# Time Systems in Astronomy

#### Good old local time

Local time is the time we use in ordinary life. For example, this class is scheduled to meet four days a week at 1:00 PM local time.

Local time is designed to follow the Sun. The goal is to arrange our clocks so that the Sun rises around 6 AM, reaches its peak around noon, and sets around 6 PM. It's convenient from a practical point of view: if you are travelling to a foreign country and know that your plane will arrive at 23:00 local time, then you know most people will probably be at home and sleeping when you touch down. You'll probably have to call a cab ...

One annoying feature of local time is that (in most states of the US) it shifts by one hour twice a year. During Daylight Savings Time, which starts April 3 this year, clocks are shifted forward one hour: what used to be 7 AM is now 8 AM. Sometime in the autumn (this year on October 30), clocks are shifted back one hour to Standard Time.

This shift can make it difficult to calculate the interval between two events, if they span the start or end of Daylight Savings Time.

#### Universal Time

When people living in different parts of the world want to coordinate their actions, the differences between time zones become a big hassle.

```
Q: What is the current difference between the time
in Rochester, NY, and Timbuktu, Mali?

```

Therefore, people decided long ago to make one time zone "special" and use it for a worldwide standard. Just as the longitude system is centered on Greenwich, England, so the time system is as well. There are several names given to the time at Greenwich (see notes below for names with asterisks *)

• Greenwich Time, or Greenwich Mean Time (GMT)
• Zulu Time (a military designation)
• Universal Time (*)
• Coordinate Universal Time (UTC) (*)

(*) There are actually small differences between several varieties of Universal-ish time. For our purposes, they may be treated the same, but if you are interested in accuracy at the sub-second level, you'll need to know the differences. See the references at the end of today's lecture.

Astronomers typically use Universal Time to refer to events. Look, for example, at the listing of asteroid occultations visible in March:

#### Atomic Time

Universal Time (at least some varieties) and local time (all varieties) are tied to the Earth's rotation. For many purposes, that's fine: the Earth rotates at a nearly constant rate. But over the course of a decade, small changes in the Earth's rotation rate can cause a significant difference to build up between a perfect clock and the location of the Sun.

• 1990 Jan 1, 16:57:00 UT: the Sun reaches its highest point in the sky over Rochester
• 24 hours later: the Sun is again at its highest point
• another 24 hours later: the Sun is again at its highest point

...

• 1000 periods of 24 hours later: the Sun is not quite at the peak of its motion as seen from Rochester ...
• (four seconds later) NOW it's at the peak

These very small drifts between the Earth's rotation and the ticking of a perfect clock lead to leap seconds: extra seconds which are added (or subtracted) from the official civil time to keep the civil clocks in line with the Earth's rotation (and, hence, with the Sun).

Leap seconds can be a nuisance if you are trying to calculate the exact interval between two events many years apart.

• event A: 1990 May 23, 12:33:41 UT
• event B: 1998 May 23, 12:33:41 UT

```
Q:  What is the time interval between events A and B?
```

To avoid the complications of leap seconds, scientists have devised a time system based on clocks which are more consistent than the Earth's rotation. International Atomic Time (TAI) is defined by the action of a set of atomic clocks. You can find tables which tell the difference between Universal Time and TAI over a range of dates.

The Global Positioning System (GPS) satellites use something like TAI: a system which runs more precisely than the Earth's rotation, and does not include leap seconds.

#### Barycentric (or heliocentric) time

Suppose that there is a distant celestial source which undergoes some regular variation: for example, an eclipsing binary star which has a period of exactly 5 hours.

By a nice coincidence, today the Earth happens to be at the point in its orbit which is closest to this distant binary star.

Measurements made last night indicate that the next set of eclipses will occur at these times:

```

1:37    6:37    11:37   16:37   21:37  ....

```

And ... they do occur at these times. Good!

But over the course of several months, the Earth will move around the Sun in its orbit. About two months later, the Earth will be located here:

When we observe the binary star from this location, we see that the eclipses are occurring a little bit later than predicted:

```

predicted:  1:37    6:37    11:37   16:37   21:37  ....

observed:   1:42    6:42    11:42   16:42   21:42  ....

```
```

Q:  Why are the eclipses not happening at the
predicted time?

```

So, if one monitors a celestial source over the course of one year, one will see small variations in the time of (what should be) regular events.

```
Q:  Will one always see these variations,
for all sources in the sky?
```

The small variations accumulate over the course of an entire year to impressive amounts: the time it takes light to travel across the distance of the Earth's orbit, from one side of the Sun to the other, is ...

```
Q:  How long does it take light to travel
across the diameter of the Earth's orbit?
```

In order to avoid variations in the timing of celestial events due to the Earth's motion around the Sun, astronomers sometimes use a time system called barycentric or "heliocentric". Basically, one calculates when the event would have been seen by an observing sitting at the position of the Sun, and thus avoids the extra time required for the signal to reach the Earth in its orbit.

• "heliocentric" means "the time measured by an observer sitting at the center of the Sun
• "barycentric" means "the time measured by an observer sitting at the center of mass of the Solar System"

Because the Sun doesn't sit perfectly still, but does move in a very small orbit due to the gravitational pull of the planets (mostly Jupiter), the best choice is barycentric. The official abbreviation is TDB, which stands for Barycentric Dynamical Time.

Using barycentric time is not always necessary. It does appear frequently in the timing of eclipses of binary stars: scientists searching for changes of just a few seconds in the period of a binary star's orbit (which may reveal properties of the interior stellar structure) must avoid any systematic errors which are minutes in size.

#### Julian Date

Can you answer the following questions?
• How many days between 2012 March 1 and 2012 March 7?
• How many days between 2012 Jan 1 and 2012 March 7?
• How many days between 2011 Jan 1 and 2012 March 7?
• How many days between 1911 Jan 1 and 2012 March 7?
• How many days between 1711 Jan 1 and 2012 March 7?

The first few are easy, but as one considers longer and longer stretches of time, another complication appears: leap days.

Leap days are extra days inserted into the modern calendar as February 29. We need these extra days to keep the calendar in sync with the Sun. The problem is that the Earth takes about 365 and a quarter days to orbit the Sun. If we simply count 365 days as one year, then the calendar will start running ahead of the Sun: the shortest day of the year might be Dec 21 in 2005, but then Dec 22 in 2009, Dec 23 in 2013, and so on. After a century, the shortest day of the year would move to roughly January 15!

Therefore, we insert one extra day roughly every four years. Actually, the rule is

• if year is not divisible by 4, it is not a leap year
• if year IS divisible by 4, then
• if divisible by 400, IS leap year, else
• if divisible by 100, IS NOT leap year, else
• IS leap year

Astronomers quickly tired of the extra work required to count the number of days between any two given calendar dates. Back in the sixteenth century, Joseph Scaliger devised a scheme to make the calculations easier: he picked a particular date, long, long ago (see references below for his choice), and started counting days from that point forward. His starting point was:

• 4713 BC January 1

Scaliger named his system after his father, Julius Caesar Scaliger. We call dates in this system Julian Dates, or JD for short.

There are many calculators on the web for converting to and from Julian Date.

Now (2012 March 13 at 9:20 AM Eastern Daylight Time) is Julian Date 2,456,000.0555. It gets a bit awkward to keep typing all those digits, and hard to keep track of them all, so astronomers frequently subtract away a big round number. For example,

```

JD  2453437.2778    turns into   437.2778    (for JD - 2,453,000)

```

This sort of modification is handy when plotting light curves of variable stars, since otherwise the labels on the time axis can be so long that they run into each other.

If you ever decide to cut off a portion of the long JD number, please be explicit about exactly what you are subtracting.

#### Local Sidereal Time

Finally, there is one time system which is designed specifically for observers out in the field. Local Sidereal Time (or LST for short), like civil time or Universal Time, is based on the Earth's rotation; but, unlike them, it does not account for the Earth's orbital motion around the Sun.

The Earth takes about 23 hours and 56 minutes to rotate once around its axis. That means that if you go outside and watch the motion of one particular star, there will be 23 hours and 56 minutes between successive star-rises or successive star-sets. Because the Earth moves a small distance around the Sun its orbit, the Sun takes an additional 4 minutes to "catch up" to the Earth: there are 24 hours between successive sunrises or successive sunsets. This introduces a gradual shift in the positions of stars from night to night (click on the image to see the nightly shift over the course of one week).

The shift is obvious if we skip ahead by 30 days at a time. You've undoubtedly noticed that stars visible early in the evening during one month aren't visible at the same time several months later.

Local Sidereal Time (LST) treats the stars in your sky like a big clock: the LST is equal to the Right Ascension of the stars which are currently overhead (or as high in the sky as they get). Tonight, for example, at 10:00 PM, the sky will look like this:

Note that Procyon, at RA = 07:39, is slightly to the west of the meridian (the line running North-South through overhead); that means that the LST is later than 07:39. On the other hand, Dubhe, at RA = 11:03, is still rising up from the East, so the LST must be earlier than 11:03.

Let's focus on the stars in the southern part of the sky tonight. What is the LST when the sky looks like this?

One hour later, the sky looks like this. What is the LST now?

One hour later, the sky looks like this. What is the LST now?

#### Homework

1. What is the Local Sideral Time tonight at 11:00 PM EDT? Provide your answer to within one minute.
2. The first manned spaceflight occurred on April 12, 1961.
• What was the most recent manned flight into space? Who was aboard this flight?
• How many days between the first and most recent flights?
(Hint: consider using Julian Dates ....)