# The many different kinds of time

#### Ordinary Civil Time

Our clocks and watches are set to civil time, which is designed to follow the Sun. We call the average time between noon and noon one day, and divide that period into 24 equal hours. It takes roughly 365.25 days for the Earth to revolve around the Sun; in order to keep the calendar in phase with the seasons, we add a leap day every fourth year.

Civil time isn't very useful for astronomical work, but it is the version embedded most deeply into our brains because we use it every day. Therefore, I find it a good idea to include civil times in observing plans, because my brain doesn't function very well late at night. An event which is listed as occuring at 5 AM can be checked simply against my own watch or bedside table.

Most states in the US turn their clocks forward an hour in April, and backward an hour in October, for Daylight Saving Time. The sudden switch makes civil time a very poor choice for any calculations.

#### Exercises:

1. On what date does Daylight Saving Time start this spring?

#### Universal Time

Universal Time is a close cousin of civil time, but much more useful for astronomical purposes. Like civil time, it is based on the Sun: there are 24 hours in a day. The main differences are
• UT never goes on Daylight Saving Time
• UT is defined at one place on Earth (Greenwich), but used by astronomers worldwide

For practical purposes, one can think of UT as being the time on clocks in Greenwich, England. In real life, the strict definition is a lot more complicated, but that's irrelevant for us.

Astronomical events are calculated and reported in UT because UT has the same value everywhere. If a variable star is due to enter its eclipse at 5:35 UT, then observers all over the world know when to look. UT is, in essence, a giant clock which can be shared by the whole world.

Observers at different places on Earth must make different corrections to turn their local civil time into UT. Here at RIT,

```
UT  =  local time + 5 hours         (during Eastern Standard Time)

=  local time + 4 hours         (during Daylight Saving Time)
```
That change of one hour due to Daylight Saving Time can be really annoying.

#### Exercises:

1. What is the current difference between UT and the local time in Seattle?
2. Below is a chart showing the path of the shadow of asteroid as it passes in front of the bright star Regulus.

Here in Rochester, on what local date, and at what local time, should we look for the event?

#### Julian Date

Suppose that we are studying a variable star which slowly grows fainter and brighter. We record the following:

```
Tuesday,   Jan 16, 2001:    faint
Wednesday, Mar 21, 2001:    very faint
Tuesday,   Jun 26, 2001:    faint
Thursday , Aug 2,  2001:    medium
Wednesday, Oct 31, 2001:    bright
Thursday , Dec 13, 2001:    very bright
Sunday,    Jan  6, 2002:    bright
Thursday,  Feb 28, 2002:    medium
Monday,    Apr 29, 2002:    faint
Friday,    Jun  7, 2002:    very faint
```

1. What is the period of this star? That is, how long does it take to make one complete cycle from very faint, to very bright, and back to very faint?

The answer is ... a real pain in the neck to calculate. Our civil calendar has months with different numbers of days, and every fourth year a leap day is added to the end of February. When performing calculations which stretch over more than a single day or two, one must keep track of all these factors.

The Julian Date system (or JD for short) is designed to simplify calculations over long periods of time. Instead of describing a date in terms of

```
month, day, year
```
we instead describe it with a single value
```
number of days since noon, Universal Time on January 1, 4713 BCE
```

Why that particular choice of a starting date? The most important reason is that it was long, long ago, so that almost any event in recorded history will have a positive value for its Julian Day. That makes calculations extra easy. I you wish, you may read a detailed explanation of this particular choice. The word "Julian", by the way, is derived from the name of the father of the scientist who suggested this system (Julius Scaliger, the father of Joseph Justus Scaliger), not from Julius Caesar.

Thus, instead of "Wednesday, Mar 21, 2001", we could write "Julian Day 2,451,990". Those long strings of numbers can be inconvenient, or hard to remember at times, but look how much simpler they make the determination of period:

```
2451926                     faint
2451990                     very faint
2452087                     faint
2452124                     medium
2452214                     bright
2452257                     very bright
2452281                     bright
2452334                     medium
2452394                     faint
2452433                     very faint
```

The time from "very faint" to "very faint" again is simply

```
2452433  -  2451990   =   443 days
```

Actually, when describing events precisely, one may add the fraction of a day since noon (Greenwich Time) to the Julian Date. For example,

```
noon UT on March 12, 2002   =   JD  2452346
```

One hour later, 13:00 UT, is 1/24 = 0.04167 of a day later. So we could write

```
13:00 UT on March 12, 2002   =   JD  2452346.04167
```

When working with Julian Dates over relatively short periods of time -- a few days, weeks or months -- it is often convenient to abbreviate the full Julian Date by omitting the first few digits; after all, those digits are the same in all of the measurements. That is, one could re-write our table of stellar measurements as:

```
full JD     abbrev. JD =
JD - 2450000

2451926        1926         faint
2451990        1990         very faint
2452087        2087         faint
2452124        2124         medium
2452214        2214         bright
2452257        2257         very bright
2452281        2281         bright
2452334        2334         medium
2452394        2394         faint
2452433        2433         very faint
```

Beware, though: some people shorten the full Julian Date by subtracting an extra half-day (the so-called "Modified Julian Date"). It is very easy to make a mistake of one-half a day when dealing with modified values. It's usually best to quote the entire Julian Date, long as it may be.

1. Last night at 7:00 PM local time, the Greenwich clock rolled over to UT 0:00. At that time, the Julian Date was exactly 2,456,686.5. What is the Julian Date right now?

#### Local Sidereal Time

Civil time, UT, and JD are all tied to the motion of the Sun. For ordinary human purposes, that makes sense. But astronomers could use a time system which is tied to the stars. The answer: Local Sidereal Time or LST for short.

One way to describe LST is "the current LST is equal to the Right Ascension of a star which is currently at its highest point in the sky." It may help to look at a picture. Let's follow the motion of a star which has a Right Ascension value of 08:00 -- that's eight hours, zero minutes. A few hours after it rises, it is still on the eastern side of the sky:

Two hours later, it reaches its highest altitude in the sky, when it crosses the meridian (a line running from due North to due South through the zenith).

And two hours after that, it is well on its way down towards the western horizon.

We can use the Right Ascension values of stars to define a time system: when a star of RA = 08:00 is crossing the meridian, we say "the Local Sidereal Time is 08:00, or eight hours." Two hours later, a star of RA = 10:00 will be crossing the meridian, and so we'll say "the LST now is ten hours."

The whole point of LST is that it indicates where celestial objects will be in the sky. For example, if the LST = ten hours, then we know

• a star at RA = 08:00 is in the western half of the sky (probably OK to observe it now)
• a star at RA = 10:00 is just crossing the meridian (definitely a good time to observe it)
• a star at RA = 12:00 is in the eastern half of the sky (probably OK to observe it now)
• a star at RA = 15:00 is just barely over the horizon (should wait a few hours to observe it)
• a star at RA = 20:00 is below the horizon (and won't be visible for another 5-6 hours at least)

The difference between the current LST and the RA of a star is called the hour angle (or HA for short).

```       Hour Angle   =   LST  -  RA
```

This is usually measured in hours, and describes how long it has been since the star crossed the meridian. In the series of figures above, the star has

• HA = -02:00 in the first figure
• HA = 00:00 in the second figure
• HA = +02:00 in the third figure

Hour Angle is sometimes used as a substitute for Right Ascension; together with Declination, it uniquely describes the position of a star in the sky. One can also use HA and Declination together to calculate the airmass (which we will discuss in a lecture or two ).

Note that LST is a Local system; an observer in Rochester and an observer in Los Angeles will agree on the UT, but not on the LST.

1. Estimate the size of the difference in LST between the observer in Rochester and the observer in Los Angeles. What are the natural units?
2. What is the sign of quantity
```          (LST_in_Rochester - LST_in_Los_Angeles)
```

3. Based on the sky chart below, answer the following questions. (Click on the figure below for a PDF version.)

1. Label the cardinal directions on the sky.
2. Estimate roughly the Declination of Procyon.
3. Estimate roughly the Right Ascension of Cor Caroli.
4. What is the current LST?
5. How long until Saturn reaches the meridian?
6. Can you guess what the dashed line running through the middle of the figure is?