Long-baseline stellar(?) parallax

[fnord]

I was reading the Navigation in Space library thread and the following got me thinking a little:

But above all else, these stars' position must be known very very accurately. Our measurements of the distance to remote stars is (today) uncertain by hundreds of light years; if we had to start doing deep-space navigation with a fast FTL drive that could cause a lot of problems. Fortunately, one of the first things you can do with advanced space flight is send off the equivalent of the Hubble Space Telescope on a fast engine, move it a light-month or two away, and take a comprehensive picture of the sky... which gives you a long parallax baseline and lets you measure the distance to distant stars much more accurately. If we had an observatory somewhere out in the Oort Cloud, we could work out the distance to distant bright stars like Rigel to within a small fraction of a percent without much trouble.

Form what I understand (astronomers and people who know more than me please correct me) the limits on direct stellar parallax are:
1 - Detection. If we can't detect a star, we can't determine its parallax and from that, distance.
2 - Angular precision
3 - Baseline length (currently 2 AU for Earth's orbit).

For a baseline (BAD PUN!), I'll use the Hubble Telescope's Wide Field Camera 3, whose angular capabilities are reported(?) here and quoted below:

Riess and the Johns Hopkins University in Baltimore, Md., in collaboration with Stefano Casertano of STScI, developed a technique to use Hubble to make measurements as small as five-billionths of a degree.

Assuming I haven't buggered up my maths, with 3.6 billion microarcseconds in a degree, that gives a (bloody small) angle of 0.72 microarcseconds, which for moment I'll use as angular precision. Combining that with taking Simon's "small fraction of a percent" as upper bounding the parallax error by 0.5%, that would mean a parallax angle of 144 +/- 0.72 microarcseconds, or maximum distance discernible by parallax given those limits of ~6,900 pc.

I'll take 30 light days between each of them flanking Sol as the new baseline for Simon's pair of observatories out woop woop way, for a total baseline of ~10,800 AU, or 5400x the current baseline. Assuming all else equal, that would mean our 6900 pc distant star would now subtend a parallax angle of 777.6 milliarcsec +/- 0.00072 milliarcsec, for a relative angular error of ~1e-6, or three fifths of one tenth of bugger all.

The upper distance limit to give the same relative angular error would similarly be multiplied, to give 37.26 Mpc, good to within half a percent.

I've ignored the engineering issues of getting the Jester Deep Oort Cloud Observatories communicating with the 3rd rock from Sol, spatial expansion over that distance, etc etc, unlimited rice pudding for all. I am definitely leaving aperture synthesis between JDOCO 1 and JDOCO 0 as an engineering exercise for the reader.

With that meaning we could then, in principle, directly range by "stellar" parallax the vast bulk of everything detectable in the Virgo Supercluster, what the hell would count as "distant" stars?

[Borgholio]

Well if you have a long enough baseline, you can measure anything by parallax. What counts as distance would then probably be variable, based on the point where you can no longer measure the parallax.

[Eternal_Freedom]

At a glance those numbers sound about right. Though I can think of an additional use for this deep Oort Cloud Observatory. Set them up for interferometry, which is a way of combining data from two telescopes so that your image is effectively taken by a telescope equal in size to the distance between the two scopes. In this case that's be ten thousand AU. Damn.

[fnord]

That's great to hear that I'm not barking up completely wrong tree from an actual astronomer. So taking baseline out from 60 light days to 2 light years to flank the Oort cloud (Jester Trans Oort Cloud Observatories?), a ~12x increase, would increase the maximum usable distance by ~12x as well, getting into a nontrivial fraction of a gigaparsec?

What sort of practical concerns would have to be tackled to enable interferometry across 60 light days with lightspeed comms? Observatories with Frickin' Laser Beams?

I'm asking because I've heard that time synchronisation to enable accurate playback of recorded raw data is a major concern with interferometers spread out over merely thousands of km - I can't see that concern lessening as distance scales up.

[Eternal_Freedom]

i said it's a cursory glance, I'd have to run the numbers to be sure, and it's been a while since I've done any parallax calcs. I'd have to dig my notes out from whatever corner of my old hard drive they lurk on these days.

Synchronizing the timing would be difficult. You'd have to run a lot of tests beforehand to work out exactly what the transmission lag is to both telescopes, then you'd have to set a very accurate time-delay when sending the command to start taking pictures. It could probably be done but you'd need some wickedly accurate atomic clocks. And you'd need corrections for being so far up the Sun's gravity well too.

[Simon_Jester]

At a glance those numbers sound about right. Though I can think of an additional use for this deep Oort Cloud Observatory. Set them up for interferometry, which is a way of combining data from two telescopes so that your image is effectively taken by a telescope equal in size to the distance between the two scopes. In this case that's be ten thousand AU. Damn.

There are, I think, some limitations to that- if nothing else because while your system may theoretically have the resolution of a telescope ten thousand AU across (that is, about 10^15 meters wide), it wouldn't have anything like the light gathering capability of a telescope 10^15 meters wide.

So you'd have, naively and this is a rough estimate, 10^30 times more pixels in your image of a distant galaxy... but you would probably have less than one photon per pixel if you took the picture over a reasonable exposure time. And pixels that don't "catch" any photons are useless for image purposes.

What sort of practical concerns would have to be tackled to enable interferometry across 60 light days with lightspeed comms? Observatories with Frickin' Laser Beams?

I... honestly don't think you could do it. I mean, if you can do optical interferometry over ten thousand kilometers' distance, it's believable that you could do radio interferometry over ten trillion kilometers, because radio waves have a wavelength about a billion times longer than visible light. Roughly.

But that's about it, I suspect.

i said it's a cursory glance, I'd have to run the numbers to be sure, and it's been a while since I've done any parallax calcs. I'd have to dig my notes out from whatever corner of my old hard drive they lurk on these days.

Synchronizing the timing would be difficult. You'd have to run a lot of tests beforehand to work out exactly what the transmission lag is to both telescopes, then you'd have to set a very accurate time-delay when sending the command to start taking pictures. It could probably be done but you'd need some wickedly accurate atomic clocks. And you'd need corrections for being so far up the Sun's gravity well too.

Plus, it would be difficult to establish the positions of the observatories aren't "drifting" over time. If taking a single distance measurement between two objects takes sixty days, then taking enough distance measurements to determine "we're drifting apart at a rate of one millimeter per second" is going to take freaking forever.

[Borgholio]

I think the most practical limit for an interferometer is a few AU across. Synchronizing several telescopes which are only one light-hour or so apart would be substantially easier than doing it 60 light DAYS apart. And as Simon noted, you'd need to have more than just two telescopes. The VLA in New Mexico can be spread out to simulate a single receiver over 20 miles in diameter, but it has nearly 30 dishes...not just two or three. A proper space-based interferometer would have dozens of individual units, possibly hundreds if you're talking 60 light days apart. Synchronizing a couple hundred dishes is going to be a complete nightmare.

[Eternal_Freedom]

At a glance those numbers sound about right. Though I can think of an additional use for this deep Oort Cloud Observatory. Set them up for interferometry, which is a way of combining data from two telescopes so that your image is effectively taken by a telescope equal in size to the distance between the two scopes. In this case that's be ten thousand AU. Damn.

There are, I think, some limitations to that- if nothing else because while your system may theoretically have the resolution of a telescope ten thousand AU across (that is, about 10^15 meters wide), it wouldn't have anything like the light gathering capability of a telescope 10^15 meters wide.

So you'd have, naively and this is a rough estimate, 10^30 times more pixels in your image of a distant galaxy... but you would probably have less than one photon per pixel if you took the picture over a reasonable exposure time. And pixels that don't "catch" any photons are useless for image purposes.

I knew there was a catch with interferometry.

i said it's a cursory glance, I'd have to run the numbers to be sure, and it's been a while since I've done any parallax calcs. I'd have to dig my notes out from whatever corner of my old hard drive they lurk on these days.

Synchronizing the timing would be difficult. You'd have to run a lot of tests beforehand to work out exactly what the transmission lag is to both telescopes, then you'd have to set a very accurate time-delay when sending the command to start taking pictures. It could probably be done but you'd need some wickedly accurate atomic clocks. And you'd need corrections for being so far up the Sun's gravity well too.

Plus, it would be difficult to establish the positions of the observatories aren't "drifting" over time. If taking a single distance measurement between two objects takes sixty days, then taking enough distance measurements to determine "we're drifting apart at a rate of one millimeter per second" is going to take freaking forever.

That's true. And any more active system needs power and fuel, and you can't use solar panels out in the bloody Oort cloud. I know for this idea we had a magical sublight drive to get them out there in reasonable time (and presumably slow them down to station-keeping, relative to the Sun) but adding more weight and more power demands on something that has to be self-contained is a losing proposition.

So, if we aren't allowing a practical FTL drive in this scenario, you'd need at least FTL comms to be able to sync the telescopes properly. A suitable on-board power source woudl be needed as well.

And since the magic-sublight-drive has to slow them down again once they get to their destination, you might as well go the whole hog and build a long-duration spaceship for the mission and send the astronomers out for the ride.