A comment under When was the distance to a star measured for the first time without using parallax? mentions that the distance to stars was measured before parallax was possible. How was this done?
As far as I know direct parallax measurements are the only way to directly measure the distances to stars.
Once parallaxs of hundreds of stars were known and diagrams of the relationship between stellar luminosity and spectral types, such as the Hertzsrpung-Russel diagram, were made, it became possible to estimate a star's absolute magnitude more or less accurately and thus calculate its distance from its apparent magnitude.
It may be noted that stars in some spectral types can have any one of up to nine luminosity classes. A star's luminosity class is included as Roman numerals in its spectral classification if it is known. Calculating the distance to a star without knowing its luminosity class can be very inaccurate.
The heliocentric theory, that the Earth revolves around the Sun, was first suggested in classical Greece. Aristotle (384-322 BC) rejected that theory, because of the lack of detectable stellar parallax caused by Earth's motion around the Sun.
Exploration of the Universe Brief Edition, George Abell, 1964, 1969, page 18.
That same argument was used against the heliocentric theory in the early modern age.
Stellar parallax is so small that it was unobservable until the 19th century, and its apparent absence was used as a scientific argument against heliocentrism during the early modern age. It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons, such gigantic distances involved seemed entirely implausible: it was one of Tycho Brahe's principal objections to Copernican heliocentrism that for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere (the fixed stars).2
As astronomers gradually accepted the heiocentric theory after about 1600, there were attempts to meaure stellar parallaxes which ended in failure after failure. And each astronomer who failed to measure stellar parallax could have calculated the smallest stellar parallax he could have measured, and thus the distance that the star(s) he studied must have exceeded. So astronomers should have gradually increased their estimates of the minimum possible distances to various stars whose parallaxes had failed to be measured, while perhaps hoping that some stars might possibly be a lot closer.
And as the distance between the Sun and the Earth was repeatedly measured more and more accurately, astronomers could have estimated the Sun's luminosity more and more accurately. By assuming that any particular star was as luminous as the Sun, and by measuring its apparant magnitude, astronomers could have estimated how far away it was.
But of course the actual luminosities of stars vary greatly, and in the 17th and 18th centuries measurements of the apparent brightness of the Sun and of distant stars would probably have been very inaccurate.
I doubt if any estimates of the distances to stars were very accurate before the first stellar parallaxes were measured in the 1830s, because the first measured parallaxes seemed too small, and thus the distances too great, for astronomers to believe.
For example, the first actual measurement of a stellar parallax was made by Thomas Henderson, but his is usually listed as the second measurement.
The large proper motion of Alpha Centauri AB was discovered by Manuel John Johnson, observing from Saint Helena, who informed Thomas Henderson at the Royal Observatory, Cape of Good Hope of it. The parallax of Alpha Centauri was subsequently determined by Henderson from many exacting positional observations of the AB system between April 1832 and May 1833. He withheld his results, however, because he suspected they were too large to be true, but eventually published them in 1839 after Friedrich Wilhelm Bessel released his own accurately determined parallax for 61 Cygni in 1838. For this reason, Alpha Centauri is sometimes considered as the second star to have its distance measured because Henderson's work was not fully acknowledged at first.[62)
The distance to Vega can be determined by measuring its parallax shift against the background stars as the Earth orbits the Sun. The first person to publish a star's parallax was Friedrich G. W. von Struve, when he announced a value of 0.125 arcseconds (0.125″) for Vega. Friedrich Bessel was skeptical about Struve's data, and, when Bessel published a parallax of 0.314″ for the star system 61 Cygni, Struve revised his value for Vega's parallax to nearly double the original estimate. This change cast further doubt on Struve's data. Thus most astronomers at the time, including Struve, credited Bessel with the first published parallax result. However, Struve's initial result was actually close to the currently accepted value of 0.129″, as determined by the Hipparcos astrometry satellite.
So Henderson and Struve suffered failures of nerve, being unable to accept how distanct Alpha Centauri and Vega were according to their measurements, and so lost the honor of making the first measurement of stellar parallaxes to Bessel.
And in my opinion that would not have happened if astronomers of the time commonly accepted that even the nearest stars must be several hundred thosuand Astronomical Units, and multiples of light years and parsecs (units which had not yet been invented) from the Sun.
So any estimates of the distances to stars made before the first successful parallax measurements probably greatly underestimated the distances.
I'm not looking stuff up to write this so any inaccuracies are secondary to my feeble 63 year old memory yet again betraying me.
In A Treatise on the System of The World. (His own Principia for Dummies which was published posthumously because he didn’t want to give his critics and those that wanted to dispute the new science ammunition against him) Newton calculated the distance to Sirius, which he assumed had the same intrinsic luminosity as the Sun, by comparing its luminosity to that of Saturn which he guessed correctly had an albedo of .5. He got a result of some few light years, which, being the correct order of magnitude for nearby stars, should be considered a brilliant and very insightful calculation.
Euler must have made a similar calculation, in his Letters to a German Princess on Different Subjects in Natural Philosophy, written some time in the 1700’s, in the middle of a discussion about luminosity and distance he gives an estimate of a typical distance to a nearby star of 6 light years and of a more distant, dimmer star of, some 100 light years.
Huygens did a similar calculation to the one that Newton did. In fact I think most of those guys back then did some such calculation.
I recall reading about some guy who blackened a chamber all except for one tiny pin hole which faced the sun and which he varied until it looked about the brightness of a bright star. He then measured the diameter of the pin hole to figure out what fraction of the luminosity of the sun it had. As I recall he also got a distance of some few light years for a nearby star. That might have been Newton or Huygens also. I don’t remember.
Hooke claimed to have measured the parallax a star, what he had actually done was shown that they had to be at least a light year or two away. His telescope design, while very clever, did not have the precision needed to actually measure the distance to a star. It gave a lower bound to the distance of a star...
Before actual parallax measurements in the early 19th century they had a pretty good idea of a rough estimate of how far away nearby stars are but they were of course anxious to get an actual measurement.