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Comment by perihelions | Hacker News Reader

The really neat part is the instrument precision. It's terrifyingly good and I have no idea how it (really) works.

- "Gaia measures their positions to an accuracy of 24 microarcseconds, comparable to measuring the diameter of a human hair at a distance of 1000 km"

https://www.esa.int/Science_Exploration/Space_Science/Gaia/C...

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To nitpick with the grammar in the quote: It's capable of measuring to the accuracy of 120 μm at 1000 km. So it cannot accurately measure the diameter of a human hair (which ranges from around 20 to 200 μm) at that distance, but only to the accuracy of a human hair.

You're right: this precision is hundreds of times below the diffraction limit of even the James Webb telescope. It can't possibly measure the width of an object that finely; rather, only the relative displacement of its centroid position between two points in time. (And it's a seriously confusing physics miracle that that much is possible).

For point source astrometry, there are a few ways to beat the diffraction limit. For instance, some observers will purposely defocus their optics to spread the target photons over a larger number of pixels, which with sufficient SNR lets you gain a better lower bound (from a Cramer Rao perspective) on precision. I think Gaia actually does something similar to this but “blurs” through time, rather than across space, by purposely not perfectly tracking stars so that they drift at sub-pixel rates across the FPA.

Yes, Gaia slowly spins to that the stars move across its CCD array.

It takes about 14 pictures of each star during orbit (which is quite close to Earth’s orbit around the Sun), so approximately once per month, and then compares those to calculate the star’s distance from the parallax.

Isn't that just the distance between pixels and the image projected onto them?

No: it's far weirder and I'm not knowledgeable enough to explain it.

Probably not. The accuracy with which you know the pointing of the telescope probably also plays into it (unless the FOV is large enough to have other stars as a reference?), and you can do subpixel positioning of objects to get more accuracy than full pixel steps.

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