Decision Aid for Conjunction Risk Mitigation by Differential Drag

In the previous five years, the rate of conjunctions that the NASA Conjunction Assessment Risk Analysis (CARA) team processed and analyzed has more than tripled. (NASA CARA, 2024) New missions in the early development phases are now required to plan for dealing with conjunctions under the present space environment, and also projecting forward into a future likely with even further increased utilization of the space environment. Some missions are investigating the possibility of using differential drag to remediate conjunctions without expending limited fuel or for missions without propulsive capabilities. The NASA CARA team studied the historical record of conjunctions to evaluate the circumstances under which differential drag may be successfully applied and have developed a series of tables to use as a decision aid for missions considering differential drag.

Currently, if a CARA-protected mission with maneuvering capabilities is predicted to have a conjunction with probability of collision (Pc) greater than 7E-5 (the default value of the ‘yellow threshold’, which may have some other value agreed by CARA and the mission during the Orbital Collison Avoidance Planning (OCAP) process), CARA will use its Maneuver Trade Space (MTS) tool to evaluate and recommend options for the timing and magnitude of a risk mitigation maneuver (RMM), based on the mission’s capabilities. If the conjunction’s Pc is greater than 1E-4, the ‘red threshold’, then an RMM must be executed per NASA Procedural Requirements (NPR) 8079.1 (NASA, 2023), although missions may execute an RMM even if the Pc is lower.

The magnitude of the maneuver is typically a few cm/s, and CARA estimates how many will be required for the mission’s nominal lifetime – typically a few per year – during the OCAP process, to inform the mission’s delta-V requirement. For traditional satellites, this is usually smaller than other requirements for orbit insertion, maintenance, and disposal, but for CubeSats or other small satellite missions, a propulsion system may not provide much more than a few cm/s of delta-V or may not fit at all within the available budget of money, time, size, weight, and/or power (SWaP). Conversely, CubeSats often have deployable solar panels, which offer the capacity to have much higher areas facing some directions than others. Such a mission can instead use ‘differential drag’ to remediate a conjunction -- in other words, change its drag area (usually increasing) to deviate from the predicted collision course. This is how Planet’s Dove spacecraft maintain their formations and remediate conjunction risks without having on-board propulsion (Foster, et al., 2017) (Griffith, et al., 2021). CARA has been developing improvements to MTS to support differential-drag for NASA's missions -- where it is effective.

CARA records all conjunctions of their protected payloads, with historical records starting in 2005 (with significant conjunction events starting to occur on or after 2013). From this record, approximately 7,300 had a Pc greater than 1E-4 at 3 days prior to the time of closest approach, the time analyzed for differential drag efficacy. Of those, approximately 4,300 had fully-defined covariance matrices stored for both the primary and secondary objects; this set of conjunctions is the basis for the analysis of this work.

CARA’s MTS tool was used to propagate the primary satellite forward from that decision point with varying degrees of increase to ballistic coefficient (BC). Because these conjunctions came from multiple missions, the nondimensional ‘delta-BC’ factor was used to quantify and normalize the increase in ballistic coefficient, defined as follows:

Delta-BC = BC_new / BC_old - 1

Positive delta-BC factors represent an increase in drag compared to the nominal attitude, while negative delta-BC factors (to a minimum of -1) represent a decrease in drag. At the conclusion of the differential-drag ‘maneuver’, the Pc was recalculated to evaluate whether or not the conjunction was mitigated (Pc < 3E-6). These results were then binned and sorted along several axes, including altitude, amount of delta-BC, and (pre-maneuver) rate of energy dissipation (EDR), to identify underlying patterns. The altitude plot is shown in Figure 1.

To validate this analysis, we consulted the record of a NASA mission which uses differential drag to maintain its orbit and remediate conjunction risk. CARA’s empirical record of the mission’s orbit history suggests it achieves a delta-BC of 2.2. Of the twenty-one RMM plans that were submitted by this mission, eighteen were matched with conjunctions in the historical record; of those, twelve were successfully remediated (final measured Pc < 3E-6), and six were not. This is consistent with the expected efficacy for missions orbiting at that altitude. We are presently simulating this mission’s RMMs with MTS; this work is ongoing, but so far, the MTS results are qualitatively in agreement with the empirical results -- correctly predicting that a maneuver would or would not remediate a conjunction, if not exactly matching the final post-remediation Pc value.

We found that differential drag was most successful for satellites with perigees below 560 km, and which could adopt an average delta-BC of 2 or greater (that is, increasing their ballistic coefficient by a factor of 3). However, this is a difficult threshold for a mission to clear; very few spacecraft are capable of adopting a high-drag configuration for 72 hours continuously. Planet’s Dove spacecraft use differential drag to remediate conjunctions (Griffith, et al., 2021), and they have a maximum delta-BC factor of 9, but in practice (with mission and charging constraints) they achieve a time-averaged delta-BC that is closer to 2 (Foster, et al., 2017). A mission’s differential drag utility strongly depends on the operational constraints that has the capacity to limit the time-averaged delta-BC. A mission with a high maximum delta-BC of 5 or more can have an effective delta-BC of less than 1 due to operational constraints such as instrument and solar panel pointing, especially if this constraint results in holding an intermediate drag value for most of its orbit.

CARA has developed tables that can be used as decision aids to advise missions-in-development about the best way to utilize their differential drag capabilities. For missions below 560 km with the operational flexibility to devote multiple days to holding a high-drag configuration (or a sufficiently high drag ratio to compensate for limitations on that time), they are -- more likely than not -- able to successfully remediate high-risk conjunctions. Conversely, missions that do not meet these exacting criteria -- most missions -- can instead be advised to use on-board propulsion systems to perform RMMs, or to turn their minimum-area face towards the approach vector, thereby reducing Pc at the moment of conjunction due to the decreased Hard-Body Radius (HBR), that is a strongly correlated variable in the Pc calculations. (NASA, 2023)