By Simone D'Amico and Justin Kruger, September 1st, 2023
Let's get technical in this news post! This is astrodynamics at its best: where we analyze the relative motion of the Starling Satellites Swarm as of August 11th, 2023!
The Space Rendezvous Laboratory (SLAB) has been hard at work preparing for the Starling’s Formation-Flying Optical Experiment (StarFOX) which is currently scheduled to start on 9/9/23 as a payload of the NASA’s Starling 4x 6U CubeSat swarm mission.
As part of the preparation activities, we have been processing GPS telemetry data from each of the swarm satellites downlinked during the Commissioning phase and passing them through the SLAB’s ARTMS flight software (played on the ground). We created the two figures below which display the status of the 4 Starling CubeSats (denoted as SV1, SV2, SV3, and SV4) in a way as compact and insightful as possible.
Figure 1 displays the so-called Relative Orbital Elements (ROE) of SV1, 2, and 3 with respect to SV4, while Figure 2 displays the Empirical Accelerations experienced by SV1 and SV2 in their respective radial-tangential-normal (RTN) coordinate frames over a time frame of one week during the commissioning phase.
From Figure 1 (left). δλ (relative mean longitude) represents the mean along-track separation between the satellites (i.e. mean distance along the orbit path), while δa (relative semi-major axis) represents a mean offset in radial direction (i.e. Zenith). Here, SV2 and SV3 are falling behind SV4 with a nearly constant δa of about 500m. On the contrary, SV1 is experiencing a stark decrease in δa (to -500m) that can be caused by more atmospheric drag experienced than SV4 (e.g. due to a different ballistic coefficient).
From Figure 1 (right). The length of δe (relative eccentricity vector) provides the amplitude of oscillations in the orbit plane, while the length of δi (relative inclination vector) provides the amplitude of oscillations perpendicular to the orbit plane. Here, the majority of the ROEs are fairly steady. However, δe for SV4 displays significant growth. This rapid change may occur during spacecraft orbit maneuvers. The non-spherical gravity field of the Earth also causes changes in δe and δi over much longer periods: δe will observe a periodic rotation and δi will observe gradual vertical drift (these trends are visible in the zoomed portion of the subplot).
From Figure 2. ‘Empirical’ accelerations are the forces and disturbances experienced by a spacecraft which are not accounted for by its nominal force model. SV2, on the right, displays the expected behavior with uniform empirical accelerations with a zero mean. SV1, on the left, shows very different behavior with non-zero mean accelerations, most prominently in the radial direction. Consistent accelerations in the radial and tangential direction can cause drifts in δe, similar to what is seen in the ROE figure. Integrating empirical accelerations over time provides an estimated delta-v of the order of 1 to 2 m/s and mission control can verify this assessment by monitoring of the propulsion system.
Stay tuned for more news on the analyses of the Starling Formation Flying mission!
Simone D'Amico is the founding director of the Stanford Space Rendezvous Lab, while Justin Kruger is a PhD Candidate and the StarFOX Experimental Lead for the Starling Formation Flying mission
