This has the makings of a great mission (and a great screenplay - "Mission
to Oumuamua"? "Rendezvous with Oumuamua"?).
Thanks for starting this discussion, Bill. And thanks for giving us some
thoughtful BOTE numbers to think about, Henry V. and Henry S.
Bill B.
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On Fri, Feb 26, 2021 at 9:41 PM Henry Vanderbilt <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> 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 Earth outbound, .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> 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