“I
have approximate answers and possible beliefs in different degrees of certainty
about different things, but I'm not absolutely sure of anything.”- Richard Feynman, Interview in BBC program Horizon, 1981
The asteroid 99942 Apophis is a near-Earth object (NEO) estimated to be about 1,100 feet (340 meters) across. In other words, about the same dimension as the rock that took out the dinosaurs 65 m years ago. Apophis was discovered in 2004 and immediately identified as one of the most hazardous asteroids that could impact Earth. But that impact assessment changed after astronomers tracked Apophis and its orbit became better determined.
To fix ideas: a radar observation campaign in
March 2021, combined with precise orbit analysis, has allowed planetary astronomers to
conclude that there is no risk of Apophis impacting our planet for
at least a century. But is this information you can "take to the bank" - as it were? No, it isn't. It's a "best guess" based on the partial orbital data we have up to now. It does not factor in any potential displacement in orbit which could occur, say, from another object - comet or other near earth asteroid. In this sense, the situation echoes Richard Feynman's remark that: "I'm not absolutely sure about anything."
Now, one can perhaps use instead the "bead" model of British astrophysicist E.A. Milne, e.g.
0 <-------------------------------o---------------------->
1
which he used to assess probabilities. Milne argued that this was a useful device by which to gauge one’s acceptance of assorted claims, from unicorns, to Martians to whether an asteroid impacts Earth. The 1 end of the string defined absolute certainty, or a probability of 1.0, meaning there could be no doubt at all. The 0 end meant absolute impossibility of an event - i.e. an associated probability of zero for occurrence.
Milne contended - basically like Feynman - that no truly serious person then could write off any event as having probability 0, i.e. putting his bead at the 0 end. In this sense a collision of Earth with Apophis cannot be summarily ruled out, never mind how close astronomers wish to place that bead near zero on Milne's scale. So one cannot assert there is "no risk" of Apophis colliding with Earth. There may well be a minuscule or "almost nonexistent" risk, but one can't say there is "no risk" - which comes over as absolute certainty.
Estimated to be about 1,100 feet (340 meters) across, Apophis quickly gained notoriety as an asteroid that could pose a serious threat to Earth when astronomers predicted that it would come uncomfortably close in 2029. Thanks to additional observations of Apophis, the risk of an impact in 2029 was later ruled out, as was the potential impact risk posed by another close approach in 2036. But again these updated risk assessments have been based on partial observations to that point, and have not factored in potential "intruder" objects - however low that possibility. We refer to such possibilities as "perturbations" of the orbit in celestial mechanics.
The diagram shown below is useful in making some sense of what I mean by perturbations applicable to the Apophis approach in 2029:
Here, we let m2 be the Earth, m1 the Sun, r the Earth -Sun distance (1.5 x 10 11 m ) and m3 Apophis (just outside Earth's orbit at the time, 1.0993 A.U.) and m4 some additional, intruding body. If the distance r 1 separating m3 and m4 is small enough the gravitational effect of m4 (if large enough) will be to perturb the assumed orbit of Apophis which may then be sufficient that it directly impacts Earth in 2029. The relevant perturbation is expressed in terms of Delaunay variables (L, ℓ ) :
R = k 2 m 4 {1/ D (L, ℓ ) + r · r 1 / r 1 2 }
And the relevant Hamiltonian:
H (L, ℓ ) = - m 2 / 2 L 2 - k 2 m 4 {1/ D (L, ℓ ) + r · r 1 / r 1 2 }
What is this intruder m4? We don't know because it has not yet appeared, and we can't be certain if it ever will. But that is my point, as well as Milne's and Feynman's We have to be honest enough to admit that such celestial forecasts are only as good as the data up to that point. But taking the intruder as a massive comet - say 1/3 the mass of Apophis - and r 1 = 5 x 10 6 m at closest approach to Apophis (r 1 ), we see a possible shift of 0.0015 rad in the inclination i of the asteroid's orbit. That is probably enough to alter its course from "no likely impact" to likely impact.
When Apophis made a flyby
of Earth around March 5, 2021, astronomers took the opportunity to use powerful
radar observations to refine the estimate of its orbit around the Sun with
extreme precision, enabling them to confidently rule out any impact risk in
2068 and long after. But again, this confidence can be only partial, since it is based on partial orbital data. As Feynman tells us, "We cannot be absolutely sure of anything" - even an intruder object (another asteroid, comet?) showing up to screw up the earlier computations for the orbital elements.
This is why the recent statement of Davide Farnocchia of NASA’s Center for Near-Earth Object Studies (CNEOS), i.e.:
“A 2068 impact is not in the realm of possibility anymore, and our calculations don’t show any impact risk for at least the next 100 years,”
Is simply not credible. It's not credible because Farnocchia flouts Milne's and Feynman's warning about scientific absolutism. This he does by making the absolutist statement "a 2068 impact is simply not in the realm of possibility.' Which discounts any other eventualities and factors, like a hitherto unknown mass showing up not previously observed. Say a new, massive comet from the Oort cloud - hitherto unobserved - makes its debut and perturbs Apophis's' orbit. Then all assumptions and computations are blown into a cocked act and Farnocchia ends up with egg on his face. But given he may (or may not) not be around in 46 years to take the blame for a miscalculation, that may not matter.
In fairness, it is true that the recently refined optical observations and additional radar observations, lower the uncertainty attached to Apophis’ orbit. They have, effectively, "collapsed it" from hundreds of kilometers to just a handful of kilometers when projected to 2029 - according to Farnocchia. (Farnocchia was referring to the Sentry Impact Risk Table. Maintained by CNEOS, the table keeps tabs on the few asteroids whose orbits take them so close to Earth that an impact can’t be ruled out).
But let's be clear that a "handful of kilometers" is not zero kilometers (The actual uncertainty in the distance is given as + 150 meters by CNEOS) And if a perturbing body is introduced - as I showed above - those handful of kilometers may well be doubled, tripled or even quadrupled. In which case all bets may be off. This also nullifies Farnocchia's claim that "this greatly improved knowledge of its position in 2029" also means "we can now remove Apophis from the risk list.” No, we cannot, because at some future date - maybe in 3 years - a variable in the form of an intruding object may appear that blows out the extrapolation.
In some ways, the claim of the "CNEOS Risk Table no longer including Apophis" reminds me of the 1986 NASA risk assessment of a Shuttle mishap with the crew killed. Then assessed at 1 in 100,000. It was left to Richard Feynman - as part of a presidential commission following the January 28, 1986 'Challenger' disaster - to show the actual risk for that occurrence was 1 in 200 . This was based in NASA's other claim of the Shuttle being "99.4% safe" for missions. (E.g. 0.6 out of every 100 missions was unsafe, or 1.2 out of every 200.)
Lastly, let us note that relying on optical telescopes and ground-based radar to help characterize every known near-Earth object’s orbit to enhance long-term hazard assessments, is done in support of NASA’s Planetary Defense Coordination Office. Is this iteration of NASA better than the one that figured out the 1 in 100,000 Shuttle risks before the Challenger blasted off? Maybe, but more needs to be done - and known. We do know that teams of Astronomers are still working to develop a better understanding of the asteroid’s rotation rate and the axis it spins around. That knowledge will enable them to determine the orientation the asteroid will have with Earth as it encounters our planet’s gravitational field in 2029.
Which difference in distance could change that spin state and even cause “asteroid quakes.” NASA space jockeys and asteroid hunters did not elaborate on what that means.
Is all of the preceding merely an exercise in advanced improbabilism? Maybe, but it also is based on the Milne and Feynman warnings about being cavalier about outcomes predicated on any scientific observations.
And what if an intruding massive object enters the picture before 2029? Stay tuned.
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