125 SYSTEMS: MOTION CONTROL SYSTEM—NAVIGATOR OF THE HEAVENS CHAPTER 7 ISS orbit. The angle between the sun vector and the ISS orbit noon vector, shown in Figure 7, is known as the beta angle (β). The beta angle varies between +75 degrees (low to the left of the ISS when flying in LVLH), 0 degrees (directly overhead), and -75 degrees (low to the right of the ISS). The exact beta angle is dependent on where the Earth is in orbit around the sun (the sun is over the northern hemisphere in June and over the southern hemisphere in December), and the orientation of the ISS orbit about the Earth (which shifts westward a few degrees per day due to the bulged center of the Earth). The beta angle slowly swings between negative and positive extremes over the course of several months, by a few degrees per day. The most visible effect of beta angle on the ISS is that of the secondary gimbals on the ISS solar arrays, also known as the beta gimbals. These gimbals are used to turn the arrays to the left or right when the sun is lower in the sky (see Figure 8, Chapter 9). A reference frame called X-Perpendicular Out of Plane (XPOP) was used for attitude control in the early parts of the ISS assembly, before the full complement of solar arrays and gimbals were installed. See Figure 8. XPOP is a reference frame that is the equivalent of LVLH with a 90-degree yaw, but only at orbit noon. The frame stays essentially fixed in inertial space, meaning it doesn’t rotate as the ISS goes around the Earth, as does LVLH. XPOP was designed to point the ISS toward the sun, which was useful at higher beta angles when the arrays could be placed only in limited positions. How the International Space Station knows its Position: Orbit Determination The orbit of the ISS can be described by a vector consisting of six elements: three elements for position relative to the Earth (X, Y, and Z) as described previously and shown in Figure 4, and a corresponding three elements to describe velocity in each of those axes. That vector is known as a state vector, and is used by the ISS to know its location in space so that it can, for example, properly point antennas at data relay satellites and solar panels at the sun. The state vector is also used by Mission Control to know where to target cargo vehicles. In fact, if one uses personal-computer-based tracking software at home to track the location of the ISS and determine when the space station may be visible, that software is downloading an up-to-date ISS state vector from the internet. Once the position and velocity are known at a given time, mathematical equations can be used to calculate the position at a future time. This is accomplished through a computer process called propagation however, the more days a state vector is propagated forward, the more error appears in the result. Because of this, the state vector on the ISS as well as on the ground needs to be updated with sensor-based position determination to correct and update the mathematical propagations. Figure 9. GPS antenna, one of four.The GPS antennas were designed to be replaceable by spacewalking astronauts. In this image, a technician fit checks an antenna while wearing spacesuit gloves to verify the design. Orbit position and velocity determinations can be made in a variety of ways for the ISS. The US Segment has a pair of GPS receivers along with an array of four GPS