Orbital Deflection

Version 2.0
Copyright ©2017 by Paul Niquette. All rights reserved.

Research programs throughout the worldwide community of nations have resulted in various proposals for avoiding impacts by Near Earth Objects (NEOs).  For success, they must addressing the overall requirements for Detection, Prediction, and Deflection

Here is a link-list of references, where solvers will be able to assess the progress and current status of ten
Deflection concepts...


Orbital Deflection puzzle has chosen a concept that deploys a Nuclear Explosive Device and asks solvers this question...

What is your proposal for how the worldwide community of nations might deploy requisite resources to deflect the orbit of asteroid Égaré thereby avoiding its collision with Planet Earth on Thursday, July 21, 2022?

Solvers saw in Figure 4 that simply setting off a thermonuclear blast on the surface of Égaré throws away most of its energy, and what's left irradiates the asteroid but does not show a whole lot of competence in the vectored-thrust department. Thus, we have concluded that our objective comes down to using part of the asteroid's own mass to produce the thrust.

Placement of Energy Source

Obviously, placing the thermonuclear explosion inside asteroid Égaré would be far more effective in discharging mass into space thereby generating thrust.  Just imagine...

Concentric 'processing' of nuclear energy released insitu as shown in Figure 5, melting and vaporizing metals, causing rapid thermal expansion, fracturing rocky masses, and ejecting solids mixed with gases at high speed.  Thrust! 



The effort now is to place our Nuclear Explosive Device under the surface of
Égaré.  While searching the web, your puzzle master came upon a reference on Earth-Penetrating Weapons (EPWs) and learned that...

"For example, exploding a 10-kiloton nuclear weapon at a depth of one meter would increase the effective yield by a factor of 20, resulting in underground damage equivalent to that of a 200-kiloton weapon exploded at the surface of the ground."

Of course, the expression 'effective yield' pertains particularly to the Nuclear Bunker Buster, which is designed to deliver a nuclear warhead underground to destroy military targets that have been buried in -- well, 'bunkers' -- and hardened by reinforced concrete structures. 

The policy issues for nuclear EPWs pertain to radioactive 'containment depth' and 'nuclear fallout' but also include the uncontainable release of active biological and chemical agents from hostile underground storage sites into the environment. 


None of those issues are concerns for our Deflection spacecraft.  Dare we give it the name Asteroid-Buster?  We do share a common technical limitation with EPWs: Penetration Depth.

"While the penetration depth increases with higher impact velocity, the weapon casing will be crushed—destroying the warhead inside—if it strikes the ground at too high a speed.  Empirical and theoretical data show that the maximum impact velocity is roughly one kilometer per second and the maximum achievable penetration depth of such a projectile in concrete is roughly 10-20 feet [3-6 meters]."

Solvers will find several references with proposed features for a hardened penetrator, from which we have made a few design choices for the Asteroid-Buster, as a theoretical spacecraft...

orbdef61. Guidance Module includes autonomic controls and radioisotope thermoelectric generator (RTG).
Tungsten Cladding uses highest melting point alloy for hardening the penetrator module with secant ogive capable of enduring penetration of 30 m.

3. Depleted Uranium (D-38) for inertial ballast inside the penetrator.

4. Pneumatic Shock absorber and...
5. Steel Framing together cushion the thermonuclear module during impact, with bore and stroke designed to provide an appropriate deceleration distance. 

6. Energy Sphere
is centered in the delayed thermonuclear detonation at depth inside the asteroid surface.

7. Attitude Thrusters
are arrayed around the recessed orientation module.

8. Propellant Tanks must be sized for sufficient cryogenic supplies to complete post-boost orbiting maneuvers plus rendezvous, station-keeping and final asteroid Égarpenetration burn.

9. Spacecraft Engine
provides orbiting burns plus acceleration to impact the asteroid at 1.2 km/s.

10. Gimballed Nozzle
assures thrust vectoring for directional stability.

EPW operating in Earth's gravitational field can be simply dropped from an aircraft and guided aerodynamicallyHowever, in the vacuum of space, the Asteroid-Buster must be self-propelled by high-thrust rocket engine all the way to its impact with the asteroid.

Of course, section 1 in Figure 6 will be crushed inconsequentially upon contact with the asteroid's surface.   For maximum penetration depths, sections 2 - 6 must be given slender aspect ratios.  Sections 7-10 can bulge out to any appropriate diameter and be separated either by explosive bolts or frangible fasteners, thus left behind at the surface not to impede the delivery of section 6 by inertia to the deepest level possible within the asteroid.

The length of section 4 Pneumatic Shock may actually be quite significant in determining the ultimate depth of the thermonuclear blast.

The Asteroid-Buster is not merely a re-purposed nuclear weapon, but a dedicated spacecraft, and its timely development is fully justified by the imperative of protecting Planet Earth from the threat of destruction by a Near-Earth Asteroid.


Final Spacecraft Maneuvers

As sketched in Figure 7 our Asteroid-Buster must execute complex maneuvers to penetrate the asteroid and to facilitate thermonuclear-energized vectored thrust for V perpendicular to the orbital plane (see Figure 3).


That will necessitate delivering the spacecraft from Earth to an orbit inside that of Égaré with the same eccentricity -- but slightly behind Égaré in phase.  With its shorter orbital period, the satellite will gradually catch up to the asteroid.  At precisely the right moment a ∆V Tangential burn must be autonomically administered to put the spacecraft into a Transfer Orbit.  Finally, the spacecraft must be repositioned by Attitude Burns below the orbital plane, then turned toward the asteroid for the ∆V Normal Impact Burn.

Model for Proposed Solution

To the question posed by the Orbital Deflection puzzle poses this question...

"What is your proposal for how the worldwide community of nations might deploy requisite resources to deflect the orbit of asteroid Égaré thereby avoiding its collision with Planet Earth on Thursday, July 21, 2022?"

...to which we have provided one answer in narrative form.  Analyses with numerical specificity for the orbital mechanics and the detailed design of Asteroid Buster are beyond the scope of this entry in Puzzles with a Purpose.  Nevertheless, in Figure 8 are a few elementary tools that some solvers may find useful for exploring these subjects further.


The sketch in Figure 8 depicts an elementary model in which the mass of the asteroid mA gets slightly reduced by the mass of ejecta mE following the internal detonation.


Let us assume that the asteroid has uniform density.  Whatever the shape of the ablation boundary inside the asteroid, proportionality applies: mE / mA = (dP / dA)3, where…


dA = diameter of the asteroid; for Égaré, dA = 100 m.

dP = depth of the placement of the thermonuclear device

Using the limitation cited above, dP = 6 m.  Since mA =
9 kg, mE = 520,000 kg.

By Conservation of Momentum, we find vE = (mA – mE) V / mE, where...

= average velocity of solids and gases ejected by the explosion

V = intentional change in asteroid’s velocity normal to its orbital plane


From the derivation on the puzzle page, V = 11.7 m/s, thus vE = 54,000 m/s.

By Conservation of Energy, hYhL = (mAmE)V 2 / 2 + mE vE 2 / 2, where…


hY = heat energy yield from the thermonuclear explosion,

hL = heat energy loss eventually to space

Making the indicated substitutions for asteroid

hYhL = 7.6×1014 Joules = 181 kilotons of TNT

...which is an estimate of net energy required for V Normal andi = 1/10 degree.

Base Case and Perturbations

The calculations in the model formulated above can be regarded as a Base Case.  Our estimate for the required thermonuclear energy (181 KtnTNT) needs to be tested for its sensitivity to the assumptions in the model.  Thus we will 'perturb' three key parameters ↕10% and ascertain the consequences by re-running the model. 

Here is what is called a 'star diagram' for the results...


For Égaré, we assumed dA to be 100 m.  As indicated in the diagram, if the asteroid's actual diameter is 10% larger (110 m), the required orbital deflection energy will be 321 KtnTNT, which is larger by 140 KtnTNT (77%).  But if the design of the Asteroid Buster can increase its dP by 10% (from 6 m to 6.6 m), the hihger estimate for required deflection energy might be reduced to 95 KtnTNT (53%).  Meanwhile, a reduction in energy yield (hY - hL) by 10% (to 146 KtnTNT), will decrease by 10% (to 10.5 m/s) and i by a comparable amount.


Solvers, your comments are invited.