already spotted one undercaffed error, albeit non-fatal: 1/1000 AU
error over 110 AU is, duh, a one part in 110,000 error. g'night!
On 2/26/2021 10:41 PM, Henry Vanderbilt 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