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<p>From a friend who likes to (over)think things like many of us
here do...<br>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Subject:
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<td>SpaceX's Starlink constellation and space debris</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Date: </th>
<td>Thu, 30 May 2019 08:23:08 -0500</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">From: </th>
<td>Jack Horner <a class="moz-txt-link-rfc2396E" href="mailto:jhorner@cybermesa.com"><jhorner@cybermesa.com></a></td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">To: </th>
<td>'Jack Horner' <a class="moz-txt-link-rfc2396E" href="mailto:jhorner@cybermesa.com"><jhorner@cybermesa.com></a></td>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">This blurb may be of some interest to you.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">----------------------------------- begin
blurb<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">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, <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="text-indent:.25in">“Won’t Starlink
eventually trash the LEO region?”. To wit:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<ol style="margin-top:0in" start="1" type="1">
<li class="MsoListParagraph"
style="margin-left:0in;mso-list:l0 level1 lfo1">Space is a
big place.<o:p></o:p></li>
<li class="MsoListParagraph"
style="margin-left:0in;mso-list:l0 level1 lfo1">The
satellites know how to avoid colliding with one another.<o:p></o:p></li>
<li class="MsoListParagraph"
style="margin-left:0in;mso-list:l0 level1 lfo1">If a
satellite’s orbit falls outside its prescribed bounds, the
satellite will deorbit and burn up in the atmosphere.<o:p></o:p></li>
</ol>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">For example, a SpaceX press release says,
in part:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">----------- begin excerpt from SpaceX
press release
(<a class="moz-txt-link-freetext" href="https://www.spacex.com/sites/spacex/files/starlink_press_kit.pdf">https://www.spacex.com/sites/spacex/files/starlink_press_kit.pdf</a>)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">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,<span style="color:red">
Starlink satellites are capable of tracking on-orbit debris
and autonomously avoiding collision (JKH: emphasis mine). </span>Additionally,
<span style="color:red">95 percent of all components of this
design will quickly burn in Earth’s atmosphere at the end of
each satellite’s lifecycle</span> <span style="color:red">(JKH:
emphasis mine)—</span>exceeding all current safety
standards—with future iterative designs moving to complete
disintegration.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">------------- end excerpt from SpaceX press
release<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">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. <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">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?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">------------------------------- end blurb<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Jack<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Jack K. Horner<o:p></o:p></p>
<p class="MsoNormal">2130 Owens Lane<o:p></o:p></p>
<p class="MsoNormal">Lawrence KS 66046<o:p></o:p></p>
<p class="MsoNormal">Email: <a
href="mailto:jhorner@cybermesa.com" moz-do-not-send="true">jhorner@cybermesa.com</a><o:p></o:p></p>
<p class="MsoNormal">Voice: 785-424-7579<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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