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This is somewhat of a follow-up to When was the parallax of a star first measured? Once the distance to the nearest stars was determined, it was possible to discover physical properties of stars (such as the relation between intrinsic luminosity and color, or the relation between luminosity and period for Cepheid variables), then use the knowledge of those physical properties to find the distance of stars with no visible parallax.

When was the distance to a star (other than the Sun) determined for the first time with a method other than parallax?

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  • $\begingroup$ I made a small edit that takes advantage of a Stack Exchange feature. Please feel free to roll back or edit further if it conflicts with your intention. $\endgroup$
    – uhoh
    Nov 10 '20 at 0:01
  • $\begingroup$ Will you allow for answers that provide distance determinations and/or distance estimates, or should they qualify as actual measurements? I don't actually know how to define the distinction exactly, but I suppose it depends on how much modeling is required. Parallax is an angular measurement, and distance is inferred through a model of Earth's orbit around the Sun as well as an assumption that there are no other period 1 year motions of the Sun. Those are pretty solid assumptions. $\endgroup$
    – uhoh
    Nov 10 '20 at 0:05
  • $\begingroup$ Models of stellar luminosity or variability are much more involved; would you allow distance determinations based on those to be called "measurements" as well? $\endgroup$
    – uhoh
    Nov 10 '20 at 0:05
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    $\begingroup$ @uhoh I guess "determinations" would be a better term for what I intend. $\endgroup$
    – usernumber
    Nov 10 '20 at 7:56
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    $\begingroup$ People assumed that stars were like the Sun and estimated distance well before parallaxes were measured. $\endgroup$
    – ProfRob
    Nov 10 '20 at 8:03
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Henrietta Swan Levitt was the first person to develop the "standard candle" technique for measuring the distance to stars, while studying Cepheid variables around 1912-1913.

Of course, the standard candle technique just extends the parallax technique to farther distances; in order to figure out how bright Cepheid variables are, Levitt had to know the parallax distances to enough of them to fit their brightness and period on a logarithmic curve. (Levitt's Law) To this day there are still no ways to measure the distances to stars that do not ultimately rely on parallax measurements.

However, we can make completely independent measurements of the distance to gravitational wave events. Their "absolute brightness" depends solely on their mass, and their mass can be calculated from their waveform. A few things like orientation, redshift, gravitational lensing etc make this more complicated, but theorists have been able to correct for most of the confounding factors. More info: https://physicstoday.scitation.org/doi/10.1063/PT.3.4090

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  • $\begingroup$ We know the distance to the Sun and it's luminosity, independently of parallax. The distance to any star could be estimated by assuming it was similar to the Sun. $\endgroup$
    – ProfRob
    Nov 13 '20 at 7:39
  • $\begingroup$ We learned the distance to the sun by observing a transit of Venus from two different points on earth - so it all comes back to parallax. en.wikipedia.org/wiki/… $\endgroup$
    – dieki
    Nov 13 '20 at 11:57
  • $\begingroup$ Also, stars vary by a factor of over 100,000,000 in brightness, so this doesn't help you tell a distant bright star from a close dim star. And until we knew how far away the stars were, we had no reason to assume they were the same brightness as the sun. $\endgroup$
    – dieki
    Nov 13 '20 at 12:00
  • $\begingroup$ I take issue with your comment that all distances are ultimately based on parallax. The astronomical unit is now based on radar distance measurements, not the parallax of Venus. Indeed many stars are very different to the Sun, which is why earlier estimates of the distances to stars were often erroneous. That does not mean that they were not estimated and Steve Linton provides an example. $\endgroup$
    – ProfRob
    Nov 13 '20 at 13:00
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From Wikipedia

In his 1698 book, Cosmotheoros, Christiaan Huygens estimated the distance to Sirius at 27664 times the distance from the Earth to the Sun (about 0.437 light years, translating to a parallax of roughly 7.5 arcseconds).

and

It was also in this book that Huygens published his method for estimating stellar distances. He made a series of smaller holes in a screen facing the Sun, until he estimated the light was of the same intensity as that of the star Sirius. He then calculated that the angle of this hole was {\displaystyle 1/27,664}1/27,664th the diameter of the Sun, and thus it was about 30,000 times as far away, on the (incorrect) assumption that Sirius is as luminous as the Sun. The subject of photometry remained in its infancy until the time of Pierre Bouguer and Johann Heinrich Lambert.[124]

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