Prepositions in Space
  Version 1.1
Copyright ©2017 by Paul Niquette. All rights reserved.
Sculpture: eps foam, urethane, resin enforced hydrocal, latex paint, steel, site specific installation. 
Commissioned for a 2008 exhibition, curated by David Norr, Institute for Research in Art,
Contemporary Art Museum, University of South Florida.  Photograph by Anthony Wong Palms.

olvers of the Rock from the Sky puzzle might allow themselves to imagine that the sculpture in the photograph depicts the remains of asteroid Égaré (French for stray) after its fiery arrival on Thursday July 21, 2022.  If so, the proposal in the Orbital Deflection puzzle must not have been implemented in time to prevent the impact.

Oh, but Égaré, with a diameter dA = 100 m and a mass mA = 2.4x109 kg, ranks alongside the meteoroid that caused the Tunguska Event -- the largest impact in recorded historyThe appropriate sculpture for that would take up 2,000 km2.
Let us consider three alternative explanations for the Impact Sight sculpture:

1. Insufficient

Perhaps the orbit of Égaré was indeed deflected -- but not quite enough:  Upon reaching the inbound orbital intersection traveling at V = 39.4 km/s, the rocky, iron-rich sphere may have arrived at an extremely shallow angle to the atmosphere -- a near tangent, possibly -- such that the huge bolide,  like a stone on the surface of a pond, skipped around the earth, lighting up the sky over continents and oceans, shrinking and slowing to, say, V = 1.0 km/s, about the speed of an unarmed Bunker Buster and finally smashing into that wall.

2. Deflection Shrapnel  

An unwelcome alternative needs to be considered.  Suppose that our proposed method for orbital deflection using a Nuclear Explosive Device worked fine but has an unintended consequence -- that the orbital inclination of the asteroid
was successfully changed to avoid collision with Earth but left sizable pieces of Égaré in a coplanar orbit destined to impact Earth on Thursday July 21, 2022.

3. Deflection Direction

The solution page for the Rock from the Sky puzzle set forth our objective.  Excerpting, with emphasis added: "[T]o achieve a maximum possible vectored thrust ∆V normal to the orbital plane in the direction that assures an increase in whatever orbital inclination already exists." In meeting that objective, the solution page for the Orbital Deflection puzzle encountered something of an awkwardness in the language of space.  Whereas there are some 80 common prepositions in the English language...

aboard, about, above, absent, across, after, against, along, amid, among, around, as, astride, at, atop, bar, before, behind, below, beneath, beside, besides, between, beyond, but, by, circa, despite, down, during, except, for, from, in, inside, into, less, like, minus, near, notwithstanding, of, off, on, onto, opposite, out, outside, over, past, per, plus, save, short, since, than, through, throughout, to, toward, under, underneath, unlike, until, up, upon, upside, versus, via, vis-à-vis, with, within, and without

...something like 10% are inconvenient for expressing relationships in space...

 above, atop, below, beneath, down, over, under, underneath

How does one describe a direction perpendicular to the asteroid's orbital plane without using one of those prepositions?  It's not easy.  For example, the maneuvers specified in Figure 7 of the Orbital Deflection puzzle concluded as follows, with emphasis added: "Finally, the spacecraft must be repositioned by Attitude Burns below the orbital plane, then turned toward the asteroid for the ∆V Normal Impact Burn."

What is your explanation for Impact Sight sculpture?

1.     Insufficient Deflection

2.     Deflection Shrapnel

3.     Directional Preposition

4.     Something else entirely