Time in Astronomy

The most common reference for time keeping is the day, the time it takes for the earth to make one revolution on its axis. To measure this time, a reference is needed to mark the beginning and end points for the revolution.  The most obvious reference is the sun and thus we have solar days.  The clocks that use the sun as a reference are called solar clocks. Solar time is used in everyday life as the location of the sun in the sky is critical.  We assume that at 6am, is close to sunrise, 12 noon is lunch time, and 6pm is close to sunset.

Because there are slight variations in the length of a day and other parameters what is presented here does not detail these slight variations.  Leap seconds have at the end of the year but recently none have been added.

Solar Time

There are three kinds of solar time. 

Apparent solar time is based on the real sun which varies in speed due to our elliptical orbit around the sun, and the inclination of the poles.  The exact speed is given by the graph called equation of time. An analemma  (a-nə-le-mə) is a plot or graph in the shape of a figure eight that shows the position of the sun in the sky at a given time of day (such as noon) at one specific locale measured throughout the year.

Mean solar time is based on an imaginary sun that always moves at a uniform speed.  This averaged sun is sometimes faster or slower than the average or mean sun.  Uniform speed makes clock manufacture much easier.

Local mean time takes into account of the longitude of observer.  If a person moves one degree longitude to the east, the time increases by four minutes per degree.  If a person moves one degree to the west, the time decreases by four minutes per degree.

Standard time is the legal clock time we use everyday.  For the convenience of travelers, many legal bodies approved a total of twenty four standard time zones spaced approximately 15 degrees around the world.  Everyone in the same time zone uses the local solar time at the center of their time zone of the mean sun.  Sometimes during the summer the clocks read one hour fast and this is call Daylight Savings time.  In different parts of the world, Daylight Savings Time may add different amounts of time such as fifteen minutes or a half hour.

Sidereal Time and the Celestial Sphere

There is an alternative to using the sun as a reference, we can use the stars instead. This type of time is called sidereal time. There is no need for an average star as each star moves as a constant speed.  The stars flow across the sky rising in the east and setting in the west.  Some stars, called polar stars, near the north and south pole never rise or set. A sidereal day is the time it takes for a non-polar star to move between reference points.

Knowing what time it is using a sidereal clock makes it simple to see what stars are visible. Stars are mapped on what is called a celestial sphere.  The celestial sphere is an imaginary globe that surrounds the earth.  Imagine all the stars being move onto the celestial sphere. This star map has a grid system like the earth. The lines have different names. The longitudinal lines are called right descendant lines (RA) latitude and the latitudinal lines are called declination lines (DEC).

The sun moves in a circle on the background of stars, on the celestial sphere, called an ecliptic. The travels about one degree per day on the ecliptic. Due to the fact that the earth is going around the sun, 360 degree, and there are 365 days in a year, the earth travels a little less than one degree per day around the ecliptic.

Difference Between Solar and Sidereal Time

The difference between sidereal time and solar time is the result that is that the earth has two motions with respect to the sun.  Because turns both counter clockwise as it turns on its axis, and the earth moves counter clockwise in its orbit around the sun they both create the same effect.  As the earth orbits the sun, the angle of the sun with respect to the stars is a little larger.  This larger angle makes the solar day four minutes longer than a sidereal day and the sidereal day the sidereal day is about four minutes shorter than a solar day. 

The four minutes keeps adding up, so after a solar year, the sidereal time is 1,460 minutes ahead of solar time.  This is about 24 hours.  So there is one more day in a sidereal year (366 days) than in a solar year (365 days). A solar year is about 365.25 days long, so we have leap year roughly every four years, so leap years and sidereal years have the same number of days neglecting fractions.  More exact numbers A sidereal year is 365.25636 days long and an year is 365.2422 days

Leap Year Determination

Certain years designated as leap years have an extra day inserted into the year as February 29th.  If a year is divisible by four, it is considered as a leap year.  There are exceptions to this rule. Leap years do not occur if the year is divisible by 100 with no remainder. There is also exceptions to this rule. If the year is evenly divisible by 100 and also evenly divisible by 400 it is still a Leap Year. For example, the years 1600 and 2000 were still Leap Years, while the years 1700 and 1900 were not.

The Equation of Time

The Equation of Time (EOT) is a mathematical expression that represents the difference between apparent solar time (AST) and mean solar time (MST). It arises due to the combined effects of the Earth's elliptical orbit around the Sun and its axial tilt relative to its orbital plane. Let's explore how the Equation of Time works and why it is significant in the realm of astronomy and timekeeping:

Basics of Solar Time:

Apparent Solar Time (AST): Apparent solar time is based on the actual position of the Sun in the sky. It is measured by the apparent motion of the Sun across the celestial meridian, the imaginary line that runs from the north to the south pole, passing directly overhead.

Mean Solar Time (MST): Mean solar time is a uniform timekeeping system that divides each day into 24 equal hours. It is based on an imaginary "mean Sun" that moves along the celestial equator at a constant rate, completing one full circuit every 24 hours.

Factors Influencing the Equation of Time:

Earth's Elliptical Orbit: The Earth orbits the Sun in an elliptical path rather than a perfect circle. As a result, its distance from the Sun varies over the course of the year. When the Earth is closer to the Sun (perihelion), it moves faster in its orbit, leading to differences between apparent and mean solar time.

Axial Tilt: The Earth's axis is tilted relative to its orbital plane by approximately 23.5 degrees. This tilt causes variations in the angle of sunlight received at different latitudes throughout the year, contributing to differences in the length of solar days.

Calculation of the Equation of Time:

Direct Calculation: The Equation of Time can be directly calculated by subtracting mean solar time from apparent solar time for a given date and location on Earth. A positive value indicates that apparent solar time is ahead of mean solar time, while a negative value indicates the opposite.

Graphical Representation:** The Equation of Time is often represented graphically using an analemma, a figure-eight-shaped chart that plots the position of the Sun in the sky at the same time each day over the course of a year. The analemma illustrates the seasonal variations in the Equation of Time, with loops corresponding to differences between apparent and mean solar time.

Significance of the Equation of Time:

Timekeeping: The Equation of Time helps reconcile the variations in the length of solar days throughout the year due to the Earth's elliptical orbit and axial tilt. It provides corrections to mean solar time, ensuring accurate timekeeping and synchronization with astronomical events.

Astronomical Observations: Astronomers use the Equation of Time to accurately predict the positions of celestial objects and plan observations. It aids in coordinating observations with precise timings relative to apparent solar time, accounting for the Earth's orbital dynamics.

Tilt of Earth's Axis and Apparent Speed of the Sun:

It is more difficult to understand how the apparent speed of the sun is influenced by the tilt of the Earth's axis.  Here are more details.

Tilted Path: Due to the tilt of the Earth's axis relative to its orbital plane, the Sun's path across the sky appears to be tilted throughout the year. This tilt causes the Sun's apparent motion to follow a sinusoidal pattern, rising and setting at different points along the horizon as the seasons change.

Changing Angle of Path: The angle of the Sun's path across the sky changes throughout the year, depending on the Earth's position in its orbit around the Sun. During some months, the Sun's path is more perpendicular to the observer's horizon, while in other months, it is more parallel.

Variation in Apparent Speed:

Months Ahead and Behind: Due to the changing angle of the Sun's path, its apparent speed as observed from Earth appears to vary. In some months, the Sun's path is ahead of the mean Sun (the theoretical Sun that moves at a constant speed along the celestial equator), while in other months, it lags behind.

Perpendicular Path: When the Sun's path is more perpendicular to the observer's horizon, its apparent speed is faster. This is because the Sun covers more angular distance across the sky in a shorter period when its path is more vertical. For example, during the summer months in the Northern Hemisphere, the Sun's path is more perpendicular to the horizon, resulting in longer daylight hours and a faster apparent speed.

Parallel Path Conversely, when the Sun's path is more parallel to the observer's horizon, its apparent speed appears slower. This is because the Sun covers less angular distance across the sky in a given period when its path is more horizontal. For instance, during the winter months in the Northern Hemisphere, the Sun's path is more parallel to the horizon, leading to shorter daylight hours and a slower apparent speed.

Explanation:

Angle and Speed Relationship: The apparent speed of the Sun is directly related to the angle of its path across the sky relative to the observer's horizon. When the Sun's path is steeper (more perpendicular), it covers more ground per unit time, resulting in a faster apparent speed. Conversely, when its path is shallower (more parallel), it covers less ground per unit time, leading to a slower apparent speed.

Seasonal Variations: The changing angle of the Sun's path throughout the year is a consequence of the tilt of the Earth's axis. As the Earth orbits the Sun, different parts of its surface receive varying amounts of sunlight, leading to the changing seasons and the apparent motion of the Sun across the sky.

Thus the apparent speed of the Sun as observed from Earth varies due to the changing angle of its path across the sky, which is influenced by the tilt of the Earth's axis. When the Sun's path is more perpendicular to the observer's horizon, its apparent speed is faster, while a more parallel path results in a slower apparent speed. These variations contribute to the changing lengths of daylight hours and the patterns of daylight and darkness experienced on Earth throughout the year.

Time Zones

History of the Time Zones

The development of railroads played a significant role in the establishment and standardization of time zones. Before the widespread use of railroads, local time was determined based on the position of the sun, leading to a plethora of local times across regions. This system worked reasonably well for local communities but became increasingly problematic as transportation networks expanded, particularly with the rise of the railroad industry in the 19th century. Railroads necessitated accurate and synchronized schedules to ensure safe and efficient operations. However, the existence of numerous local times along railroad routes created confusion and posed logistical challenges for scheduling trains and coordinating arrivals and departures.

The need for standardized timekeeping became evident as railroads expanded across vast distances, spanning multiple towns, cities, and even states or countries. Without uniform timekeeping, scheduling trains and coordinating operations across different regions with varying local times was nearly impossible.
To address this issue, railway companies began adopting their own standard time systems, which often differed from one another. This led to further confusion and inefficiency, particularly at junctions where trains from different railway companies intersected.

The solution to this problem came with the introduction of standardized time zones. In 1883, the United States implemented a system of four time zones (Eastern, Central, Mountain, and Pacific) based on the division of the country's territory into longitudinal sections, each encompassing roughly 15 degrees of longitude. This system was proposed and promoted by William F. Allen, an official of the Baltimore & Ohio Railroad.

Time Zones Description

Time zones were established to address the challenges posed by the Earth's rotation and its division into 24 hours. Since the Earth rotates 360 degrees in roughly 24 hours, each hour corresponds to 15 degrees of longitude. This means that every 15 degrees of longitude represents a one-hour difference in time.  The time zone boundaries are altered due to political boundaries and other factors. 

The starting point for time zones is the Prime Meridian, which passes through Greenwich, England, and is designated as 0 degrees longitude. The time at the Prime Meridian is known as Greenwich Mean Time (GMT) or Coordinated Universal Time (UTC).  If the Prime Meridian is extended over the North Pole, it would turn into the International Date Line (IDL). 

Time Zone Exceptions

Local governments can dictate the standard time in their local area. Newfoundland Standard Time (NST) is UTC-3:30. India Standard Time is used throughout India and is UTC+5:30. Nepal Time is UTC+5:45. Australian Central Western Time is used in a small region of Western Australia, specifically in the town of Eucla.  is UTC+8:45.

The IDL time zone, is divided into two smaller time zones on either side of the IDL. These little time zones are called IDLW-WestI(UTC+12) and
IDLE-East(UTC-12).  Each of the smaller time zones are only 7.5 degrees wide. We will explain this in greater detail later.

Daylight Saving Time

 The main purpose of Daylight Saving Time (DST) is to make better use of daylight during the longer days of summer by adjusting the clocks one hour ahead. DST is usually implemented during the summer time, but in the United State DST is observed in most states from the second Sunday in March to the first Sunday in November. Hawaii, and the overseas territories of the USA do not observe DST.   Arizona (except for the Navajo Nation) does not observe DST.

Movement of Time Around the Globe

Looking down on the earth from over the North Pole, the earth would be seen turning counter-clockwise.  Rotating a globe counter-clockwise and pointing a finger towards the globe, as the globe moves, the world spins to the east under the finger.  But if we are on the globe, we would see the finger (or the sun) move west.

If you travel towards the east you will enter time zones which are one hour later.  If you wait in your time zone for an hour, the time in the time zone to east will move into your time zone to west.  So if it is 9:59am CST (UTC-6) it will be 10:59 EST (UTC-5) and a minute later it will be 10am CST (UTC-6) and
11am EST (UTC-5). So 10 o'clock seem to move west.

Time and the International Date Line

International Date Line

As one moves through the time zones going east, you would pick up an hour with every time you entered a new time zone.  If one kept going, you would pass a time zone that just experienced midnight and thus the day would have to be incremented as well. Going around the earth again, you would gain another day. And this would be confusing.  The same place would have different dates.

To keep this from happening, an International Date Line (IDL) was created.

The IDL was set on top of the 180 degree meridian line. If you traveled north on the Prime Meridian Line over the North Pole you would be on the 180 degree meridian line.  This meridian runs down the middle of the Pacific Ocean, so it was thought nobody would care.  But they were wrong.  The IDL passes near and over some small islands, the people were not happy to have to cope with two different days as they traveled to met their neighbores.

The local governments were eager to fix the problem by moving the IDL for their convenience. In the process, the IDL zigzags all over the place. It is worst than political jerry meandering. In fact, traveling north or south you can cross the IDL several times and also cross different time zone boundaries.  One must use a map that has the updated IDL locations and time zone locations.  One solution would be to use UTC.

The Movement of Time

As we mentioned before time moves from east to west.  It is an hour later one time zone to the east.  If you wait an hour, the time in the time to the east will be your time.  So time moves from time zone to time zone at the rate of 1 hour per hour.

Also days move from east to west.  Once a day, each time zone experiences midnight and a new day. Midnight moves 1 hour per hour too.  So there is only one midnight in a day, every 24 hours the day increases.  But the day increase will occur in the time zone to your east one hour before occurs in your time zone.  So you can picture a day moving once an hour west though all the time zones. The time zones offset is increasingly more negative as we move west of the prime meridian. The time zones offset becomes increasingly more positive as we move east of the prime meridian.

How a New Day is Created

One either side of the IDT there are two narrow time zones, that are only 7.5 degrees wide. One is IDLW-West (UTC+12) and the other is IDLE-East (UTC-12).  Note that the difference between +12 and -12 is 24 hours.

When midnight moves into the IDLW and IDLE both time zones are increment at the same time to one day later.  IDLW (UTC+12) is one day ahead of
IDLE (UTC-12)

In the diagram below it starts with the first row where UTC-9 time zone just changed from the 20th to the 21st.  This is shown in the yellow square.  An hour later UTC-10 increments its day from  the 20th to the 21st.  This happens again for UTC-11 and UTC-12.  But UTC+12 is one day ahead of UTC-12, so the UTC+12 time zone increments from the 21st to the 22nd.  A new day, the 22nd is created.  An hour later the same things happens to UTC+11. One more hour at UTC+10 does the same thing. 

The new day moves around the world one time zone at a time. As it comes into UTC-9 time zone (not shown) the day is increment to the 22nd, and this propagates in the same manner.  As midnight passes into UTC-12, the day changes to the 22nd, but UTC+12 also increments at the same time and produces a brand new day, namely the 23rd.  The 23rd goes around the world can comes back through UTC+12 where it is incremented to the 24th, and the 24th goes around the world. 

Note that UTC date changes do not show up on the chart, as the chart covers only seven time zones.

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