User-Agent: Microsoft-Entourage/12.36.0.130206 Date: Wed, 07 Mar 2012 17:19:34 -0700 Subject: Re: The Risk Corridor From: Daniel Adamo Message-ID: Thread-Topic: The Risk Corridor Thread-Index: Acz6T+d9M4pxX2rJD0qAsxAi4UcxzwCaNopG Mime-version: 1.0 Content-type: multipart/mixed; boundary="B_3552803688_4293547" > This message is in MIME format. Since your mail reader does not understand this format, some or all of this message may not be legible. --B_3552803688_4293547 Content-type: multipart/related; boundary="B_3552803688_4278005" --B_3552803688_4278005 Content-type: multipart/alternative; boundary="B_3552803688_4302080" --B_3552803688_4302080 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit ATIG Members- It seems Nature has supplied a timely footnote for my 2011 AG5 risk corridor analysis. Attached are heliocentric and geocentric plots spanning NEO 2012 DA14's close Earth approach on 15 Feb 2013. Recent Horizons prediction data (reference ephemeris JPL#15) for that event appear in the following table. Date (CT) Body CA Dist MinDist MaxDist Vrel TCA3Sg Nsigs P_i/p ---------------------- ----- ------- ------- ------- ------ ------ ------ ------- A.D. 2013 Feb 15.81141 Earth .000182 .000181 .001436 8.195 73.09 2013.0 .000000 Converting CA Dist, MinDist, and MaxDist from AU to km units, I couldn't help noticing the nominal perigee distance of 27,200 km is nearly the same as the minimum possible perigee (to 3-sigma confidence) of 27,100 km and yet is appreciably removed from the maximum possible perigee (to 3-sigma confidence) of 214,800 km. Perigee distance uncertainty is confirmed by TCA3Sg's value. At 73.09 minutes, that's a lot of potential Earth-relative motion! The attached geocentric plot gives geometric perspective on perigee distance uncertainty. The line of variations (LOV) is effectively the plotted trajectory, and it's nearly perpendicular to Earth's heliocentric velocity (directed roughly out of the plot at the viewer). Thus, variations in the time of perigee can affect perigee distance, but they can't appreciably decrease the current best guess for that distance. So, as indicated by the P_i/p value, there is no credible prospect for Earth collision (nor for a risk corridor plot) associated with this approach. -Dan From: Daniel Adamo Date: Sun, 04 Mar 2012 15:43:58 -0600 Conversation: The Risk Corridor Subject: The Risk Corridor ATIG Members- Arguably the most compelling reason for space exploration (human or robotic) is planetary defense from impact by potentially hazardous objects (PHOs), comprised of near-Earth objects (NEOs) and long-period comets. The attached white paper is motivated by NEO 2011 AG5's possible Earth impact in 2040 (reference http://www.space.com/14683-big-asteroid-2011-ag5-threat-earth.html), which if it actually took place, would then be confined to a 15-km-wide locus of terrestrial locations called the risk corridor. A non-conventional risk corridor generation method documented by the paper is inspired by a strategy ATIG members familiar with Shuttle ascent/entry onboard state vector management will recognize: to correct a down-track navigation error (the most common type), simply modify the state vector time tag as appropriate. In applying this strategy to risk corridor computation, the time bias is varied to systematically sample a PHO's one-dimensional uncertainty region for the subset of conditions resulting in Earth impact. I welcome feedback on this paper and its implications for planetary defense. -Dan --B_3552803688_4302080 Content-type: text/html; charset="US-ASCII" Content-transfer-encoding: quoted-printable Re: The Risk Corridor ATIG Members-

It seems Nature has supplied a timely footnote for my 2011 AG5 risk corrido= r analysis.  Attached are heliocentric and geocentric plots spanning NE= O 2012 DA14's close Earth approach on 15 Feb 2013.  Recent Horizons<= /I> prediction data (reference ephemeris JPL#15) for that event appear in th= e following table.

 &nb= sp;        Date (CT)   &nb= sp;   Body   CA Dist  MinDist  MaxDist &n= bsp; Vrel  TCA3Sg  Nsigs  P_i/p
  ----------------------  -----  -------  ------- &= nbsp;-------  ------ ------ ------ -------
  A.D. 2013 Feb 15.81141  Earth  .000182  .000181 =  .001436   8.195  73.09 2013.0 .000000

Converting CA Dist, MinDist, and MaxDist from AU to km units, I couldn't help noticing the nominal perigee d= istance of 27,200 km is nearly the same as the minimum possible perigee (to = 3-sigma confidence) of 27,100 km and yet is appreciably removed from the max= imum possible perigee (to 3-sigma confidence) of 214,800 km.

Perigee distance uncertainty is confirmed by 's value.  At 73.09 minutes, t= hat's a lot of potential Earth-relative motion!  The attached geocentri= c plot gives geometric perspective on perigee distance uncertainty.  Th= e line of variations (LOV) is effectively the plotted trajectory, and it's n= early perpendicular to Earth's heliocentric velocity (directed roughly out o= f the plot at the viewer).  Thus, variations in the time of perigee can= affect perigee distance, but they can't appreciably decrease the current be= st guess for that distance.

So, as indicated by the P_i/p= value, there is no credible prospect for Earth collision= (nor for a risk corridor plot) associated with this approach.

-Dan


From: Daniel Adamo <adamod@earthlink.net>
Date: Sun, 04 Mar 2012 15:43:58 -0600
Conversation: The Risk Corridor
Subject: The Risk Corridor

ATIG Members-

Arguably the most compelling reason for space exploration (human or robotic= ) is planetary defense from impact by potentially hazardous objects (PHOs), = comprised of near-Earth objects (NEOs) and long-period comets.  The att= ached white paper is motivated by NEO 2011 AG5's possible Earth impact in 20= 40 (reference http://www.space.com/14683-big-asteroid-2011-ag5-threat-earth= .html), which if it actually took place, would then be confined to a 15-= km-wide locus of terrestrial locations called the risk corridor.

A non-conventional risk corridor generation method documented by the paper = is inspired by a strategy ATIG members familiar with Shuttle ascent/entry on= board state vector management will recognize: to correct a down-track naviga= tion error (the most common type), simply modify the state vector time tag a= s appropriate.  In applying this strategy to risk corridor computation,= the time bias is varied to systematically sample a PHO's one-dimensional un= certainty region for the subset of conditions resulting in Earth impact.

I welcome feedback on this paper and its implications for planetary defense= .

-Dan

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