Abstract

Orbital debris are known to pose a severe threat of damage or destruction to orbital assets such as communications satellites and the International Space Station. It is estimated that there are over 2 million objects in the 3-10 cm diameter size range in Low Earth Orbit (LEO), each with the capability to destroy a satellite. In fact, since 2000, these objects have destroyed 10 satellites totaling 3.2 billion dollars in damage. Most of these objects are byproducts of normal human space activities such as rocket propulsion. The average potential collision speed of one of these objects with an orbital asset exceeds 10 km/s. Although current ground-based radar systems can track objects in LEO with diameters as low as 10 cm, little data exists to determine the flux of debris in the 3-10cm size range in Earth orbit. This study developed a system to provide empirical data for orbital debris flux through an on-orbit solution. Preliminary simulations showed that a beam-break laser array would be the most effective method of debris detection and characterization. This system was then developed to be packaged into the form-factor of a 6U CubeSat to minimize the system’s cost of deployment. Finally, large scale-system analysis was conducted to optimize the satellite constellation size and deployment pattern as well as to characterize the expected data processing resources and concept of operations for such a program. This system will provide much-needed empirical data that will allow orbital assets and astronauts to be much safer as humans venture into space more frequently.

Background

According to NASA, as of 2021, the Space Surveillance Network (SSN) tracked over 27,000 pieces of orbital debris ranging from defunct satellites the size of school buses to captured asteroids the size of a softball (Garcia, 2021). Keeping track of all of these objects is critical to avoid collisions that could exacerbate the issue. In recent years, this task has been made more difficult by the rise of “mega-constellations” which have pushed the number of active orbital objects to over 4,500 (Every Satellite Orbiting Earth, 2021). With so many satellites in orbit, and the number only predicted to grow, there are now more valuable assets than ever in orbit to protect from these risks. Currently, ground-based systems can track debris down to 5cm (NASA - Frequently Asked Questions, n.d.). However, this technology cannot reliably track objects below this size range (Brumbaugh et al., 2012; Fonder et al., 2019). These smaller debris come from a variety of sources including collisions between satellites as well as ejecta from burning rocket propellant (Mehrholz et al., 2002). This size class of objects still pose a significant risk to spacecraft with the average conjunction speed between two objects in orbit being over 10 km/s resulting in an energy release of over 8 million joules (NASA - Frequently Asked Questions, n.d.; Space Debris 101 | The Aerospace Corporation, n.d.). To minimize the risks of such an impact happening for tracked debris, NASA currently has the following guidelines (Garcia, 2021):

If the probability of a collision is greater than 1 in 100000, a course adjustment will be made if there will be no significant impact on mission objectives.

If the probability of a collision is greater than 1 in 10000, a course adjustment will be made if it will not cause further risk to the spacecraft.

However, without accurate detection of debris smaller than 5cm, spacecraft are exposed to potentially mission-ending risk. In addition to active satellites, inaccurate information could even impact satellites that have not even been built yet. When creating the concept of operations and design for a spacecraft, one of the major factors taken into account is the probability of debris impacts (Johnson, 2010). Based on the orbit that a spacecraft will be in, different mitigation strategies can be taken, ranging from simply accepting the risk to installing specialized protection panels, such as those on the International Space Station (Garcia, 2021). Being able to make informed decisions on which methods to use is critical to overall mission success as over-budgeting protection can result in a loss of mission capabilities, whereas underestimating the risk could result in a loss of the spacecraft.

Methods

The main goal of the simulation was to optimize the various parameters of the sensor system. Three major tests were conducted with each test building upon the data from the previous test. The first test that was conducted was chosen in order to charachterize the nescessary performance of the sensing and computational hardware. For this usecase, the limiting factor for data collection is sample rate. The planned depth of they system was 1 meter with a maximum relative velocity to the debris of 15km/s. This meant that the debris object would only be within the detection volume for just 67µs. As such, it was critical to determine how quickly data samples would need to be taken to accurately measure the debris’ trajectory. In order to optimize this parameter, the first set of simulations, henceforth refered to as Experiment 1. In Experiment 1, all variables were held constant except for the time step. The time step represents the time in between each sample, so a higher time step represents a slower sample rate. In Experiment 1, the time step was tested at 7 values (equivalent frequency in parentheses): 5000ns (0.2MHz), 2000ns (0.5MHz), 1000ns (1MHz), 750ns (1.3MHz), 500ns (2MHz), 250ns (4MHz), and 150ns (6.7MHz). To determine how well the sensor was performing in a given configuration, error was calculated by subtracting the true value of a parameter (the radius for example) from the value calculated by the sensor array. For each of the experimental groups, 100 trials were conducted in order to reduce the impact of any ourliers for a total of 700 simulations during Experiment 1 and 2100 individual data points. This data was then recorded to a local file for further analysis. In total, Experiment 1 took 22 hours to complete simulation. Once Experiment 1 was completed, it was determined that the next parameter than needed to be optimized was the plane speration parameter. This experiment, known as Experiment 2, tested two independent variables. The first variable was plane seperation, which was tested at 5cm, 2.5cm, 1cm, and 0.5cm. In addition to this, further data was collected on the impact of sample rate by testing the system across all plane seperations at both 350ns and 150ns time steps. This resulted in a total of 8 experimental groups with 100 trials run for each group and 800 trials total. This resulted in a total of 2400 data points that could them be analyzed. In total, Experiment 2 took 17 hours to complete its simulation. Finally, Experiment 3 was conducted to complete the optimization of the sensor array system by varying the independent variables depth and plane seperation. These variables were chosen because it was observed that the X-axis velocity measurement was performing significantly worse than the Y-axis velocity measuremnt, and thus, needed further tweaking. In order to achieve this goal, the X-axis velocity error was recorded at sensor array depths of 0.1m, 0.2m, and 0.3m. Additionally, the plane seperation was varried at 2.5cm, 1cm, and 0.5cm resulting in 9 experimental groups, each of which consisted of 100 trials for a total of 900 trials. The rsulting 2800 data points were collected during the 20 hours that it took for the simulation to complete.