  CHAPTER 24, Inc., MADISON, WI
SBE 24 GeoSat Pt3

## GEOSTATIONARY ORBITS PART 3:POINTING ANGLES

by Neal McLain, CSBE

In Part 2, we noted that, for communications purposes, the geostationary orbit offers two significant advantages over any other orbit:

• The satellite remains above the horizon, and therefore visible, at all times.

• The satellite remains at a fixed point in the sky at all times.

These advantages allow us to use fixed antennas. However, to do this, we need accomplish two things: • We need to know exactly where that fixed point is. In other words, we need to know the position of the satellite in the sky, as it appears from the antenna. This position is defined in terms of angles known as pointing angles.

• We need a mechanism to support the antenna so that it is aimed at the correct pointing angles. This mechanism is called the antenna mount, or simply the mount.

### POINTING ANGLES

The position of a geostationary satellite is specified in terms of angles known as pointing angles. There are two systems for measuring pointing angles:

EL/AZ. This system uses pointing angles known as azimuth and elevation.

Polar. This system uses pointing angles known as hour angle and declination.

We will define each of these terms in sequence, using the definitions commonly accepted in the satellite communications industry. These definitions do not necessarily agree with the definitions used in the fields of astronomy, navigation, or land surveying.

### AZIMUTH and ELEVATION

By definition:

Azimuth is the angle, in degrees, measured along the horizon, between true north and the point on the horizon directly beneath the satellite. Azimuth is always measured clockwise from true north, and it is always a positive number.

Elevation is the angle, measured along a vertical line, between the horizon and the satellite. Theoretically, elevation can be either a positive or a negative number; however, satellites with negative elevations are below the horizon, and hence, are invisible.
We can plot these angles as lines on the "two big arches in the sky" we discussed in Part 2: In this figure:

Scale A shows the range of azimuths occupied by the Clarke Belt when viewed from the Northern Hemisphere (43° North Latitude), looking south. Since north is defined to be at 0°, south always falls at azimuth 180°.

Scale B shows the range of azimuths occupied by the Clarke Belt when viewed from the Southern Hemisphere (43° South Latitude), looking north. Note that the definition of azimuth holds worldwide: 0° azimuth is always true north, even in the Southern Hemisphere.

Elevation is the vertical axis; it is calibrated in degrees above or below the horizon. Angles above the horizon are positive; angles below the horizon are negative. Satellites with negative elevations are, of course, not visible to an observer. Note that elevation is always measured along a vertical line; i.e., a line which is perpendicular to the horizon. The concepts of azimuth and elevation were borrowed from the field of astronomy. In astronomy:

Azimuth is used to specify the position of an astronomical object, measured clockwise along the horizon from a specified reference point. North is generally used as the zero reference point, although some authors define south as the zero reference.

Elevation is called "altitude" in astronomy, but it means the same thing: the angle to an astronomical object above the horizon, measured along a line which is perpendicular to the horizon.

### HOUR ANGLE and DECLINATION

By definition:

Hour angle is the angle, in degrees, measured along the Celestial Equator, between two points: the point on the Celestial Equator nearest the satellite, and the peak point in the Celestial Equator. Angles to the right are positive, and angles to the left are negative.

Declination is the angle, in degrees, between the Celestial Equator and a satellite, measured along a line which is perpendicular to the Celestial Equator. Declination is always:
NEGATIVE for antenna sites located in the Northern Hemisphere (why?).
POSITIVE for antenna sites located in the Southern Hemisphere (why?).
ZERO for antenna sites located on the Equator.
Again, we can plot these angles as lines on the "two big arches in the sky" we discussed in Part 2: This is our familiar view of the sky, as seen from 43° latitude. The axes are azimuth and elevation.

The hour angle to any given satellite is the angle between the following points on the Celestial Equator:

Point S: The point on the Celestial Equator nearest the satellite. In mathematical terminology, we would call this point the projection of the satellite on the Celestial Equator.

Point P: The peak point of the Celestial Equator. This point lies directly south of an antenna located in the Northern Hemisphere, and directly north of an antenna located in the Southern Hemisphere.
Hour Angle is analogous to azimuth in that both terms define the position of a satellite east or west of some specified reference point. But there are three significant differences:
• Azimuth is measured along the horizon; hour angle is measured along the Celestial Equator.

• 0° azimuth is always north; 0° hour angle is always toward the equator.

• Azimuth is always a positive number; hour angle can be either positive or negative.
In the figure above, the declination angle to any given satellite is the angle between the satellite and the nearest point on the Celestial Equator. This angle is shown as a line between the satellite and Point S on the Celestial Equator, perpendicular to the Celestial Equator.

Declination is analogous to elevation in that both terms specify the position of a satellite above or below some specified reference point. But there are three significant differences:
• Elevation is perpendicular to the horizon; declination is perpendicular to the Celestial Equator.

• 0° elevation is the horizon; 0° declination is the Celestial Equator.

• Elevation is positive if the satellite is above the horizon (and negative if it's below); declination is positive if the antenna is located in the Southern Hemisphere (and negative in the Northern Hemisphere).
The concepts of hour angle and declination were borrowed from the field of astronomy. In astronomy:

• Hour angle has a similar meaning. However, things are a lot more complicated in astronomy, because, unlike geostationary satellites, astronomical objects are in constant motion: they rise in the east and set in the west. Thus, the hour angle to any given object changes continuously, depending on the time and date. This, of course, accounts for the name "hour" angle.

• Declination is used to specify the position of an astronomical object, in degrees, north or south of the Celestial Equator. Angles to objects north of the equator are positive; angles to objects south of the equator are negative.

### SATELLITE ANTENNA MOUNTS

Antenna mount is the name given to the mechanism which supports a ground-based satellite antenna. Ideally, the mount must allow the antenna to be adjusted precisely to the specified pointing angles, and it must hold the antenna securely in that position.

In Part 4, we'll discuss antenna mounts in detail.

CONTINUE TO PART 4 - ANTENNA MOUNTS
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