# Chapter 2: Reference Systems

### The Celestial Sphere

A useful construct for describing locations of objects in the sky is the celestial sphere, which is considered to have an infinite radius.

The center of the Earth is the center of the celestial sphere, and the sphere's pole and equatorial plane are coincident with those of the Earth. See the illustration of the Celestial Sphere.

We can specify precise location of objects on the celestial sphere by giving the celestial equivalent of their latitudes and longitudes.

The point on the celestial sphere directly overhead for an observer is the zenith. An imaginary arc passing through the celestial poles and through the zenith is called the observer's meridian.

The nadir is the direction opposite the zenith: for example, straight down from a spacecraft to the center of the planet.

### Declination and Right Ascension

Declination (DEC) is the celestial sphere's equivalent of latitude and it is expressed in degrees, as is latitude. For DEC, + and - refer to north and south, respectively. The celestial equator is 0° DEC, and the poles are +90° and -90°.

Right ascension (RA) is the celestial equivalent of longitude. RA can be expressed in degrees, but it is more common to specify it in hours, minutes, and seconds of time: the sky appears to turn 360° in 24 hours, or 15° in one hour. So an hour of RA equals 15° of sky rotation.

Another important feature intersecting the celestial sphere is the ecliptic plane. This is the plane in which the Earth orbits the Sun, 23.4° from the celestial equator. The great circle marking the intersection of the ecliptic plane on the celestial sphere is where the Sun and planets appear to travel, and it's where the Sun and Moon converge during their eclipses (hence the name).

The zero point for RA is one of the points where the ecliptic circle intersects the celestial equator circle. It's defined to be the point where the Sun crosses into the northern hemisphere beginning spring: the vernal equinox, also known as the first point of Aries, often identified by the symbol of the ram.

### The Equinoxes

The equinoxes are times at which the center of the Sun is directly above the equator, marking the beginning of spring and autumn. The day and night would be of equal length at that time, if the Sun were a point and not a disc, and if there were no atmospheric refraction. Given the apparent disc of the Sun, and the refraction, day and night actually become equal at a point within a few days of each equinox.

The RA and DEC of an object specify its position uniquely on the celestial sphere just as the latitude and longitude do for an object on the Earth's surface. For example, the very bright star Sirius has celestial coordinates 6 hr 45 min RA and -16° 43' DEC.

### The International Celestial Reference System

The International Celestial Reference System (ICRS) is the fundamental celestial reference system that has been adopted by the International Astronomical Union (IAU) for high-precision positional astronomy. The ICRS, with its origin at the solar system barycenter and "space fixed" axis directions, is meant to represent the most appropriate coordinate system for positions and motions of celestial objects. RA and DEC measurements can be transformed to the ICRS sytem, which is compatible with the J2000.0-based system. The reference frame created by the ICRS is called the International Celestial Reference Frame, or ICRF.

### HA-DEC versus AZ-EL Radio Telescopes

The discussion gets a little more involved here, but this section serves only to explain the old design for Deep Space Network antennas, as well as large optical and radio telescopes, and why it all changed not too long ago.

Before you can use RA and DEC to point to an object in the sky, you have to know where the RA is at present for your location, since the Earth's rotation continuously moves the fixed stars (and their RA) with respect to your horizon. If the RA of the object happens to place it overhead on your meridian, you're fine. But it probably isn't, so you determine the object's hour angle (HA), which is the distance in hours, minutes, and seconds westward along the celestial equator from the observer's meridian to the object's RA. In effect, HA represents the RA for a particular location and time of day. HA is zero when the object is on your meridian.

Older radio telescopes were designed with one mechanical axis parallel to Earth's axis. To track an interplanetary spacecraft, the telescope would point to the spacecraft's known HA and DEC, and then for the rest of the tracking period it would simply rotate in HA about the tilted axis (called its polar axis), as the Earth turns. This kind of mounting is traditionally called an equatorial mount when used for optical telescopes. It's a fine mount for a small instrument, but unsuited to very heavy structures because the tilted polar bearing has to sustain large asymmetric loads. These loads include not only the whole reflector dish, but also an HA counterweight heavy enough to balance the antenna, the DEC bearing, and its DEC counterweight! Also the structure has to be designed specifically for its location, since the polar bearing's angle depends on the station's latitude. This image shows the first Deep Space Network (DSN) antenna installed at the Canberra, Australia site, looking down along the polar bearing, which is the axis of the antenna's large central wheel. This HA-DEC antenna is no longer in service, nor is its sister at the DSN site at Madrid, Spain. Its counterpart at the Goldstone, California site has been converted to a radio telescope dedicated to educational use.

A simpler system was needed for larger Deep Space Network antennas. The solution is an azimuth-elevation configuration. The design permits mechanical loads to be symmetric, resulting in less cumbersome, less expensive hardware that is easier to maintain. It locates a point in the sky by elevation (EL) in degrees above the horizon, and azimuth (AZ) in degrees clockwise (eastward) from true north. These coordinates are derived from published RA and DEC by computer programs. This computerization was the key that permitted the complex mechanical structures to be simplified.

In an AZ-EL system anywhere on Earth, east is 90 degrees AZ, and halfway up in EL or altitude (ALT) would be 45 degrees. AZ-EL and ALT-AZ are simply different names for the same reference system, ALTitude being the same measurement as ELevation.

The DSN antenna at Goldstone has a 70-meter aperture, over twice that of the Australian HA-DEC antenna shown above. The whole structure rotates in AZ clockwise or counterclockwise atop the large cylindrical concrete pedestal. It is pointing generally east in the image (around 90° azimuth), probably beginning to track a distant spacecraft as it rises over the desert horizon. All newly designed radio telescopes use the AZ-EL system.

### Then There's X-Y

To complete our survey of mounting schemes for DSN antennas (including steerable non-DSN radio telescopes as well), we need to describe the X-Y mount. Like AZ-EL, the X-Y mount also has two perpendicular axes. By examining the image of DSS16 here you can see that it cannot, however, directly swivel in azimuth as can the AZ-EL (ALT-AZ) -mounted antenna. But the X-Y mount has advantages over AZ-EL.

Its first advantage is that it can rotate freely in any direction from its upward-looking zenith central position without any cable wrap-up issues anywhere within its view.

The other advantage is a matter of keyholes. A keyhole is an area in the sky where an antenna cannot track a spacecraft. Imagine an AZ-EL antenna like the 70-m DSS in the section above. If a spacecraft were to pass directly overhead, the AZ-EL antenna would rise in elevation until it reached its straight-up maximum near 90°. But then the antenna would have to whip around rapidly in azimuth as the spacecraft is first on the east side of the antenna, and then a moment later is on the west. The antennas' slew rate isn't fast enough to track that way, so there would be an interruption in tracking until acquiring on the other side. (AZ-EL antennas in the DSN aren't designed to bend over backwards, or "plunge" in elevation.)

For an HA-DEC antenna, the keyhole is large and, in the northern hemisphere, is centered near the North Star. To track through that area the antenna would have to whip around prohibitively fast in hour angle.

The X-Y antenna is mechanically similar to the old HA-DEC antenna, but with its "polar" axis laid down horizontally, and not necessarily aligned to a cardinal direction. The X-Y antenna is situated so that its keyholes (two of them) are at the eastern and western horizon. This leaves the whole sky open for tracking spacecraft without needing impossibly high angular rates around either axis... it can bend over backwards and every which way. The X-Y's were first built for tracking Earth-orbiting spacecraft that require high angular rates and overhead passes. Earth-orbiters usually have an inclination that avoids the east and west keyholes, as well. Interplanetary spacecraft typically do not pass overhead, but rather stay near the ecliptic plane in most cases. Of course X-Y's can be used with interplanetary spacecraft also, but in the DSN they are only equipped with a 26-m aperture, smaller than most other DSN stations, and thus not useful for most interplanetary craft.

A "keyhole" is an area in the sky where an antenna cannot track a spacecraft because the required angular rates would be too high. Mechanical limitations may also contribute to keyhole size, for example the 70-m antennas are not allowed to track above 88° elevation.

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