ghg_kessler_capacity

This repo includes scripts and data that are useful for learning how instantaneous Kessler capacity (IKC) is calculated, and to see how projected GHG emissions will reduce capacity in LEO.

Each script should be able to run quickly using the provided data files by default. If key parameters are changed in the scripts, they may take some time to generate a new datafile and produce results. Be careful to ensure that data files are re-computed when changes are made to the processing scripts, otherwise those changes may be neglected.

SCRIPT FILE DESCRIPTIONS

• read_brown_ssp_projections.py: This script reads in the NetCDF file containing the atmospheric mass density forecasts as were computed in Brown et al (2024) and stored here: https://edata.bham.ac.uk/1075/. A projection for F10.7 is generated by fitting a sinusoid to a history of measured F10.7. Density trends for the shared socioeconomic pathways according to the projected F10.7 are created and stored in data/dens_forecast_ssp.mat. The space weather data used in this script comes from data/SW-All.mat, which can be updated by visiting https://celestrak.org/SpaceData/.

• get_tles_for_sat.py: Define a satellite catalog (SATCAT) identifier of interest, and download all of the available TLEs for that satellite from Space-Track.org. This script will prompt the user for their Space-Track.org log-in credentials, and then download the TLEs for the satellite of interest.

• plot_altitude_decay_from_tless.py: This script is used to plot the decay of a tracked object in the NORAD catalog over time. It reads in a history of TLEs, which are processed to compute the time-averaged altitude (as well as perigee and apogee altitudes) of the object over time. The script also plots the mass density of the atmosphere over time and altitude, as computed by MSIS 2.0.

• satellite_deorbit_altitudes.py: This script loads in the density forecast data for the various SSPs and the baseline,then uses these time and altitude-resolved densities to compute the altitude at which an object of interest (with ballisitic coefficient of interest) will deorbit within a desired time frame. Here, we consider 5 and 25-year deorbit timeframes. The baseline case shows changes in the operational altitude for the reference object due to the solar cycle alone, while the SSP cases show the impact of greenhouse gasses on deorbit timelines.

• compute_ikc_with_contraction.py: This script computes the optimal distribution of characteristic satellites across altitude shells of interest that maximizes the number of satellites while preventing long-term debris instability. Equilibrium points are found for each shell according to a 2-species source-sink model. We start at the top shell, then use the number of characteristic satellites in that shell to compute a debris flux rate into the lower shells. Since the optimal strategy for maximizing the number of satellites involves balancing adding new satellites and minimizing debris flux, an iterative optimization scheme is used to assign the best weights on the populations within each shell.

DATA FILE DESCRIPTIONS

• DEN-CO2scaling2000-2100_v3.nc: This is the data file in NetCDF format from Brown (2024) showing the projected density reductions relative to the year 2000 for each of the SSPs. This dataset may also be accessed here: https://doi.org/10.25500/edata.bham.00001197.

• dens_forecast_ssp_v3_msis2.mat: This file is generated by read_brown_ssp_projections.py, and provides the actual projected densities for each scenario considering the F10.7 forecast fit from the historical record.

• SW-All.csv: This file contains the history of measured space weather indices up to the day of download (~October 2023 for this file). An up-to-date version in CSV format may be downloaded from https://celestrak.org/SpaceData/.

• dens_msis2.pkl: An grid of time and altitude-resolved thermospheric mass density (globally-averaged at constant altitude) measurements from MSIS 2.0. Used to show the density of the background in plot_satellite_decay_from_tles.py.

• 4006.txt: An example file containing all of the TLEs generated for SATCAT 4006 over it's lifetime. Additional files like this can be generated using get_tles_for_sat.py.

• alt_ref_5y_30_10_v3.pkl and alt_ref_25y_30_30_v3.pkl: Example data files that are used to plot the altitudes for 5 and 25-year deorbit altitudes for an object with a ballistic coefficient of 2e-8 km^2/kg. The first of the two numbers in the file name is the timestep between query epochs (i.e. timestep for plotting). The second number is the timestep for the test propagations (both in days). A lower timestep is needed for the 5-year deorbit case to prevent noticeable discretization error.

• opt_mult_contraction_ssp_hd_v3.mat: A data file that contains the optimized distribution of active satellites that maximizes the population size across the shells of interest while also preventing unstable debris growth. This file is used in compute_ikc_with_contraction.py to plot the instantaneous Kessler capacity as a function of time (with a 1-month timestep) and across each scenario of interest in the paper (the baseline case and three SSP cases). The optimization process takes some time to run, so having this data file on hand helps to get results for plotting quickly.

Please direct any questions to William Parker (wparker@mit.edu).

Acknowledgments

This work was supported by the US National Science Foundation (under Graduate Research Fellowship grant number 1745302 to W.E.P. and grant number NSF-PHY-2028125 to R.L.) and the United Kingdom Natural Environment Research Council (NERC) Space Weather Instrumentation, Measurement, Modelling and Risk (SWIMMR) Programme (grant NE/V002708/1 to M.K.B.). This research was also sponsored by the Department of the Air Force Artificial Intelligence Accelerator and was accomplished under Cooperative Agreement Number FA8750-19-2-1000 to R.L. and W.E.P. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Department of the Air Force or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.