Celestial Latitude Galactic Latitude

THE PRESENT SYSTEM OF GALACTIC COORDINATES, ADOPTED IN 1flS8. DEFINES THE NORTH GALACTIC POLE AS BE ING AT o • 182.28°. > • +27.«° AND THE GALACTIC CENTER AS AT a • 2SSj5°. A - -2&9l7a.

THE PRESENT SYSTEM OF GALACTIC COORDINATES, ADOPTED IN 1flS8. DEFINES THE NORTH GALACTIC POLE AS BE ING AT o • 182.28°. > • +27.«° AND THE GALACTIC CENTER AS AT a • 2SSj5°. A - -2&9l7a.

*In addition to the mean motion due to precession, the Earth's true spin axis wobbles with an amplitude of 92 arc seconds (0.0026 deg) and a period of 19 years due to the changing inertial orientation of the Moon's orbit. TOD coordinates are updated to the epoch time using the true processional motion. If the coordinates are updated using the mean precessional motion, they are referred to as Mean of Date, or MOD.

rFor a definition of ascending node and other orbit parameters, see Chapter 3.

known as roll, pitch, and yaw or RPY, and are illustrated in Fig. 2-4. In this system, the yaw axis is directed toward the nadir (i.e., toward the center of the Earth), the pitch axis is directed toward the negative orbit normal, and the roll axis is perpendicular to the other two such that unit vectors along the three axes have the relation R = PxY. Thus, in a circular orbit, the roll axis will be along the velocity vector. The roll, pitch, and yaw angles (£,.£,, and are defined as right-handed rotations about their respective axes. Therefore, for a spacecraft in a circular orbit and an observer on the spacecraft facing in the direction of motion with the Earth below, a positive pitch rotation brings the nose of the spacecraft upward, positive yaw moves it to the right, and positive roll rotates the spacecraft clockwise. The RPY system is most commonly used for Earth-oriented spacecraft. Caution: The preceding definition will be used throughout this book. However, individual spacecraft ordinarily define RPY systems unique to that spacecraft and may even define them as spacecraft-fixed coordinates rather than orbit-defined coordinates. Therefore, when reading other material, it is important to know precisely how roll, pitch, and yaw are being defined.

2.23 Nonspacecraft-Centered Coordinate Systems

For attitude work, the most important coordinate systems are all centered on the spacecraft. However, occasionally the use of nonspacecraft-centered coordinates is convenient, primarily as a means of obtaining reference vectors such as the magnetic field vector or position vectors to objects seen by the spacecraft. Thus, orbit work is ordinarily done in geocentric inertial coordinates, equivalent to the celestial coordinates defined above, except that the center of the coordinate system is at the center of the Earth. The position vector of the Earth in spacecraft-centered celestial coordinates is just the negative of the position vector of the spacecraft in geocentric inertial coordinates. Similarly, the positions of the planets within the solar system are ordinarily calculated in heliocentric coordinates, or coordinates centered on the Sun. Heliocentric longitude and latitude are defined relative to the ecliptic plane and the vernal equinox as references. Selenocentric coordinates are used for spacecraft in lunar orbit and are the same as celestial coordinates except that they are centered on the Moon; that is, the vernal equinox and the celestial equator are used as references.

Fig. 2-4. Roll, Pitch, and Yaw (RPY) Coordinates

In some cases, such as analysis of the Earth's magnetic or gravitational field, we may wish to associate a vector with each point in a spherical coordinate system. To do this it is convenient to define at each point in space an orthogonal coordinate system whose three axes are each parallel to the change in one of the three spherical coordinates, as illustrated in Fig. 2-5. Such systems are called local horizontal coordinates or local tangent coordinates, since the reference plane at any point is always tangent to the sphere centered on the origin of the system and passing through the point in question. If the components of the global spherical coordinate system are r, A, and <f» (the radius, elevation, and azimuth, respectively), then at any point in space, the three reference axes of the local horizontal system are: north axis {N) in the direction of increasing A, east axis (E) in the direction of increasing <j>, and zenith axis (Z) in the direction of increasing r. South (S), west ( W), and nadir (n) are used for the negatives of the three axes. Thus, the names for the axes would correspond to the usual definitions of the four directions, the zenith, and nadir on the surface of a spherical Earth. Within the local horizontal coordinate system, the reference plane is the N-S-E-W plane and the reference direction of 0 azimuth is north. Elevation is used for the angular height above the reference plane (i.e., toward the zenith), and azimuth is used for the rotation angle in the reference plane measured from north toward east.

Fig. 2-5. Local Horizontal Coordinates

22.4 Parallax

Parallax-is the shift in the direction of a nearby object when the observer moves, as illustrated in Fig. 2-6 for the case of the Sun shifting its position relative to the background of the fixed stars. (The amount of parallax for a normal spacecraft orbit is exaggerated in Fig. 2-6.) There is no parallax due to the shift of the center of a coordinate system from one place to another, because the axes are moved parallel to themselves and are defined as maintaining fixed directions in space rather than pointing toward a real object, with the exception of the roll, pitch, yaw coordinates. For example, the pole-to-pole axis of spacecraft-centered celestial coordinates is parallel to the Earth's axis.

In principle, there is a very small parallax because attitude sensors are not mounted precisely at the center of the spacecraft. In practice, this shift is totally negligible. For example, the shift in the position of the Earth's horizon 200 km away for an instrument offset of 1 m is 1 arc sec or 3 X 10~4 deg. Therefore, for attitude-sensing hardware, the orientation of the field of view of the hardware in the spacecraft system is normally important, but the location of the -hardware within the spacecraft is not.

Two types of parallax can be important in some circumstances. Solar parallax is the shift in the direction of the Sun as an Earth satellite moves in its orbit. (This definition differs from that used in Earth-based astronomy.) The amount of shift as the satellite moves the full diameter of its orbit perpendicular to the direction of the Sun (as illustrated in Fig. 2-6) is 0.005 deg in low Earth orbit, 0.032 deg at

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