Coordinate Systems

• To describe the motion of objects in space, we use various coordinate systems that define the position and orientation of the object relative to a reference frame.

• One of the most common frames is the Earth-Centered Inertial (ECI) frame, which is fixed with respect to the stars and does not rotate with the Earth.

• Geocentric Equatorial Coordinate System (IJK) is a coordinate system in ECI frame; which uses specifically defined cartesian axes to describe the position of objects in space.

• Often, Geocentric Equatorial Coordinate System is used interchangeably with Earth-Centered Inertial (ECI) frame.

Geocentric Equatorial Coordinate System (IJK)

• This is a right-handed Cartesian coordinate system with the origin at the center of the Earth.

• The X-axis points towards the vernal equinox (the point where the Sun crosses the celestial equator from south to north). As shown in Figure 4.1, the vernal equinox direction is along the intersection of the equatorial plane and the ecliptic plane.

• The Vernal Equinox direction is fixed at a specific epoch. For example, the J2000 epoch is a standard epoch used in astrodynamics, which corresponds to January 1st, 2000, at 12:00 TT (Terrestrial Time). In short, the X-axis direction is “frozen” at the direction in which the vernal equinox would be if the Earth’s orientation at that epoch is considered.

Figure 4.1: Vernal Equinox Direction

• The Z-axis points towards the North pole of the Earth’s rotational axis.
• The Y-axis completes the right-handed system, pointing towards the East (orthogonal to X and Z axes).

Figure 4.2: Geocentric Equatorial Coordinate system (IJK)