1. Solution to the Sagan Dilemma via Surface Albedo Modification Technique
Shen Ge1, Virgiliu Pop2
1Shen Ge, Graduate Research Assistant, Texas A&M University,
2Virgiliu Pop, Researcher, Romanian Space Agency,

2. Introduction to NEOs and PHAs
Near-Earth object (NEO) is a solar system object whose orbit intersects with that of Earth.
All NEOs have a perihelion distance less than 1.3 AU
Potentially hazardous objects (PHAs) are NEOs that can be less than 0.05 AU from Earth and is at least 150 m
Many studies have gone into deflection of such bodies away from Earth
Flyby of asteroid 2004 FH, closest miss ever noticed

3. Sagan Dilemma
In early 1990s, Carl Sagan and other authors posed this challenge:
“if one can deflect an asteroid away from a collision, one can also deflect an asteroid toward a collision”

4. Offensive Deflection
Consider a system capable of deflecting an asteroid in a time interval tr where
RE = deflection distance
ΔV = velocity increment
P = asteroid orbital period
Below one orbital period, deflect along-track. Above one orbital period, deflect across-track
Finding the approximate phase space is just doing the same thing in reverse.
Note AE is the cross-sectional area of the Earth allowing gravitational focusing of bodies approaching 10 km/s
Ratio Q is the probability that an asteroid can be misdirected among asteroid that need to be mitigated!
Harris, A., Canavan, G., Sagan, C., Ostro, S. “Deflection Dilemma: Use vs Misuse of Technologies for Avoiding Interplanetary Collision Hazards.” 5 Nov

5. Impulsive Techniques
Impulsive techniques create instantaneous large velocity changes.
They include techniques such as
Stand-off nuclear detonation
Kinetic impactors

6. Impulsive Technique Deflection Distance
Sanchez has studied the ΔV requirements for deflecting an asteroid by 1 Earth radius given sufficient warning years
Sanchez, Cuartielles, J.P. “Asteroid Hazard Mitigation: Deflection Models and Mission Analysis.” PhD Thesis

7. Q Ratio for Impulsive Technique
Looking at the asteroid Apophis, we obtain 4.6% harmful deflection probability if we assume we can deflect across-track and
tr = P = years
RE = 6371 km
ΔV = 0.1 m/s

8. Yarkovsky Effect
Yarkovsky effect is the result of anisotropic heating of a celestial object.
As the sunlit side of the asteroid rotates away from the sun, the warmer dusk side radiates more energy than on the cooler dawn side.
The resulting net force acts in a direction that is determined by the asteroid’s spin axis, rotation rate, and orbital period.

9. Earlier Deflection -> Smaller ΔV
The Yarkovsky effect can be modified by painting the surface to change the thermal distribution
Whereas in the past, Yarkovsky effect modification will never be considered for an asteroid as large as Apophis unless given decades of forewarning, studies at JPL and elsewhere have shown its efficacy if enough surface modification is applied before the close approach near Earth in 2029 using the concept of keyholes.

10. Background on Keyholes
Keyholes are cross-sectional regions in space which may intersect an asteroid’s orbit. If the asteroid passes through this keyhole, then upon some future cyclic return near Earth, the asteroid will have a definite chance of impact.
For Apophis, the 2036 impact will only occur if it passes through a ~610 m keyhole in 2029

11. Deflection Time for Apophis
Studies done at Texas A&M has sown that mitigation efforts can start in 2023 for estimation error to match
Any malevolent intent for this mission can also only begin at this time to have enough certainty of striking Earth
It also cannot start too late since the deflection distance will be too little!

12. Q Ratio for Surface Albedo Modifier
Looking at the asteroid Apophis, we obtain O(10-5)% harmful deflection probability if we assume we can deflect along-track and
tr = 6 years
P = years
RE = 610 m
ΔV = O(10-7) m/s
Minuscule compared to 4.6%

13. Legal Implication: Nuclear Technique
Nuclear explosive device used for peaceful purposes has no distinction from a nuclear explosive device that can be used as a weapon
Article IV of Outer Space Treaty prohibits installation of weapons of mass destruction (WMDs) on celestial bodies and in Earth orbit

14. Legal Implication: Nuclear Technique
Article II.2.d. of Peaceful Nuclear Explosions (PNE) Treaty forbids any explosion except in compliance with provisions of 1963 Moscow Treat
Therefore, use of PNE says deflection of asteroids by nuclear explosions are illegal!

15. Legal Implication: Impactors
Bilateral USA-USSR 1972 Anti-ballistic Missile (ABM) Treaty prohibits in Art. V the development, testing, and deployment of ABM systems, including space-based ones
Asteroid deflection systems using missiles (nuclear or not), etc. may be accused of having real ABM capabilities.

16. Conclusion Modifying the Yarkovsky effect offers several advantages:
Minuscule ΔV dramatically lowers probability of impact misusage
Long-term mitigation timeline negates tampering with system at last minute
Answers legal obstacles encountered by other more aggressive techniques

17. Questions?