# Could we parallax measure stars just based on the Earth's size?

Imagine two major surface observatories, perhaps the "northermost" and "southernmost" such (ideally on a similar longitude).

For nearby stars, could they each take a photo at the same time, and achieve a distance measurement to that star, based on about the size of the Earth as the baseline?

(I appreciate that either of the scopes need only wait a few days, for their viewpoint to have moved a much longer baseline distance!)

Or is that distance far too short?

What then is about the minimum baseline we could parallax-measure the nearest stars, with our currently best telescopes? 100,000km, a million? Far more?

In principle, it's not impossible.

The Gaia spacecraft, designed primarily for measuring stellar positions, is able to measure parallaxes up to 10 kpc away with 20% uncertainty. Its baseline is 2 AU; $2.3\times10^{4}$ times larger than the diameter of Earth. Thus, placing two Gaias on each side of Earth would be able to measure parallaxes of stars up to a distance of $10\,\mathrm{kpc} \,/\, 2.3\times10^{4} \simeq 0.4\,\mathrm{pc}$, meaning that you would almost be able to measure the distance of our nearest neighboring star, $\alpha$ Centauri, which lies at 1.3 pc. So you would just need improve your Gaias a little bit.

This ignores small complications such as the atmosphere, but if you're willing to put them outside the atmosphere, you could do it. Of course, it would sort of be a waste of time, since we already know the distances to the nearest stars, but hey, go ahead.

• Totally awesome dude. Nov 15 '16 at 0:26
• was hoping for alt text ;) Nov 15 '16 at 2:14
• If I'm not wrong, it should be $2.2\times 10^5$. Nov 15 '16 at 7:20
• @MartinArgerami: I did the calculation in my head, and I was actually a bit off, but it was almost correct: $2\,\mathrm{AU} \,/\, 2R_\oplus = 3\times10^{13}/1.3\times10^{9} = 2.3\times10^4$, not $\times10^5$.
– pela
Nov 15 '16 at 9:15
• I hope you didn't do the 1300 megaeuros in your head too. The ESA won't be happy about that one. Nov 16 '16 at 0:40

What you're describing is an interferometer, and in fact we already have an interferometer with a set up as you describe.

If you don't happen to know, an interferometer is a set of two or more telescopes, separated by some distance, that work in tandem to take an image of an object. By the basic principles of optics, the effective size of your telescope is governed not by the total, cumulative size of the two or more telescopes, but by the physical separation of the telescopes. That means, if you have one telescope on the north pole and another on the south pole such that they can both observe the same object at the same time, then what you effectively have is a telescope whose aperture is the size of the Earth!

If you know your optics, you'll know a larger aperture size means better resolution. The already existing, Earth-sized interferometer I alluded to above would be the Very Long Baseline Interferometer (VLBI). This telescope can measure at a sub-milli-arcsecond resolution!

Here is a list of 70 pulsars who have had their parallax measured, a good portion of which have been done using the VLBI.

Some notes:

1. The concept of interferometry is vastly complex and difficult to implement in practice. Because of the physics, the longer the wavelength, the easier it is to having working interferometric systems. As such, most interferometers such as the VLBI, are in the microwave/radio regime. The NPOI is the only optical interferometer I know of and that only exists because it is funded by the US Military as a necessity for satellites and navigation.

2. Technically, there's a lot more involved that the brief conceptual introduction I gave above but to be frank, you'll need to read an entire textbook to really understand the process and even to me some of it just seems like magic.

3. In researching the VLBI, you may see references to the VLBA. This is a related, but distinct collection of telescopes. Effectively, the VLBA is the Very Long Baseline Array which is comprised of telescopes all around the world that are owned and operated by the United States. The VLBI however includes all the telescopes within the VLBA, but also includes other telescopes owned and operated by other countries.

• Hmm; I'm not describing an interferometer! :) In a parallax measurement you just take two photos and compare the "jiggle" of the nearby star (compared to the distant background). {Regarding interferometers; optical interferometers are only a few hundred yards apart at most; radio interferometers are different.} The purpose of interferometers is to achieve very high resolution (so, separating the tiny gaps between binaries and addressing similar problems). I don't immediately see any way an interferometer could be used to take pairs of parallax photos? (Cont...) Nov 14 '16 at 22:18
• .. except in as much as, of course, you could use an interferometer like any other telescope to make a pair of parallax photos: take a photo (radiogram .. whatever) in January and then in July. So I'm not really sure if interferometers as such relate to taking parallax pair photos?? Nov 14 '16 at 22:20
• I do realize what I described it's not precisely what you're asking, but I think it effectively is. True you weren't talking about interferometers, but interferometers can be used to effectively do what you're talking about where they use the earth as the baseline (rather than the earth orbit as is the standard practice). It's not exactly what you might want but it is as close as I know of using actual techniques. Try checking out the sources in the pulsar parallax I linked. Nov 14 '16 at 22:28
• @JoeBlow this may turn out to not really answer your question but at the very least it meets the requirement of using the earth as the baseline of measuring parallax. Nov 14 '16 at 22:32

For stars, no.

It is quite actively used to determine the distance of objects within the solar system though. For example, a NEO asteroid will show a marked deflection in position between observations from the north and southern hemispheres (or even between Mainland USA and Hawaii). What helps is that the two observations can be synchronized to any arbitrary accuracy, down to milliseconds if you really have to, thus completely eliminating the time factor between observations.

For stars though? The inaccuracy caused by atmospheric interference (even with the very best adaptive optics) would limit the use of this method to objects closer than a parsec or so. Which is not much use, as very few (*) stars are that close.

(*) Zero is an instance of "very few", too.

Interesting write-up about it here: http://astro.if.ufrgs.br/clea/Ast_sm.pdf

• Fantastic information there, PcMan! A good answer after all these years. Jun 27 at 14:54