the stars, and since the position of the Sun relative to the stars changes over the course of the year, does this mean that the difference between the two times increases and decreases over the course of the year?

Once a year, mean solar time and sidereal time will be the same. Is that right?

The 3m56s mean difference between solar and sidereal days is due to the Earth's orbital motion around the Sun. This adds up to 1 day per year; for every 365¼ solar days there are 366¼ sidereal days.

Sidereal time equals the right ascension of what's on the celestial meridian at that time. The Sun is on the meridian at 12:00 apparent solar time. These align at the September equinox, when the Sun is at RA 12h. Mean solar time is ~7.5 minutes behind apparent solar time on that date and aligns with sidereal time ~1.9 days earlier.

the sidereal time is the time measured by the angle between the sight line of an observer and the direct ray of a fixed star to the observer, whereas the solar time is the time measured by looking at the position of the sun in the sky like you can say it's around noon when the sun is overhead… they are just different versions of the same time… like metre and mile are of length 1 mile is not equal to 1 metre… similarly sidereal and solar time are different units of the same time… it's often said that the solar day is 4 mins less than a sidereal day

A tall pole vertically fixed in the ground casts a shadow on any sunny day. At one moment during the day, the shadow will point exactly north or south (or disappear when and if the Sun moves directly overhead). That instant is local apparent noon, or 12:00 local apparent time. About 24 hours later the shadow will again point north–south, the Sun seeming to have covered a 360-degree arc around the Earth's axis. When the Sun has covered exactly 15 degrees (1/24 of a circle, both angles being measured in a plane perpendicular to the Earth's axis), local apparent time is 13:00 exactly after 15 more degrees it will be 14:00 exactly.

The problem is that in September the Sun takes less time (as measured by an accurate clock) to make an apparent revolution than it does in December 24 "hours" of solar time can be 21 seconds less or 29 seconds more than 24 hours of clock time. This change is quantified by the equation of time, and is due to the eccentricity of the Earth's orbit (i.e. the Earth's orbit is not perfectly circular, meaning that the Earth–Sun distance varies throughout the year), and the fact that the Earth's axis is not perpendicular to the plane of its orbit (the so-called obliquity of the ecliptic).

The effect of this is that a clock running at a constant rate – e.g. completing the same number of pendulum swings in each hour – cannot follow the actual Sun instead it follows an imaginary "mean Sun" that moves along the celestial equator at a constant rate that matches the real Sun's average rate over the year. [1] This is "mean solar time", which is still not perfectly constant from one century to the next but is close enough for most purposes. Currently a mean solar day is about 86,400.002 SI seconds. [2]

The two kinds of solar time (apparent solar time and mean solar time) are among the three kinds of time reckoning that were employed by astronomers until the 1950s. (The third kind of traditional time reckoning is sidereal time, which is based on the apparent motions of stars other than the Sun.) [3] By the 1950s it had become clear that the Earth's rotation rate was not constant, so astronomers developed ephemeris time, a time scale based on the positions of solar system bodies in their orbits.

The apparent sun is the true sun as seen by an observer on Earth. [4] Apparent solar time or true solar time is based on the apparent motion of the actual Sun. It is based on the apparent solar day, the interval between two successive returns of the Sun to the local meridian. [5] [6] Apparent solar time can be crudely measured by a sundial. The equivalent on other planets is termed local true solar time (LTST). [7] [8]

The length of a solar day varies through the year, and the accumulated effect produces seasonal deviations of up to 16 minutes from the mean. The effect has two main causes. First, due to the eccentricity of Earth's orbit, the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see Kepler's laws of planetary motion). Second, due to Earth's axial tilt (known as the obliquity of the ecliptic), the Sun's annual motion is along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its average for the year when the Sun is farthest from the equator at both solstices, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see tropical year). In June and December when the sun is farthest from the celestial equator a given shift along the ecliptic corresponds to a large shift at the equator. So apparent solar days are shorter in March and September than in June or December.

Length of apparent solar day (1998) [9]
Date Duration in mean solar time
February 11 24 hours
March 26 24 hours − 18.1 seconds
May 14 24 hours
June 19 24 hours + 13.1 seconds
July 25/26 24 hours
September 16 24 hours − 21.3 seconds
November 2/3 24 hours
December 22 24 hours + 29.9 seconds

These lengths will change slightly in a few years and significantly in thousands of years.

Mean solar time is the hour angle of the mean Sun plus 12 hours. This 12 hour offset comes from the decision to make each day start at midnight for civil purposes whereas the hour angle or the mean sun is measured from the local meridian. [10] Currently (2009) this is realized with the UT1 time scale, constructed mathematically from very long baseline interferometry observations of the diurnal motions of radio sources located in other galaxies, and other observations. [11] [12] The duration of daylight varies during the year but the length of a mean solar day is nearly constant, unlike that of an apparent solar day. [13] An apparent solar day can be 20 seconds shorter or 30 seconds longer than a mean solar day. [9] [14] Long or short days occur in succession, so the difference builds up until mean time is ahead of apparent time by about 14 minutes near February 6 and behind apparent time by about 16 minutes near November 3. The equation of time is this difference, which is cyclical and does not accumulate from year to year.

Mean time follows the mean sun. Jean Meeus describes the mean sun as follows:

Consider a first fictitious Sun travelling along the ecliptic with a constant speed and coinciding with the true sun at the perigee and apogee (when the Earth is in perihelion and aphelion, respectively). Then consider a second fictitious Sun travelling along the celestial equator at a constant speed and coinciding with the first fictitious Sun at the equinoxes. This second fictitious sun is the mean Sun. " [15]

The length of the mean solar day is slowly increasing due to the tidal acceleration of the Moon by the Earth and the corresponding slowing of Earth's rotation by the Moon.

Many methods have been used to simulate mean solar time. The earliest were clepsydras or water clocks, used for almost four millennia from as early as the middle of the 2nd millennium BC until the early 2nd millennium. Before the middle of the 1st millennium BC, the water clocks were only adjusted to agree with the apparent solar day, thus were no better than the shadow cast by a gnomon (a vertical pole), except that they could be used at night.

But it has long been known that the Sun moves eastward relative to the fixed stars along the ecliptic. Since the middle of the first millennium BC the diurnal rotation of the fixed stars has been used to determine mean solar time, against which clocks were compared to determine their error rate. Babylonian astronomers knew of the equation of time and were correcting for it as well as the different rotation rate of the stars, sidereal time, to obtain a mean solar time much more accurate than their water clocks. This ideal mean solar time has been used ever since then to describe the motions of the planets, Moon, and Sun.

Mechanical clocks did not achieve the accuracy of Earth's "star clock" until the beginning of the 20th century. Today's atomic clocks have a much more constant rate than the Earth, but its star clock is still used to determine mean solar time. Since sometime in the late 20th century, Earth's rotation has been defined relative to an ensemble of extra-galactic radio sources and then converted to mean solar time by an adopted ratio. The difference between this calculated mean solar time and Coordinated Universal Time (UTC) determines whether a leap second is needed. (The UTC time scale now runs on SI seconds, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time. [16] )

## 4.3 Keeping Time

The measurement of time is based on the rotation of Earth. Throughout most of human history, time has been reckoned by positions of the Sun and stars in the sky. Only recently have mechanical and electronic clocks taken over this function in regulating our lives.

### The Length of the Day

The most fundamental astronomical unit of time is the day, measured in terms of the rotation of Earth. There is, however, more than one way to define the day. Usually, we think of it as the rotation period of Earth with respect to the Sun, called the solar day . After all, for most people sunrise is more important than the rising time of Arcturus or some other star, so we set our clocks to some version of Sun-time. However, astronomers also use a sidereal day , which is defined in terms of the rotation period of Earth with respect to the stars.

A solar day is slightly longer than a sidereal day because (as you can see from Figure 4.10) Earth not only turns but also moves along its path around the Sun in a day. Suppose we start when Earth’s orbital position is at day 1, with both the Sun and some distant star (located in the direction indicated by the long white arrow pointing left), directly in line with the zenith for the observer on Earth. When Earth has completed one rotation with respect to the distant star and is at day 2, the long arrow again points to the same distant star. However, notice that because of the movement of Earth along its orbit from day 1 to 2, the Sun has not yet reached a position above the observer. To complete a solar day, Earth must rotate an additional amount, equal to 1/365 of a full turn. The time required for this extra rotation is 1/365 of a day, or about 4 minutes. So the solar day is about 4 minutes longer than the sidereal day.

Because our ordinary clocks are set to solar time, stars rise 4 minutes earlier each day. Astronomers prefer sidereal time for planning their observations because in that system, a star rises at the same time every day.

### Example 4.3

#### Solution

It will rise at about 1:00 p.m. and be high in the sky at around sunset instead of midnight. Sirius is the brightest star in the constellation of Canis Major (the big dog). So, some other constellation will be prominently visible high in the sky at this later date.

In two months, the star will rise:
60 days × 4 minutes day = 24 0 minutes or 4 hours earlier. 60 days × 4 minutes day = 24 0 minutes or 4 hours earlier.
This means it will rise at 4:30 p.m.

### Apparent Solar Time

We can define apparent solar time as time reckoned by the actual position of the Sun in the sky (or, during the night, its position below the horizon). This is the kind of time indicated by sundials, and it probably represents the earliest measure of time used by ancient civilizations. Today, we adopt the middle of the night as the starting point of the day and measure time in hours elapsed since midnight.

During the first half of the day, the Sun has not yet reached the meridian (the great circle in the sky that passes through our zenith). We designate those hours as before midday (ante meridiem, or a.m.), before the Sun reaches the local meridian. We customarily start numbering the hours after noon over again and designate them by p.m. (post meridiem), after the Sun reaches the local meridian.

Although apparent solar time seems simple, it is not really very convenient to use. The exact length of an apparent solar day varies slightly during the year. The eastward progress of the Sun in its annual journey around the sky is not uniform because the speed of Earth varies slightly in its elliptical orbit. Another complication is that Earth’s axis of rotation is not perpendicular to the plane of its revolution. Thus, apparent solar time does not advance at a uniform rate. After the invention of mechanical clocks that run at a uniform rate, it became necessary to abandon the apparent solar day as the fundamental unit of time.

### Mean Solar Time and Standard Time

Instead, we can consider the mean solar time , which is based on the average value of the solar day over the course of the year. A mean solar day contains exactly 24 hours and is what we use in our everyday timekeeping. Although mean solar time has the advantage of progressing at a uniform rate, it is still inconvenient for practical use because it is determined by the position of the Sun. For example, noon occurs when the Sun is highest in the sky on the meridian (but not necessarily at the zenith). But because we live on a round Earth, the exact time of noon is different as you change your longitude by moving east or west.

If mean solar time were strictly observed, people traveling east or west would have to reset their watches continually as the longitude changed, just to read the local mean time correctly. For instance, a commuter traveling from Oyster Bay on Long Island to New York City would have to adjust the time on the trip through the East River tunnel because Oyster Bay time is actually about 1.6 minutes more advanced than that of Manhattan. (Imagine an airplane trip in which an obnoxious flight attendant gets on the intercom every minute, saying, “Please reset your watch for local mean time.”)

Until near the end of the nineteenth century, every city and town in the United States kept its own local mean time. With the development of railroads and the telegraph, however, the need for some kind of standardization became evident. In 1883, the United States was divided into four standard time zones (now six, including Hawaii and Alaska), each with one system of time within that zone.

By 1900, most of the world was using the system of 24 standardized global time zones. Within each zone, all places keep the same standard time, with the local mean solar time of a standard line of longitude running more or less through the middle of each zone. Now travelers reset their watches only when the time change has amounted to a full hour. Pacific standard time is 3 hours earlier than eastern standard time, a fact that becomes painfully obvious in California when someone on the East Coast forgets and calls you at 5:00 a.m.

Globally, almost all countries have adopted one or more standard time zones, although one of the largest nations, India, has settled on a half-zone, being 5.5 hours from Greenwich standard. Also, China officially uses only one time zone, so all the clocks in that country keep the same time. In Tibet, for example, the Sun rises while the clocks (which keep Beijing time) say it is midmorning already.

Daylight saving time is simply the local standard time of the place plus 1 hour. It has been adopted for spring and summer use in most states in the United States, as well as in many countries, to prolong the sunlight into evening hours, on the apparent theory that it is easier to change the time by government action than it would be for individuals or businesses to adjust their own schedules to produce the same effect. It does not, of course, “save” any daylight at all—because the amount of sunlight is not determined by what we do with our clocks—and its observance is a point of legislative debate in some states.

### The International Date Line

The fact that time is always advancing as you move toward the east presents a problem. Suppose you travel eastward around the world. You pass into a new time zone, on the average, about every 15° of longitude you travel, and each time you dutifully set your watch ahead an hour. By the time you have completed your trip, you have set your watch ahead a full 24 hours and thus gained a day over those who stayed at home.

The solution to this dilemma is the International Date Line , set by international agreement to run approximately along the 180° meridian of longitude. The date line runs down the middle of the Pacific Ocean, although it jogs a bit in a few places to avoid cutting through groups of islands and through Alaska (Figure 4.11). By convention, at the date line, the date of the calendar is changed by one day. Crossing the date line from west to east, thus advancing your time, you compensate by decreasing the date crossing from east to west, you increase the date by one day. To maintain our planet on a rational system of timekeeping, we simply must accept that the date will differ in different cities at the same time. A good example is the date when the Imperial Japanese Navy bombed Pearl Harbor in Hawaii, known in the United States as Sunday, December 7, 1941, but taught to Japanese students as Monday, December 8.

## Stellarium

All you have to do is turn on the equatorial grid and the meridian line (look
south). The Local Sidereal Time is the right ascension that is indicated by
the meridian line. If you zoom in enough you get an accurate value.

I strongly suspect that anyone asking for Stellarium to be able to explicitly show sidereal time knows that an approximation of it can be read from the RA at the meridian (or, for that matter, from the HA of the vernal equinox). That's entirely not the point though. The task of computers is to make things easier for the users and to rid them of having to perform chores just to get some information (you have to change your viewing direction and zoom level, and turn on displaying the meridian and the RA/Dec grid, and even then the accuracy of your reading is limited).

I won't even get into trying to argue the significance of local sidereal time - suffice to say that every planetarium program I know (including ancient software for DOS from the 80s/90s), foremostly CDC and C2A, can display the sidereal time. It seems quite obvious that Stellarium shouldn't be missing this functionality either, probably the best way to implement it would be via a "Clock" plugin somewhat similar to CDC's clock feature (picture), only displaying the clock readings as a transparent text overlay in the upper or lower right corner, with user-configurable clocks to display.

Two other great features to accompany this would be:

the addition of a Hour Angle/Declination grid, optimally allowing to count the HA not only from the local meridian, but also from other meridians like the central meridian of the current time zone, or the zero meridian

a feature allowing to display the mean Sun's current position on the celestial equator.

The above features would have great educational value in that they would make it possible to show very clearly how the different clock readings (UTC, local timezone, local mean solar, local true solar, sidereal etc.) are really just hour angles (shifted by 12h in the case of the Sun) of either the mean Sun, the true Sun, or the vernal equinox, from the perspective of different meridians (zero, timezone central, or local).

## PHY115: Professional Skills in Physics and Astronomy

where HA ☉ and RA ☉ are the hour angle and right ascension of the Sun. But of course, the Sun moves around the ecliptic, so RA ☉ changes through the year. If we had to go to work every day at the same local sidereal time, sometimes this would be in the day, and sometimes at night!

It's hardly surprising then, that we use solar time to govern civil timekeeping. The solar time is related to the hour angle of the sun, so that the Sun is always near the observer's meridian at noon. By convention, local noon is at 12:00, so that the solar time is given by

The 12 hour correction ensures that the solar time is always 12:00 when the Sun is on the meridian.

In reality, things are a little more complicated than described above, as the Earth's orbit is elliptical, which means that the length of the solar day varies throughout the year. This means that the Sun might be up to 15 minutes in front or behind the meridian at local noon. We won't go into that in this course, but it is discussed in more detail in Vik Dhillon's excellent notes from the discontinued PHY105.

Universal Time

The hour angle of the Sun depends on the observer's longitude and so solar time is different for observers at different longitudes. It is convenient to define a reference longitude to use for setting clocks by. This reference point is the Royal Observatory at Greenwich, the same point used to define the zero of the longitude scale. We can then define Greenwich Mean Time (GMT), or Universal Time (UT), with reference to the hour angle of the Sun for an observer at Greenwich (HA ☉,G ) as

Sidereal Time & Solar Time

Quite often we will want to convert between sidereal time and solar time (either local or GMT). For example, we may wish to know if a certain star transits during the day or not. This is quite easy, given the relationships presented here, provided one knows the right ascension of the Sun on any given day. You can roughly calculate the Sun's right ascension from it's motion around the ecliptic, or (if you want a precise value), use the online calculator from the US Department of Energy.

For a given LST, the hour angle of the Sun is simply given by

And the local solar time is just

Converting from local solar time to UT is just as easy. The relationship between local time and UT is clearly a function of longitude, as the local solar time at Greenwich is the same as UT. Since the Earth rotates 15° in one hour, we have,

where l is the longitude of the observer. The plus sign is used when the longitude is to the east, and the minus sign when the longitude is to the west.

## Does mean solar time and sidereal time sometimes indicate the same time? - Astronomy

The time it takes for the Earth to rotate on its axis 360 degrees, or one rotation relative to the "fixed" stars, is a Sidereal Day . (Sidereal means stars.) A Sidereal Day is 23 hours, 56 minutes and 4 seconds.

By comparison, the time is takes for the Earth to rotate in such a way that the Sun goes from local noon to local noon is a Solar Day . Local noon is when the Sun is highest in the sky for an observer at a particular latitude. A Solar Day is also called an Earth Synodic Day .

A Solar Day on average is 24 hours, although it can vary as much as plus or minus 25 seconds. The average Solar Day (24 hours) is called the Mean Solar Day .

The four minute difference between the Sidereal Day and the Mean Solar Day has to do with the Earth moving forward in its orbit around the Sun as it rotates on its axis. Since the Earth moves forward in its orbit about a degree relative to the Sun each day, the Earth must rotate an extra degree (or 361 degrees total) each day to realign itself with the Sun for local noon to occur again.

The Sidereal Day is 4 minutes shorter than the Mean Solar Day, because the rotation of the Earth on its axis, and the orbiting of the Earth around the Sun, are both counterclockwise, as viewed from above (or north of) the Ecliptic Plane. See planetary retrograde motion for an example of the opposite situation.

The reason that the Solar Day varies around the Mean Solar Day is that the Earth moves at different speeds through its orbit around the Sun. This is in keeping with Kepler's Second Law of Planetary Motion.

Please note that the Mean Solar Day changes over a long period of time, due to the slowing of the rotation of the Earth due to tidal forces exerted on the Earth primarily by the Moon. For example, the Mean Solar Day was about 23 hours about 250 million years ago.

## Atomic Times

### TDB - Barycentric Dynamic Time

There is a subtle relativistic distinction between coordinate time and dynamic time, which is not significant for most practical purposes. The counterpart to TDB is Barycentric Coordinate Time (TCB) which differs in rate from TDB by about 15.5 parts per billion [ref 5]. TDB and TCB were coincident on January 1, 1977 and now differ by 9.3 seconds. The rate difference from TDB can be important to long term measurements, so make sure you know which time is being used when comparing observations. Some physical constants are different in coordinate time. You are not likely to encounter TCB in the literature.

## Does mean solar time and sidereal time sometimes indicate the same time? - Astronomy

I have read about different times called sidereal time, etc. I am a bit confused about all of it. Could you please enlighten me on it?

Solar time is the sort of time we're used to, where a day is 24 hours, the average time it takes for the Sun to complete one trip around the sky and return to its original position. (Technically, civil time and time zones are based on mean solar time.) Sidereal time is measured according to the positions of the stars in the sky. A sidereal day is the time it takes for a particular star to travel around and reach same position in the sky. A sidereal day is slightly shorter than a mean day, lasting 23 hours, 56 minutes, and 4.1 seconds. A sidereal day is divided into 24 sidereal hours, which are each divided into 60 sidereal minutes, and so on.

The reason that sidereal days are shorter is that while the Earth rotates on its axis, it is also moving around the Sun. Both motions are counter-clockwise as viewed from above Earth's north pole. You may find it helpful to draw a diagram. The Sun can be represented with a point. Draw the Earth. Let it be noon for an observer on the Earth, so sketch a little stick person with his feet on the Earth and his head pointed at the Sun, because at noon, the Sun is directly overhead. Draw a line from the Earth to the Sun, and let it extend far beyond the Sun. Draw a star on this line. From the observer's point of view, the star is also overhead, although of course it would be hidden behind the Sun. Now, imagine that the observer is carried for one mean day on the Earth as it makes a rotation while also moving through space. Draw the Earth at its new position in the orbit (it's okay to exaggerate this motion for purposes of illustration) and notice that when you add the person pointing at the Sun, he's no longer pointed toward the star! More than one sidereal day has passed!

You might ask whether the star's distance would affect the length of the sidereal day. Try moving the star farther from the Sun, and you'll notice that as the star gets very far away, the differences become quite small. Even the closest stars to us are so far away that the sidereal day is the same, no matter what star you use to measure it.

#### Dave Kornreich

Dave was the founder of Ask an Astronomer. He got his PhD from Cornell in 2001 and is now an assistant professor in the Department of Physics and Physical Science at Humboldt State University in California. There he runs his own version of Ask the Astronomer. He also helps us out with the odd cosmology question.

## PY124: Solar System Astronomy

Right Ascension is a coordinate on the celestial sphere that is similar to, but not identical to, longitude on the Earth's surface. Right ascension measures the positions of celestial objects in an east-west direction, like longitude, but unlike longitude right ascension is a time-based coordinate.

The other celestial coordinate, Declination, is similar to the terrestrial coordinate latitude. A diagram of Right Ascension and Declination appears below:

As the Earth rotates on its axis, the celestial sphere appears to revolve around the Earth, making one complete revolution in one sidereal day (23 hours, 56 minutes, 4 seconds). A sidereal day is thus about 4 minutes shorter than a mean solar day. This time difference between a sidereal and a solar day is the result of the Earth moving 1/365 th of the way around the sun during this period.

Think of the celestial sphere as a giant plastic ball with the Earth at the center. The stars are painted on the inside of the plastic ball, along with the lines of the celestial coordinates Right Ascension and Declination. The ball does not move as the Earth turns in the center, but as we here on Earth see it, it looks like the ball (the celestial sphere) is turning around the Earth. Because the ball is just sitting there, the things that are painted onto the ball (stars and coordinate lines) do not move in relation to each other. The whole celestial sphere, stars, coordinate lines, and everything, appear to us on Earth to move together, making a complete circle every sidereal day.

Right Ascension is essentially a time measurement. You can think of RA in this way: Whenever the point on the celestial sphere that we have set as the "start" of Right Ascension transits our local meridian, start a stopwatch. When the celestial object of interest (a star, for example) transits our local meridian, stop the stopwatch. The time on the stopwatch is that object's Right Ascension. Right Ascension is expressed in units of time on a 24 hour format. A star could have a RA of 17 h 32 m , for example. This would mean that the star transited our meridian 17 hours and 32 minutes after the "start" of Right Ascension transited.

Where IS the "start" of Right Ascension? Astronomers needed to pick someplace on the celestial sphere to start timing for Right Ascension. The most obvious place is one of the points on the celestial sphere where the two principle celestial paths, the ecliptic and the celestial equator, cross. There are two such points, one when the ecliptic moves from south of the celestial equator to north of the celestial equator (known as the point of the Vernal Equinox) , and one where the ecliptic moves from north of the celestial equator to south of the celestial equator (known as the point of the Autumnal Equinox.)

The point chosen was the point of the Vernal Equinox. It is important to understand that the term "Vernal Equinox" can refer to two different things. In this situation we mean the point on the celestial sphere where the paths of the ecliptic and the celestial equator cross near the constellation Aries. (The term "Vernal Equinox" can also mean the moment in time when the sun is actually located at that point, but this is not the meaning in this context.)

Astronomers use Sidereal Time to measure the movement of the celestial sphere. Local sidereal time, that is the sidereal time where we are located, is equal to the right ascension of any celestial object that is transiting our meridian at this particular moment.

Avoid a common misunderstanding:

Celestial objects (stars, planets, etc. ) have a Right Ascension . They do NOT have a sidereal time. It does not make sense to say, for example, that the Moon's sidereal time is 15 h 00 m . The Moon does not have a sidereal time. The Moon (or the sun, stars, etc.. does have a Right Ascension.

Locations on the Earth have a Sidereal Time . They do NOT have a Right Ascension. It also does not make sense to say, for example, that the Right Ascension of Raleigh is now 21 h 00 m . Places do not have a Right Ascension.

Look at the diagram below. Let's say that star 2 has a Right Ascension of 06h 00m. The entire celestial sphere slowly moves from left to right over the course of the night, so the positions in relation to the horizon and the meridian of all the stars shown slowly change.

In the diagram, star 2 is just now transiting our local meridian, so our local sidereal time is 06h 00m.

Star 1 has a right ascension of 05 h 00 m . Star 1 already transited 1 hour ago. When star 1 was on our meridian, our sidereal time then was 05h 00m.

Star 3 has a right ascension of 07 h 00 m . When star 3 transits our local sidereal time will be 07 h 00 m . Since our local sidereal time is now 06 h 00 m , star 3 will transit in one hour.

So you see that the celestial sphere is like a giant clock keeping sidereal time.