Issue 53

Over the summer, Jack Anthony will break down each of the six orbital elements required to uniquely identify a specific orbit and satellite in that orbit. This week we examine Right Ascension of the Ascending Node (RAAN). For those who can’t wait the entire summer, please visit Jack’s “Orbit Element Dance” on YouTube, featuring Jack demonstrating this way to learn the six classical orbital elements (COE). Orbit Element Dance.

Jack uses the STP method of remembering the 6 COEs: Size, Shape, Tilt, Twist, Position of Perigee and Position of the Satellite at a particular time. The second “T”, the Twist of the orbit, is Right Ascension of the Ascending Node (RAAN).

The Ascending Node is where the satellite passes through the equatorial plane as it ascends from the south hemisphere to the north. The principal axis of the Earth-Centered Inertial (ECI) coordinate frame is the I or X axis, and that is the reference used to determine RAAN.

The I-axis points toward the Vernal Equinox. It points to a direction fixed relative to the stars rather than a geographic point on Earth. Earth’s axis precession shifts this reference slowly over the centuries.

The other vector needed to determine RAAN is the Node Vector in ECI pointing to the Ascending Node of the orbit. The angle between the I-axis and the Node Vector is RAAN, denoted Ω (large Omega).

RAAN can have values from 0 to 359 degrees. It is the twist or swivel of the orbit plane and is measured eastward from the I-axis using the Right-Hand Rule.

RAAN is relative to the ECI frame. It is not tied to the longitude of the Earth; it is an inertial reference, not a geographic reference.

The article then introduces the Polar Plot used by GEO satellite operators and orbit planners. It combines inclination and RAAN in one display. Inclination and RAAN are both required to define the orbit plane.

Jack’s Polar Plot places inclination on concentric circles, with zero inclination in the center, while RAAN is shown around the plot beginning at the 3 o’clock position and increasing counter-clockwise through 360 degrees.

A worked example uses a GEO refueling satellite, the “Guardian Gas-n-Go,” that must rendezvous and dock with a client satellite. The client is in an orbit with inclination 4 degrees and RAAN 90 degrees, while the refueler begins at inclination 3 degrees and RAAN 135 degrees.

The most fuel-efficient plane match uses one combined burn that increases inclination by 1 degree and rotates RAAN by 45 degrees. The article’s spreadsheet example gives a required Delta-V of 152 m/sec.

If the operator changes only inclination, the article gives 54 m/sec for the first burn but notes the RAAN remains unmatched. A second 164 m/sec burn would then be required to twist the orbit plane, totaling 218 m/sec – 66 m/sec more than the single combined maneuver.

The bottom line is that the orbit plane is defined by Inclination and RAAN. Matching only inclination is inadequate for an orbit-plane match before rendezvous and refueling.

A GPS example shows why: GPS satellites have inclinations of about 55 degrees but occupy many different orbit planes because they have different RAANs.

Finally, the Polar Plot is used to visualize the roughly 54-year inclination/RAAN cycle of uncontrolled GEO satellites. The article describes the resulting “Conga Line” of spacecraft progressing around the plot.

In conclusion, RAAN is the angle between the I-axis of the ECI frame and the Ascending Node vector of the satellite’s orbit. The Polar Plot is a tool for keeping track of the orbit plane. Next time: Argument of Perigee.