Orbital Debris Study for Microsat-R Breakup in March 2019

A back-of-envelop (K14 education) model of the Microsat-R debris is presented with Gabbard Diagram of TLE and model orbital properties.

A Gabbard diagram illustrates the changes in orbital characteristics of fragments of debris from a satellite (natural or artificial) collision and is useful for estimating when fragments will deorbit. In this model, assumptions are made about the system mass and density to predict the size, mass, and density of fragments exist. These are compared to the TLE published by Kelso on https://celestrak.com/NORAD/elements/. The mass and size of debris for the TLE components is estimated, but this estimation should be taken with caution as it depends greatly on the assumptions of system mass and density (and statistical bin sizes for the mass distribution). The number of fragments in the system that are larger than a paperclip mass (1g) is shown. The future work of this model will include orbital properties of the statistically simulated debris and when they will de-orbit. This is a 2D model.

This model is offered for educational purposes. There is no truth to validate the model apart from the deltaV and TLE information. The model is based mostly on data analysis of Kessler looking at asteroids.

Note: The annotated mass values correspond to the deltaV velocity change which is the most probable velocity change for a given mass. The mass could be different because there is a distribution of deltaV modeled for each mass. Using the most probable velocity mass enables estimations to be made. It is not the same as the most probable mass for an associated deltaV, but rather for modeled debris fragment of a given mass, this is the most probably location for it on the Gabbard Diagram.

The code computes the deltaV associated with each debris TLE.

TODO:
* Treat the components (solar panel, electronics box, etc.) as separate mass entities and compute the expected debris from each. Use a better value of density for each.
* Find a distribution function (such as Marshall-Palmer Raindrop, Saturn ring moonlets, or standard aerosol distribution) to represent the distribution of masses that will fit the Kessler formula in the linear region, but will have a min, max, and mode for the debris sizes.
* Clean up and turn it into a lab.
* Estimate from B*, mass, and size, the decay time expected for each component (use Runge-Kutta approach)
* Sensitivity analysis of estimated inputs.