Fwd: SpaceX's Starlink constellation and space debris

[Steve Smith]

From a friend who likes to (over)think things like many of us here do...

-------- Forwarded Message --------

Subject:	SpaceX's Starlink constellation and space debris
Date:	Thu, 30 May 2019 08:23:08 -0500
From:	Jack Horner [hidden email]
To:	'Jack Horner' [hidden email]

 

This blurb may be of some interest to you.

 

----------------------------------- begin blurb

 

I’m not convinced by SpaceX’s story about how its Starlink constellation (when fully populated, ~10K satellites at LEO), at least as reported in WSJ, NYT, and SpaceX’s own press releases, is going to avoid significant debris generation.  If we take those sources at face, SpaceX is giving an insufficiently quantitative response to the question,

 

“Won’t Starlink eventually trash the LEO region?”.  To wit:

 

1. Space is a big place.
2. The satellites know how to avoid colliding with one another.
3. If a satellite’s orbit falls outside its prescribed bounds, the satellite will deorbit and burn up in the atmosphere.

 

For example, a SpaceX press release says, in part:

 

-----------  begin excerpt from SpaceX press release (https://www.spacex.com/sites/spacex/files/starlink_press_kit.pdf)

 

To adjust position on orbit, maintain intended altitude, and deorbit, Starlink satellites feature Hall thrusters powered by krypton. Designed and built upon the heritage of Dragon, each spacecraft is equipped with a Startracker navigation system that allows SpaceX to point the satellites with precision. Importantly, Starlink satellites are capable of tracking on-orbit debris and autonomously avoiding collision (JKH: emphasis mine). Additionally, 95 percent of all components of this design will quickly burn in Earth’s atmosphere at the end of each satellite’s lifecycle (JKH: emphasis mine)—exceeding all current safety standards—with future iterative designs moving to complete disintegration.

 

------------- end excerpt from SpaceX press release

 

A fundamental modeling issue in this regime is whether an “identical and independent distributions” (iid) probability model (which the “space is a big place” story almost surely assumes) tells us enough.   If one satellite collides with another, we can easily get 100 pieces whose orbital elements are not identical. So any given collision affects can change the probability of subsequent collisions.  (And those pieces, we must assume, won’t have the navigational capability to avoid anything.)  After a collision, therefore, the problem can no longer be modeled as an iid.   As Dr. Markov would say, the probabilities chain as the constellation evolves.

 

The Starlink debris-generation question begs for a Markov Chain Monte Carlo (MCMC) simulation.  I wouldn’t be surprised to learn that someone has thought about, maybe even attempted, it.  Do we have to solve something like Gauss’s orbital equations for each piece after a collision in order to generate a sufficiently informative ensemble for MCMC?   What’s kind of computational resources does this require?

 

 

------------------------------- end blurb

 

Jack

 

Jack K. Horner

2130 Owens Lane

Lawrence KS 66046

Email: [hidden email]

Voice: 785-424-7579

 

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