Subject: Re: The Risk Corridor
From: Daniel Adamo <[email-masked]>
Date: Wed, 07 Mar 2012 17:19:34 -0700

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 <[email-masked]>
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