Local Time (LT)

This is the time on our watch, designed for convenience. Most countries make an hour correction twice a year (daylight saving) to make the daylight hours fit in with sunrise and sunset. As one travels around the Earth, the local time in each country is designed to ensure that the daylight hours and the Sun’s position are aligned.

Universal Time (UT)

Perhaps the most common time system used by amateur astronomers is Universal Time. This is the local time on the north-south Meridian, which passes through Greenwich, London. It has a number of different names, including Greenwich Mean Time (GMT), Zulu Time and Coordinated Universal Time (UTC). It is synchronized with the Earth’s rotation and orbit and is accurate enough for practical purposes. Each night at a given time, however, a star’s position will change. This is attributable to the 4-minute time difference between a 24-hour day and a sidereal day.

Atomic Time

Time systems based on astronomical events are ultimately flawed. The most stable time systems are those based on atomic clocks; over the course of a decade, small changes in the Earth’s rotational speed add up. Atomic clocks use the ultra stable property of Cesium or Rubidium electronic transitions. If one uses Global Positioning Satellite (GPS) signals to locate and set your time, one is also benefitting from the stability of atomic clocks.

Barycentric or Heliocentric systems

Rather than use the Earth as a reference, this time system uses the Sun as the reference point for observation. This removes the sub-second errors incurred by the change in Earth’s orbit between measurements. One use of this system is for the timing of eclipsing binary stars.

Local Sidereal Time

Local sidereal time is a system designed for use by astronomers. It is based on the Earth’s rotation and does not account for its orbit around the Sun. Its “day” is 23 hours, 56 minutes and 4.1 seconds and allows one to form an accurate star clock. If you look at the night sky at a given LST each night, the stars appear in the same position. It is the basis of the Equatorial Coordinate system described later on.

Julian Dates (JD)

Julian dates are a day-number system that allows users to calculate the elapsed time between two dates. The formula converts dates into an integer that allows one to quickly work out the interval. For example, the 22nd January 2013 is JD 2456315. (A similar idea is used by spread-sheet programs to encode dates.) An example of an on-line calculator can be found at: htt­p:/­/aa­.us­no.­nav­y.m­il/­faq­/in­dex­.ph­p

Epoch

An epoch is a moment in time used as a reference point for a time-changing attribute, for instance, the coordinate of a star. Astrometric data often references the epoch of the measurement or coordinate system. One common instance, often as a check-box in planetarium and telescope control software, is the choice between J2000 and JNow, that is the coordinate system as defined in 2000 AD and today. As the years progress, the difference and selection will become more significant. In many cases, the underlying software translates coordinates between epochs and is transparent to the practical user.

Horizontal Coordinates

There are several fundamental coordinate systems, each with a unique frame of reference. Perhaps the most well known is that which uses the astronomer’s time and position on earth, with a localized horizon and the zenith directly above. The position of an object is measured with a bearing from north (azimuth) and its elevation (altitude) from the horizon, as shown in fig.2. This system is embodied in altazimuth telescope mounts, which are the astronomy equivalent of a pan and tilt tripod head, also abbreviated to “alt-az mounts”.

There are pros and cons with all coordinate systems; in the case of horizontal coordinates, it is very easy to judge the position of an object in the night sky but this information is only relevant to a singular location and time. In the image-planning stage, horizontal coordinates, say from a planetarium program, are an easily understood reference for determining the rough position of the subject, if it crosses the north-south divide (meridian) and if it moves too close to the horizon during an imaging session.

Equatorial Coordinates

Unlike horizontal coordinates, a star’s position, as defined by equatorial coordinates, is a constant for any place and time on the Earth’s surface. (Well, as constant as it can be in the context of star’s relative motion and Earth’s motion within its galaxy.) For a given epoch, planetarium programs or the handset with a programmable telescope mount will store the equatorial coordinates for many thousands of stars. It is a simple matter with the additional information of local time and location on the Earth for a computer to convert any star’s position into horizontal coordinates or display on a computer screen.

fig. 2 This schematic shows the normal horizontal coordinate scheme, with local horizon and true north references. The zenith is directly overhead. Celestial coordinates in this system are only relevant to your precise location and time.

fig. 3 This schematic shows the equatorial coordinate scheme, with celestial horizon and celestial pole references. Celestial coordinates in this system relate to the Earth and can be shared with users in other locations and at other times. Right ascension is measured counter-clockwise; a full circle is just less than 24 hours.

Equatorial coordinates are a little hard to explain, but as with horizontal coordinates, they have two reference points. The first reference point is the North Celestial Pole, as shown in fig.3, located on the imaginary line of the Earth’s axis of rotation. A star’s declination is the angular measure from the celestial equator. For instance, the polestar (Polaris) is very close to the North Celestial Pole and has a declination of 89.5°. If one observes the stars from the North Pole, one would see a fixed set of stars endlessly going around in a circle and parallel to your local horizon. In this special case a star’s declination is equal to its altitude.

The second reference point lies on the celestial equator, from which the stars bearing is measured in hours, minutes and seconds (for historical reasons) rather than degrees. Unlike the azimuth value in horizontal coordinates, which is measured clockwise from true north, the star’s bearing (right ascension) is measured counter-clockwise from the zero-hour reference point. This reference point is explained in fig.4 and corresponds to a special event, on the occasion of the Spring Equinox, where the Sun, moving along the ecliptic, crosses the celestial equator. (The ecliptic can conversely be thought of as the plane of the Earth’s rotation as it orbits the the Sun. It moves with the seasons and is higher in the sky during the summer and lower in the winter.)

fig. 4 This schematic expands on that in fig.3. It shows how the celestial horizon and the observer’s horizon can be inclined to one another. In one direction the observer can view objects beneath the celestial equator. The ecliptic is shown crossing the celestial equator at the Vernal Equinox, defining 0 hour’s right ascension reference point.

From an observer’s standpoint, say at the latitude of the UK or north America, the North Celestial Pole is not at the zenith but some 30–40° away, and the stars wheel around, with many appearing and disappearing across the observer’s horizon. (The North Celestial Pole is directly above the North Pole and hence Polaris has been used as a night-time compass for thousands of years.)

The equatorial coordinate system is quite confusing for an observer unless they are equipped with an aligned telescope to the NCP; unlike horizontal coordinates, the right ascension for any given direction is continually changing. Even at the same time each night, the right ascension changes by 4 minutes, the difference between a day measured in universal and sidereal time. (If you look very closely at the right ascension scale of a telescope, fig.5, you will notice a small anomaly, accounting for the time difference, between 23 and 0 hours.) Unlike the horizontal coordinate system, an astronomer armed with just a compass and equatorial coordinates would be unable to locate the general direction of an object.

The beauty, however, of the equatorial system is that any star has a fixed declination and right ascension and an equatorial mounted and aligned telescope only needs to rotate counter-clockwise on its right ascension axis in order to follow the star as the Earth spins on its axis. In addition, since all the stars move together along this axis, an image taken with an aligned system does not require a camera rotator to resolve every star as a pinprick of light.

Equatorial coordinates are not a constant, however, even if one discounts star movements: a comparison of the readouts of a star position for successive years show a small change, due to the Earth’s precession mentioned earlier, and serves as a reminder that the absolute position of a star requires its coordinates and epoch. In practice, the alignment routine of a computerized telescope mount or as part of the imaging software soon identify the initial offset and make adjustments to their pointing model. Linked planetarium programs accomplish the same correction through a “synch” command that correlates the theoretical and actual target and compensates for the manual adjustment.

Galactic Coordinates

Galactic coordinates are used for scientific purposes and remove the effect of the Earth’s orbit by using a Sun-centered system, with a reference line pointing towards the center of the Milky Way. By removing the effect of Earth’s orbit, this system improves the accuracy of measurements within our galaxy.

Ecliptic, Meridian and Celestial Equator

There are a couple of other terms that are worth explaining since they come up regularly in astronomy and astrophotography. The ecliptic is the apparent path of the Sun across the sky, essentially the plane of our solar system. The planets follow this path closely too and planetarium programs have a view option to display the ecliptic as an arc across the sky chart. It is a useful aid to locate planets and plan the best time to image them.

The meridian is an imaginary north-south divide that passes through the North Celestial Pole, the zenith and the north and south points on the observer’s horizon. This has a special significance for astrophotographers since with many telescope mounts, as a star passes across the meridian, the telescope mount has to stop tracking and perform a “meridian flip”. (This flips the telescope end-to-end and side-to-side on the mount so that it can continue to track the star without the telescope colliding with the mount’s support. At the same time, the image turns upside down and any guiding software has to change its polarity too.) During the planning stage it is useful to display the meridian on the planetarium chart and check to see if your object is going to cross the meridian during your imaging session so that you can intervene at the right time, perform a meridian flip and reset the exposures and guiding to continue with the exposure sequence.

fig. 5 This close up shows the right ascension scale from an equatorial telescope mount. Each tick-mark is 10 minutes and upon closer inspection one notices that the tick mark, labelled A is slightly closer to 0 than the one labelled B. This accounts for the fact that the right ascension scale is based on sidereal time, whose day is about 4 minutes short of the normal 24 hours in universal time.

The celestial equator has been mentioned briefly before in the discussion on equatorial coordinates. The plane of the celestial equator and our Earth’s equator are the same, just as the North Celestial Pole is directly above the North Pole. The effect of precession, however, means that as the tilt of the Earth’s axis changes, so does the projection of the celestial equator and the stars will appear to shift in relation to this reference plane.

Degrees, Minutes and Seconds

Most software accepts and outputs angular measures for longitude and latitude, arc measurements and declination. This may be in decimal degrees (DDD. DDD) or in degrees, minutes and seconds. I have encountered several formats for entering data and it is worthwhile to check the format being assumed. Common formats might be DDDMMSS, DDD° MM’ SS” or DDD:MM:SS.

In each case a minute is 1/60^th degree and a second is 1/60^th of a minute. In astrophotography the resolution of an image or sensor (the arc subtended by one pixel) is measured in arc seconds per pixel and the tracking error of a telescope may be similarly measured in arc seconds. For instance, a typical tracking error over 10 minutes, without guiding, may be ± 15 arc seconds but a sensor will have a much finer resolution of 1 to 2 arc seconds per pixel.

Light-Years

Light-years are a common measure of stellar distances and as the name suggests, is the distance travelled by light in one year, approximately 9 × 10¹⁵ meters. Conversely, when we know the distance of some cosmic event, such as a supernova explosion, we also know how long ago it occurred. Distances in light-years use the symbol “ly”.

Astronomical Unit

The astronomical unit or AU for short is also used. An AU is the mean Earth-Sun distance at about 150 × 10⁹ meters. It is most useful when used in the context of the measurement of stellar distances in parsecs.

Parsecs

A distance in parsecs is determined by the change in a star’s angular position from two positions 1 AU apart. It is a convenient practical measure used by astronomers. In practice, a star’s position is measured twice, 6 months apart. A star 1 parsec away would appear to shift by 1 arc second. It has a value of approximately 3.3 light-years. The parsec symbol is “pc”. The further the star’s distance, the smaller the shift in position. The Hipparcos satellite has sufficient resolution to determine stars up to 1,000 pc away.

All these measures of large distances require magnitude uplifts; hence kiloparsec, megaparsec, gigaparsec and the same for light-years.

Cosmic Distance Ladders

I have always wondered how some of the mind-numbing distances are determined with any certainty. The answer lies in a technique that uses cosmic distance ladders. Astronomers can only directly measure objects close to Earth (in cosmic terms). Using a succession of techniques, more distant objects can be estimated by their emission spectra, light intensity and statistics.

In these techniques, the red-shift of a distant star’s spectrum indicates its speed and hence distance from Earth using the Hubble Constant equation, whereas closer to home, the period and brightness of a variable star is a good indicator of its distance. These techniques overlap in distance terms and allow one to multiply up the shorter measures to reach the far-flung galaxies.

fig.6 Some example distances in alternative units; kilometers, astronomical units, light-years and parsecs. Note the vast range of distances favors different practical units. Parsec distances over 1,000 pc cannot be measured in the classical way from two observations.