100 megaton bombs atop Saturn V rockets

(Henry Spencer) writes:

In article ,
John Schilling wrote:
of course, we don't *yet* have the near-Earth asteroids and short-period
comets mapped well enough to be sure we'd have plenty of warning for them.

Is it even possible to map those well enough to have decades of warning
with enough precision to warrant and plan for a diversion effort?

Yes, definitely. It may not be possible, decades in advance, to say
firmly that an object *will* strike Earth, but the precision of tracking
and orbit prediction is sufficient to say whether there's a significant
probability of it. If I recall correctly, currently there is only one
well-tracked object with any noticeable chance of an Earth impact, and
that's a fairly small chance during an encounter eight or nine centuries
from now.

Yes, Louis Scheffer cited a very good reference for that one.

But it's the opposite problem, adding nines to the certainty that an
object will *not* strike the Earth. It's not entirely clear what this
implies when we're looking at the middling-high end of the probability
range for actual impactors, and I'm looking for something better than
extrapolation from the "Asteroid X will almost certainly but not
absolutely certainly miss Earth" type analyses.


If you can't pin down the CEP to an Earth radius or so, any attempt at
diversion is as likely to cause an impact as prevent one...

Only if the error ellipse of the encounter is so large that the diversion
can't shift it much. If it's currently centered on Earth and you move the
center off Earth by a fraction of the ellipse's width, then you haven't
really improved things. But if you move it by double its width, then
Earth is no longer inside the range of likely trajectories at all. And
these ellipses are often quite long and narrow -- much of the uncertainty
is usually on one axis -- so if you move it in the right direction, the
move doesn't have to be large.

Right, I hadn't considered the case of arbitrarily skinny error ellipses.
That is an important insight.

OTOH, some of the proposed long-term diversion methods, such as "paint it
black/white and let radiation pressure/Yarkovski effect do its thing",
tend to generate diversions along the long aspect of the error ellipse.
Oops...

And while the perpendicular diversion at least negates the "might make
it worse" aspect of long-term diversion, there's still the troublesome
economic and political questions involved in getting commitment to a
major effort to deal with a low-probability, long-term threat.


And even with arbitrarily good data, computers, and models, there's
a chaotic element to perturbation effects on asteroid orbits that
will prevent you from predicting the trajectory to within 1 Re
arbitrarily far into the future.

Correct, but at least for the currently known objects, the realm of
reasonably accurate prediction -- given good tracking data -- extends out
a century at least.

Hmm. The best guess I get, working backwards from the error budget in
the 1950DA paper that Scheffer cited, is that you can only get single-Re
prediction accuracy single-digit years into the future.

But there are a lot of reasons why simple interpolation from the long-term
1950DA prediction might not be the best model for this sort of thing.


...the question of whether one can then actually say, "We've
now undertaken further study of asteroid XYZ-123 and determined that yes,
it would be a Good Thing to nudge it by 1 Re thataway", reliably, twenty
years in advance, has not to the best of my knowledge been rigorously
addressed.
Have you seen anything in that regard?

Not a general study, no (with the caveat that I haven't really gone
looking).

That's what I was afraid of. People prefer to do their research on
real subjects, and all (known) real objects are of the "will almost
certainly miss the Earth" variety. So the research is on expanding
the timescale and increasing the precision of the miss predictions,
which isn't quite the same thing.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-718-0955 or 661-275-6795 * -58th Rule of Acquisition *

John Schilling wrote:
Louis Scheffer writes:

(John Schilling) writes:

A study indicating that, in particularly favorable condition, one
can identify a 0.33% impact hazard 879 years out, does not directly
address that question. [..] Simple linear interpolation gives a
(0.0033/0.5)*879 = 5.8 year timescale on such predictions.

I think a linear interpolation is not the right approximation. [...]
Let's
also guess the problem is small unknown accelerations. These cause
a
displacement that grows as t^2 to a first approximation. So if
there is a
300 Re error in 880 years, there is a 1 Re error in 880/sqrt(300)
years,
or about 50 years.

But D ~ t^2 is the equation for uniform acceleration in free space,
not for orbital perturbation. [...] both the perturbing force
and any restoring or constraining forces become cyclic.

This depends on the particular source. Uncertain masses of other
asteroids, galactic tides, etc. are cyclic on some scale or another.
Yarkovsky, however, is not. It generates force consistantly in the
direction of the orbit or against it. This causes both the position in
the orbit, and the radius of the orbit, to change quadratically with
time. See an analysis "Yarkovsky effect on small near-Earth asteroids"
at:

http://copernico.dm.unipi.it/~milani...ko_preprint.ps

Solar radiation forces are the next biggest effect, and (I think) also
will
scale as t^2, since they are uniformly directed away from the sun.
These two account for about 90% of the uncertainty.

I think the BOTE calculation has to assume secular orbit
perturbations, and uncertainties of same, evolve linearly.

If we assume the other 1/10 evolves linearly (galactic tide, numerical
error, solar mass loss, J2, other asteroids, uncertain planet masses),
we get about 58 years for these to reach 1 Re. If we assume the solar
and Yarkovsky act as t^2, we get about 50 years for these to reach 1
Re. So at 30 years the combined total should be less than 1 Re. This
analysis, of course, is worth roughly the cost of the (used) envelope,
upon the back of which it is written.

But I'd like to see something better than a BOTE calculation.

So would I, but I think if an object on a collision course is found,
the
correct calculations will be forthcoming....

Lou Scheffer

writes:


John Schilling wrote:
Louis Scheffer writes:

(John Schilling) writes:

A study indicating that, in particularly favorable condition, one
can identify a 0.33% impact hazard 879 years out, does not directly
address that question. [..] Simple linear interpolation gives a
(0.0033/0.5)*879 = 5.8 year timescale on such predictions.

I think a linear interpolation is not the right approximation. [...]
Let's also guess the problem is small unknown accelerations. These
cause a displacement that grows as t^2 to a first approximation. So
if there is a 300 Re error in 880 years, there is a 1 Re error in
880/sqrt(300) years,
or about 50 years.

But D ~ t^2 is the equation for uniform acceleration in free space,
not for orbital perturbation. [...] both the perturbing force
and any restoring or constraining forces become cyclic.

This depends on the particular source. Uncertain masses of other
asteroids, galactic tides, etc. are cyclic on some scale or another.
Yarkovsky, however, is not.

It's cyclic in an inertial frame, though obviously in 1:1 resonance
with the asteroid's orbit. That's not the same as a constant force,
though.


It generates force consistantly in the direction of the orbit or against
it. This causes both the position in the orbit, and the radius of the
orbit, to change quadratically with time. See an analysis "Yarkovsky
effect on small near-Earth asteroids" at:

http://copernico.dm.unipi.it/~milani...ko_preprint.ps

Finally got a chance to read this in enough detail to double-check the
math, and you're only half right. Mean anomaly is quadratic with time,
but semimajor axis is linear. On examination, has to be linear if
conservation of energy and angular momentum are to be preserved, as
Yarkovsky effect adds energy and momentum to the system at constant
rate.


Solar radiation forces are the next biggest effect, and (I think) also
will scale as t^2, since they are uniformly directed away from the sun.
These two account for about 90% of the uncertainty.

Except that in the case of 1950DA, the originally cited paper has the
error budget included and these only ammount to 50% of the uncertainty.
Interactions with other asteroids, and uncertainty in major planet masses,
made up most of the other 50%.

So even if we assume the Yarkovsy and solar radiation uncertainties are
pure quadradtic, that only the change in mean anomaly matters, that still
leaves us with half the uncertainty in the form of small, nonresonant,
and presumably linearly additive perturbations.



I think the BOTE calculation has to assume secular orbit
perturbations, and uncertainties of same, evolve linearly.

If we assume the other 1/10 evolves linearly (galactic tide, numerical
error, solar mass loss, J2, other asteroids, uncertain planet masses),
we get about 58 years for these to reach 1 Re. If we assume the solar
and Yarkovsky act as t^2, we get about 50 years for these to reach 1
Re. So at 30 years the combined total should be less than 1 Re. This
analysis, of course, is worth roughly the cost of the (used) envelope,
upon the back of which it is written.

But with the linear perturbations ammounting to 50% of the total, the
time to reach 1 Re of accumulated error is slightly less than ten years.

So I wouldn't wager on being able to reliably predict a 1950DA impact
more than a decade out, and wouldn't count on decade-plus timescale
diversion schemes against that threat.

And since 1950DA is known to be a nonrepresentative case, I wouldn't
even bet on that ten years against any unknown impactors that might
crop up in some future NEO survey.


This is getting interesting, and disconcerting to the degree that asteroid
impact hazards are actually worrisome, and unfortunately beyond the level
that I can justify working on without a fee or a journal article (or both)
at the end of the tunnel. OTOH, I may give that article a try.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-718-0955 or 661-275-6795 * -58th Rule of Acquisition *

writes:


John Schilling wrote:
Louis Scheffer writes:

(John Schilling) writes:

A study indicating that, in particularly favorable condition, one
can identify a 0.33% impact hazard 879 years out, does not directly
address that question. [..] Simple linear interpolation gives a
(0.0033/0.5)*879 = 5.8 year timescale on such predictions.

I think a linear interpolation is not the right approximation. [...]
Let's also guess the problem is small unknown accelerations. These
cause a displacement that grows as t^2 to a first approximation. So
if there is a 300 Re error in 880 years, there is a 1 Re error in
880/sqrt(300) years,
or about 50 years.

But D ~ t^2 is the equation for uniform acceleration in free space,
not for orbital perturbation. [...] both the perturbing force
and any restoring or constraining forces become cyclic.

This depends on the particular source. Uncertain masses of other
asteroids, galactic tides, etc. are cyclic on some scale or another.
Yarkovsky, however, is not.

It's cyclic in an inertial frame, though obviously in 1:1 resonance
with the asteroid's orbit. That's not the same as a constant force,
though.


It generates force consistantly in the direction of the orbit or against
it. This causes both the position in the orbit, and the radius of the
orbit, to change quadratically with time. See an analysis "Yarkovsky
effect on small near-Earth asteroids" at:

http://copernico.dm.unipi.it/~milani...ko_preprint.ps

Finally got a chance to read this in enough detail to double-check the
math, and you're only half right. Mean anomaly is quadratic with time,
but semimajor axis is linear. On examination, has to be linear if
conservation of energy and angular momentum are to be preserved, as
Yarkovsky effect adds energy and momentum to the system at constant
rate.


Solar radiation forces are the next biggest effect, and (I think) also
will scale as t^2, since they are uniformly directed away from the sun.
These two account for about 90% of the uncertainty.

Except that in the case of 1950DA, the originally cited paper has the
error budget included and these only ammount to 50% of the uncertainty.
Interactions with other asteroids, and uncertainty in major planet masses,
made up most of the other 50%.

So even if we assume the Yarkovsy and solar radiation uncertainties are
pure quadradtic, that only the change in mean anomaly matters, that still
leaves us with half the uncertainty in the form of small, nonresonant,
and presumably linearly additive perturbations.



I think the BOTE calculation has to assume secular orbit
perturbations, and uncertainties of same, evolve linearly.

If we assume the other 1/10 evolves linearly (galactic tide, numerical
error, solar mass loss, J2, other asteroids, uncertain planet masses),
we get about 58 years for these to reach 1 Re. If we assume the solar
and Yarkovsky act as t^2, we get about 50 years for these to reach 1
Re. So at 30 years the combined total should be less than 1 Re. This
analysis, of course, is worth roughly the cost of the (used) envelope,
upon the back of which it is written.

But with the linear perturbations ammounting to 50% of the total, the
time to reach 1 Re of accumulated error is slightly less than ten years.

So I wouldn't wager on being able to reliably predict a 1950DA impact
more than a decade out, and wouldn't count on decade-plus timescale
diversion schemes against that threat.

And since 1950DA is known to be a nonrepresentative case, I wouldn't
even bet on that ten years against any unknown impactors that might
crop up in some future NEO survey.


This is getting interesting, and disconcerting to the degree that asteroid
impact hazards are actually worrisome, and unfortunately beyond the level
that I can justify working on without a fee or a journal article (or both)
at the end of the tunnel. OTOH, I may give that article a try.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-718-0955 or 661-275-6795 * -58th Rule of Acquisition *

(John Schilling) wrote in message ...
writes:
John Schilling wrote:
Louis Scheffer writes:
(John Schilling) writes:

A study indicating that, in particularly favorable condition, one
can identify a 0.33% impact hazard 879 years out, does not directly
address that question. [..] Simple linear interpolation gives a
(0.0033/0.5)*879 = 5.8 year timescale on such predictions.

I think a linear interpolation is not the right approximation. [...]

But D ~ t^2 is the equation for uniform acceleration in free space,
not for orbital perturbation. [...] both the perturbing force
and any restoring or constraining forces become cyclic.

This depends on the particular source. Uncertain masses of other
asteroids, galactic tides, etc. are cyclic on some scale or another.
Yarkovsky, however, is not. [...]
http://copernico.dm.unipi.it/~milani/preprints/yarko_preprint.ps [...]

Solar radiation forces are the next biggest effect, and (I think) also
will scale as t^2, since they are uniformly directed away from the sun.
These two account for about 90% of the uncertainty.

Except that in the case of 1950DA, the originally cited paper has the
error budget included and these only ammount to 50% of the uncertainty.
Interactions with other asteroids, and uncertainty in major planet masses,
made up most of the other 50%.

Are you sure? Here is the table from the article in Science:

Science Magazine, 5 April 2002

Table 3. Trajectory propagation factors and their individual and
combined effect on our prediction of the along-track position of 1950
DA, on 16.0 March 2880, just before the time of nominal orbit
intersection with Earth. Differences are expressed relative to the
reference trajectory. Bracketed quantities indicate the bounding value
found by varying the parameter over the intervals described in the
text.

Trajectory propagation factor Distance (km) Time
----------------------------- ------------- -----------
(A) Galactic tide -8400 -10 min
(B) Numerical integration error -9900 -12 min
(C) Solar mass loss +13300 +16 min
(D) Solar oblateness (J2) (+42100, +17600) (+49,+21) min
(E) 61 additional asteroids -1.5×10^6 -1.2 days
(F) Planetary mass uncertainty (+1.38,-1.54)×10^6 (+1.1,-1.3) days
(G) Solar radiation pressure -11.2×10^6 -9.1 days
Combined (A-G) (-11.0,-17.6)×10^6 (-9.0,-14.3) days
Yarkovsky effect only (+11.9,-71.0)×10^6 (+9.6,-57.7) days

If I'm reading this right, the total of A-F (the cyclical forces)is
only about 2-3 days out of a total of about 60, since the two biggest
effects (by far) are Yarkovsky and solar pressure, both of which
should be of the t^2 variety.

Is there another article with a different error budget?

So even if we assume the Yarkovsy and solar radiation uncertainties are
pure quadradtic, that only the change in mean anomaly matters, that still
leaves us with half the uncertainty in the form of small, nonresonant,
and presumably linearly additive perturbations.

If the cyclic forces were half the uncertainty, I'd agree that 10
years is all the warning you can be certain of. But from the error
budget above (if that is in fact the most recent) my earlier
calculations seem more appropriate, and you can get at least 30 years
of reliable prediction of direct impact.

Lou Scheffer