OK, a transcription error here - Hubble's mirror diameter is 2.4m, not
1.4m. However, the range calcs for Hubble versus a hypothetical 3x30m
mirror array are correctly based on the actual 2.4m Hubble mirror
diameter. For range increasing from both the (Sun) light source and
from the telescope, it is the fourth power of the lightgathering-area
ratios, or about 4.6 times Hubble's ~2 AU see-Oumuamua range, all else
equal. (That signal dropping as the fourth power of range is the same
thing that makes radar require extravagant power and antenna sizes for
longer ranges. Power drops with the square of range both outbound and
return, ouch.)
On 2/26/2021 7:50 PM, Henry Vanderbilt 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