In this article for astrologers, I will show how four time scales are mathematically related:
- Local Mean Time (LMT)
- Universal Time based on the mean Sun (UT1)
- Civil Standard Time (CT)
- Coordinated Universal Time (UTC)
I will also explain which time scales are used for astrological calculations.
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Local Mean Time (LMT)
This is perhaps the most obvious way of measuring time for us.
Suppose that on one of the following dates—April 15, June 13, September 1, or December 25—we set our local clocks to 12:00 noon at the moment of true solar noon. True solar noon is when the Sun reaches its highest point and is positioned exactly on the prime meridian—the line running from South to North, passing through the zenith.
From this moment onward, throughout the entire year, noon on our clocks will correspond to local noon.
Note. In reality, you'll notice that during some months the Sun at noon will be slightly east or west of the prime meridian—due to the Earth's uneven motion. But on average, it will always be somewhere near its culmination when the clock shows local noon. In other words, the Sun oscillates throughout the year relative to a mathematical point called mean Sun. This mean Sun always appears on the prime meridian at 12:00 noon according to your local clocks.
This is why this time measurement is called Local Mean Time (LMT), or local time based on the mean Sun.
Every city has its own mean time:
- for Warsaw—Warsaw Mean Time (WMT),
- for Greenwich—Greenwich Mean Time (GMT),
- and so on.
Local time depends on the observer's longitude. If Bob at 33°E observes sunrise and sees 6:00 AM on his local clock, then Alice at 30°E doesn't see sunrise yet—she needs to wait a bit until her local time also reaches 6:00, which will coincide with her local sunrise.
How long does Alice need to wait before she sees sunrise? If we look at Bob observing sunrise from space, he would be exactly on the boundary between Earth's shadow and illuminated side. This boundary (the "terminator circle") moves at a speed of 360° per 24 hours.
Thus, one degree of longitude corresponds to:
$$ \frac{24}{360} = \frac{1}{15} \text{ hour} = 4 \text{ minutes} $$
There are 3 degrees of longitude between Bob and Alice. Therefore, if Bob at 33°E sees sunrise at 6:00, Alice at 30°E needs to wait:
$$ \frac{3}{15} = 0.2 \text{ hour} = 12 \text{ minutes} $$
until her local sunrise occurs.
GMT as Reference Time
It's very convenient to express a city's Local Mean Time relative to Greenwich Mean Time, since an observer's longitude is measured relative to the prime meridian at Greenwich.
In other words:
$$ \text{LMT} = \text{GMT} + \frac{\lambda_{\text{observer}}}{15} $$
where $\lambda_{\text{observer}}$ is the observer's longitude in degrees (eastern longitude—positive, western longitude—negative).
Universal Time (UT)
Until the 20th century, GMT (Greenwich Mean Time) was the world's time standard: it was used in navigation, astronomy, and for compiling ephemerides.
In the 20th century, astronomers learned to measure the Earth's rotation angle relative to the mean Sun with great precision using radio telescopes. Scientists began accounting for effects such as polar motion and seasonal variations in Earth's rotation. Therefore, the refined mean time at Greenwich became known as Universal Time, UT.
There were several versions of UT measurement, each with its own designation: UT0, UT1, UT2.
It turned out that UT1 most accurately reflects the Earth's actual rotation, and thus became the time standard for astronomical observations.
Astronomers agreed among themselves that for convenience, UT1 would coincide with local mean time at the zero meridian—GMT. Thus, we can express the relationship between Universal Time UT1 and Local Mean Time:
$$ \text{LMT} = \text{UT1} + \frac{\lambda_{\text{observer}}}{15} $$
Why is UT1 called Universal?
This time is called universal because it is the same for all Earth inhabitants at the same moment. This can be easily demonstrated mathematically.
Suppose Bob is at longitude 33°E, and Alice at 30°E. Bob observes sunrise at 6:00 according to his Local Mean Time. At this moment, Alice's clock shows 5:48—her sunrise will occur only in 12 minutes, as I showed earlier. Formally:
This is only possible if:
Thus, Universal Time doesn't depend on the observer's longitude—hence its name: universal.
This means that Bob and Alice, looking at the sky simultaneously, will see:
- The same Moon phase,
- The same zodiacal degree of the Moon,
since for the same moment of Universal Time UT1, the Moon will have identical celestial coordinates for all Earth observers in the geocentric coordinate system.
Civil Time (CT)
With the development of logistics and economic trade, it became impractical to adjust clocks by minutes when moving between cities. During 1878-1884, Canadian engineer Sandford Fleming proposed a system of 24 time zones, each 15° of longitude wide. At the 1884 International Meridian Conference in Washington:
- Greenwich was established as the prime meridian;
- The concept of standard time and time zones was officially adopted.
The conversion formula from LMT to the new Standard Civil Time (CT) was defined as:
$$ \text{CT} = \text{LMT} - \frac{(\lambda_{\text{observer}} - \lambda_{\text{standard}})}{15} $$
where $\lambda_{\text{observer}}$ is the observer's longitude in degrees, and $\lambda_{\text{standard}}$ is the standard meridian longitude for the time zone (e.g., 15° for the first zone, 30° for the second, etc.). Eastern longitudes are positive, western—negative.
Thus, every citizen had to adjust their local clocks forward or backward by several minutes depending on their city's longitude to conform to the new standard.
Time Standardization Example
Let's examine how this worked for Bob (33°E) and Alice (30°E), who now found themselves in the same time zone (the second one) with $\lambda_{\text{standard}} = 30^\circ$:
Before (using Local Mean Time):
- When Bob witnessed sunrise, his clock showed $\text{LMT}_1 = \text{6:00}$
- At that moment, Alice's clock showed $\text{LMT}_2 = \text{5:48}$ (Alice needed to wait 12 minutes for sunrise)
After (using Standard Civil Time):
Bob set his clock back by 12 minutes, while Alice didn't need any adjustment. Now both Bob and Alice see the same civil time—5:48—at the moment when Bob is already experiencing sunrise while Alice isn't yet.
At this exact moment, as I showed in ($\ref{1}$), the entire planet had:
$$ \text{UT1} = \text{3:48} $$
We can express this as:
Bob and Alice are experiencing the same minute of Universal Time UT1 = 3:48 AM, but now according to their "adjusted" clocks. They still observe identical positions of the Moon and planets on the zodiacal circle.
Coordinated Universal Time (UTC)
The Slowing Earth Effect
Unlike UT1, which reflects the actual Earth rotation measured by radio telescopes, UTC theoretically calculates the same mean solar day using atomic clocks.
Earth's rotation, and consequently UT1, gradually slows down over time due to tidal friction between water and land. This results in the lengthening of a day. Therefore, UT1 progressively falls behind the time measured by uniformly running atomic clocks, which aren't affected by mechanical friction.
How This Is Accounted For?
About 600 coordinated cesium clocks worldwide record International Atomic Time, TAI (Temps Atomique International).
Since atomic clocks are independent of Earth's gradually slowing rotation, TAI remains perfectly uniform. Thus, TAI always runs ahead of UT1, and this difference gradually increases. If we round this difference to whole seconds, we get time very close to UT1 but measured by atomic clocks:
$$ \text{UTC} = \text{TAI} - \Delta(\text{leap seconds}) $$
Coordinated Universal Time, UTC—is atomic clock readings minus an integer number of leap seconds, approximately matching the actually measured mean solar time UT1.
Obviously, UTC cannot precisely match UT1: Earth's rotation slows gradually and continuously, not second by second, while UTC is obtained by subtracting whole seconds from TAI.
Therefore:
$$ \text{UTC} \approx \text{UT1} \pm 0.9\,\text{seconds} $$
The coordination between UT1 and UTC scales is maintained by IERS (International Earth Rotation and Reference Systems Service)—it "synchronizes" these two scales by publishing their relationship on its official website.
Today, UTC has become the universal world time standard—all servers worldwide, databases, trading platforms, airports, etc. synchronize their time with UTC. UTC is broadcast by time services like NIST (National Institute of Standards and Technology) via radio and Internet.
Which Time Standard is Used in Astronomical Calculations
Using UT1
UT1 is directly tied to the actual observed rotation of Earth. It's perfectly suited for astronomical observations relative to the horizon—ASC, MC, house cusps, primary directions, planetary positions in houses, etc. For these calculations, UT1 is converted to Greenwich Sidereal Time, GST.
- GST represents the time when midnight on sidereal clocks in Greenwich coincides with the culmination of 0° Aries.
- Sidereal day is the time of Earth's rotation relative to the point of 0° Aries.
GST is then converted to Local Sidereal Time, LST using the formula:
$$ \text{LST} = \text{GST} + \frac{\lambda_{\text{observer}}}{15} $$
where $\lambda_{\text{observer}}$ is the observer's longitude in degrees (eastern longitude—positive, western—negative).
In other words, when Bob (at 33°E) observes 24:00 on his sidereal clock, this means 0° Aries is culminating at his local meridian (MC).
At the same moment, Alice (at 30°E) sees 23:48 on her sidereal clock, observing the final degrees of Pisces at her MC. Aries will begin culminating in her location only after 12 minutes.
Ephemeris (Theoretical) Time
When working with ephemerides, we need theoretical, continuous and uniform time. This is what's used in formulas and computer models for calculating celestial coordinates of planets.
- We can't use UT1 because Earth's rotation is slowing and irregular. Theoretical time must be uniform.
- We can't use UTC because it's piecewise-continuous due to leap second insertions.
Therefore, uniform and continuous atomic time was adopted as the basis for calculating planetary motion across the celestial sphere. Astronomers agreed:
The moment 1977-01-01 00:00:00 TAI would be the reference point for ephemeris time. This moment is also called the beginning of the atomic time epoch.
This uniform and continuous time is called Terrestrial Time (TT), sometimes referred to as theoretical or ephemeris time. It relates to atomic time through the formula:
$$ \text{TT} = \text{TAI} + 32.184\ \text{sec} $$
These 32.184 seconds represent the accumulated difference between uniform atomic time (TAI) and slowing mean solar time (UT1) from the invention of atomic clocks (1949) until the atomic time epoch (1977-01-01 00:00:00 TAI).
Usage in Calculations
Starting with the DE405 model (NASA JPL), all ephemerides are calculated based on TT—for describing objects relative to Earth, or its approximation TDB (Barycentric Dynamical Time—for describing objects and orbits relative to the Sun.
Modern computer libraries (e.g., Swiss Ephemeris) work as follows:
- They accept input time in UTC from the user (e.g., via the
jday_utcfunction). - Then convert UTC to TT.
- Using TT, they calculate planetary positions on the zodiacal circle.
Additionally, for calculating planetary positions and house positions relative to the local horizon:
- These libraries convert UTC to UT1.
- From UT1 they compute sidereal time GST.
- From GST they easily derive LST, and from it—house cusps and planetary positions in houses.
Conclusion
Key takeaways from this article:
- Historically for astronomy and navigation, GMT was used as the world standard, which later evolved into UT1. This is the actually observed continuous mean solar time, but it's irregular and gradually slowing (about 30 minutes per million years).
- For global coordination in the modern world, we use UTC as universal time. It's broadcast via radio signals and internet worldwide and is identical for all people. Based on atomic clocks, it theoretically approximates mean solar time with ±0.9 seconds accuracy. It also slows down following UT1, but in jumps by subtracting whole leap seconds from uniform atomic time.
- Civil time is derived from UTC by adding/subtracting whole hours, which is very convenient for coordinating civil life in specific regions.
- Real planetary positions relative to the horizon are calculated based on sidereal time, which is tied to UT1 and also gradually slows down.
- Real planetary positions relative to the zodiacal circle are calculated based on uniform continuous atomic time, more precisely its modification—TT or TDB (ephemeris time).
In the next article, I'll demonstrate how these time scales are applied in practice.
