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