Bill,
Something I touched on last night indeed strongly implies a shotgun
approach to reacquiring Oumuamua at 110 AU, now that I've looked at it
again in daylight. For an object under constant illumination,
all-else-equal telescope detection range varies directly with the mirror
diameter ratios, but with only the square root of the mirror area
ratios. EG, halve the mirror diameter, for one-quarter the area, and
you still get 1/sqrt (area1.0/area0.25) AKA one-half the max detection
range of the full-diameter-mirror instrument.
But if you've halved the mirror diameter, to a first approximation
you've halved all the telescope's dimensions and thus reduced its mass
by a factor of 2^3, or eight. Half the range for an eighth the mass.
So until you get down to where minimum-gauge factors start reducing the
mass savings, there's a BIG payoff in the location-uncertainty area you
can cover via subdividing your available telescope mass into a swarm of
smaller scopes.
My guess, small-U-number cubesat equivalents (3U? 1U?) would be
currently doable, without pinning success on the starchip technology
coming online as fast as needed with no hitches.
Mind, I think there's a case to be made this shotgun swarm should be
specialized pathfinders for a larger main probe following some distance
behind, not each also equipped to be the primary imager if it happens to
pass closest to Oumuamua.
My reasoning on this: I am NOT any kind of expert in telescope design,
but I do know that all else VERY seldom is equal. I gather there are
large tradeoffs available between things like maximum image-detail
resolution, high angular resolution, and maximum faint-object
sensitivity. I suspect strongly (but cannot put numbers on) that we
would be best off optimizing the reacquisition sub-sat swarm for
faint-object sensitivity, with only modest image-detail and angular
resolution. Also, since they wouldn't be expected to do the primary
Oumuamua imaging, they'd have only modest comms data-rate requirements.
All these adding up to significantly smaller cheaper individual
shotgun-sats, for less total mission mass to cover a given uncertainty
cone (whatever that might turn out to be.)
All the shotgun reacquisition sub-sats should have to do is scan for
appropriate faint objects, and when they spot one, signal back to the
main spacecraft "I see something, roughly HERE". The main spacecraft
then tells other nearby sub-sats to look THERE also, and if it is indeed
Oumuamua, maneuvers with time in hand for a close flyby, carrying with
it the relatively massy hi-res imager (and other instruments?),
maneuvering delta-V, and high-bandwidth-to-back-here comms hardware.
Henry
On 2/27/2021 9:00 AM, William Claybaugh wrote:
Henry:
These sorts of targeting requirements suggest to me that a shotgun is required rather than a bullet: dozens of small cameras that can be released a few AU before encounter to assure some will have a close pass. A few hundred of Milner’s starchips would seem perfect, as well as offering a chance to test that tech.
An alternative that increases transit time would be to use electric propulsion to slow down on final....
I would also like to understand how a true solar gravity assist might work: for an object not bound to the dynamical system (which this probe becomes near perihelion) it should be possible to extract energy from the sun’s orbit around the galaxy. That seems like it could in principle be a lot of delta-v for so small a mass compared to the mass of the sun.
I am also intrigued by the solar water rocket if 1000 sec. range Isp can be obtained.
Anyone interested might want to catch up on JPL’s “1000 AU” mission studies, which have addressed many of the issues this mission would face.
Bill
On Fri, Feb 26, 2021 at 10:41 PM Henry Vanderbilt <hvanderbilt@xxxxxxxxxxxxxx <mailto:hvanderbilt@xxxxxxxxxxxxxx>> wrote:
Bill,
When in doubt, pin down some aspect of the problem you can
quantify, then see what else falls into place. In this case, at
110 AU out, Oumuamua will be seeing 1/3025th the solar
illumination it did at 2 AU out, our
2-AU-Hubble-detection-distance illumination level.
Reducing the at-object illumination 3025 times reduces the
detection distance sqrt 3025 or 55 times. 2AU/55 is roughly 5.4M
km. So if you dragged along a 1.4m Hubble-equivalent mirror on
your 60 km/s probe, you could nominally spot Oumuamua 5.4M km
away. (Leaving aside for now how fast you could thoroughly scan
that angular size slice of sky.)
Which at 34 km/s closing speed is 44 hours before you zip past
it. If you have 1 km/s fast-burn course correction delta V
available, that's a roughly 150,000 km (or about 1/1000th AU)
error radius you could correct for.
1/1000th AU over 110 AU is about one part in 90,000. Do we have
Oumuamua's trajectory to that degree of accuracy? Much more?
Much less? Someone around here has gotta know, or know someone
who knows.
Meanwhile, you now know a couple of the spacecraft variables
you'll be trading: Telescope size on the probe - smaller-mirror
detection range should drop roughly as the square root of the
reduction of the mirror area, EG a quarter the area (half the
diameter) should give half the detection range. Also, how much
fast-burn final-correction deltaV can/should be carried, and in
what form.
Overall, I'm beginning to get a good feeling that this mission can
likely be done within current SOTA (even before we start looking
for clever optimizations) simply by throwing LOTS of brute-force
mass at it. BFM is getting quite a bit cheaper - consider
multiple F9H payloads docked in LEO then sent off. The 60 km/s
apparently is doable per GH via a couple quite large solid stages
burned during a close slingshot flyby of Jupiter. You'll need one
or two proportionately larger stages to get this large package to
Jupiter fast in the first place. And the probe itself is likely
to need quite substantial onboard optics. All pending the
inevitable clever optimizations, of course.
Mind, the preceding was ginned up late and seriously
undercaffeinated. I will look at it again in the am and see if I
can spot any gross errors before others kindly point any such out...
Henry
On 2/26/2021 8:00 PM, William Claybaugh wrote:
Henry:
Nice top level analysis.
My only question is whether it is as dark as currently assumed
(put another way, whether it is much smaller than currently
assumed). If it is small and very reflective—in keeping with it
not being detectable in the IR, despite passing the sun at .25
AU—then reflected sunlight may be much stronger at 100 AU than
current estimates.
I agree that hope is no basis for mission planning and that
finding it may require, in accordance with your estimate, some on
board capability. I’ve no basis for estimating that mass.
Bill
On Fri, Feb 26, 2021 at 7:50 PM Henry Vanderbilt
<hvanderbilt@xxxxxxxxxxxxxx <mailto:hvanderbilt@xxxxxxxxxxxxxx>>
wrote:
OK, if in fact it'll continue to be visible that far out,
plotting a course for flyby does get much simpler. Seems
unlikely for something that small and (by that point) that
poorly lit, but "seems" is not any sort of numeric
evaluation. OK, let me try for ballpark numbers...
Per the "Astronomy" article at
https://astronomy.com/magazine/2020/02/our-first-interstellar-visitor
, Oumuamua passed closest to Earthoutbound, .36 AU away, at
26 kps on 10/14/17, and ceased being visible even to the
Hubble (1.4m mirror) "after January" of 2018.
So, ~110 days at 26 kps is ~247M km or a bit over 1.6 AU,
plus the .36 AU flyby distance gives us ~2 AU Hubble max
visibility distance, near as makes no difference. (Probably
a bit less when you add the vectors but let's assume on the
generous side.)
Oumuamua is then also roughly 2 AU from the Sun, working back
to the 9/9/17 closest solar approach. So, solar illumination
of the object is (very) roughly 1/4 of the 1 AU-from-Sun
value. So, 2 AU from Hubble at 2-AU-from-Sun illumination is
the rough edge of current observability. After 20 years at
26 kps, Oumuamua will be about 110 AU away from both Earth
telescopes and the Sun, about 55 times as far.
A 30m mirror has about 156 times the area, thus 156 times the
light-gathering, of Hubble's 1.4m mirror. Three such 30m
meter mirrors combined somehow and we get about 470 times
Hubble's light-gathering.
I assume that the primary illumination of Oumuamua will be
the Sun even at 110 AU. Without running the numbers, it
should still be far brighter than the general starlight.
(Someone will no doubt correct me here if needed.)
So reflected sunlight from Oumuamua arriving back at Earth
will be declining as roughly the fourth power of the
distance, with the approximation getting closer as the
distance from Sun to Earth becomes a smaller fraction of the
total. So, 470 times the light-gathering power of Hubble
should yield fourth-root-of-470, or 4.65, times Hubble's ~2
AU Oumuamua range.
So either I dropped a decimal/made a wrong assumption, or
alas even with multiple 30m telescopes we won't be able to
track Oumuamua past 10 AU or so. In which case reacquiring a
track on it for the flyby would be a significant mission
parameter.
Henry
On 2/26/2021 5:06 PM, William Claybaugh wrote:
Henry:
I’m thinking that no special onboard imaging capability is
required.
There are three order 30 meter optical telescopes coming
online in the next five years; *if* my top level analysis
is correct (which question I am asking), the flyby would
occur out in the Kuiper belt about five times further than
Pluto.
That appears to be within the imaging capability of those
telescopes wrt the approximate position of the target.
A second level of analysis might find different, but this is
an amateur forum....
Bill
On Fri, Feb 26, 2021 at 4:24 PM Henry Vanderbilt
<hvanderbilt@xxxxxxxxxxxxxx
<mailto:hvanderbilt@xxxxxxxxxxxxxx>> wrote:
I'm thoroughly in favor of catching and taking a far
closer look at Oumuamua. Even if it isn't an artifact,
it's weird enough that we're bound to learn something
new and interesting. It had never occurred to me to
even ask if the mission might actually be in the same
county as current SOTA though - thanks for that!
I have no answers, mind. But another useful question
occurs: How massy a combination of telescope and
terminal propulsion will this mission need to reliably
spot Oumuamua early enough to have time to correct
course for a close flyby? This would seem central to
sizing the spacecraft. (Or multiple spacecraft, if the
location uncertainties point toward a shotgun approach,
or perhaps toward some sort of
initial-locator/followup-close-flyby mission.)
I assume some level of imprecision in our knowledge of
Oumuamua's departing course. Plus some additional
imprecision in our knowledge of what gravitational and
other influences there may be on it over the next
twenty-ish years - the major planets on its way out
should be fairly predictable, but it'd suck to miss the
flyby because Oumuamua did a close pass on an unknown
Kuiper belt object a few years on. A first pass at
defining the likely cone of uncertainty would be useful,
if anyone has the tools handy for that.
Henry
On 2/26/2021 3:29 PM, William Claybaugh wrote:
Since we are not talking about homebuilt rockets, I was
wondering if we might talk about homebuilt space missions:
A top level analysis suggests it would take about 60 Km
/ sec to catch in about 20 years.
Another very top level analysis suggests that a gravity
assist at Jupiter (solely to turn the plane from near
ecliptic to near that of Oumuamua; near to but less
than 90 degrees) followed by a 50 solar radii assist at
the Sun (Parker is doing 10 radii as I recall but it
carries way too much heat shield for this mission) can
pretty certainly get to 50 km / sec.
One of NASA Glenn’s Stirling cycle RTG’s tied to an
existing commercial electric thruster appears capable
of making up the difference with a big fuel tank.
Assuming a New Horizons-like spacecraft, but much
smaller, a flyby seems possible based on this very top
level analysis.
I’d be real interested in helpful comments.
Bill