Not all distance measurements depends on the heliocentric model.
Stellar parallax would also happen in a geocentric universe, but it still allows for distance calculations due to the parallax.
Redshift of starlight also works.
There are more methods which are quite interesting, perhaps you want to look them up.
Once stellar parallax was found and said to be a heliocentric fact, they then claimed the distance between the Earth and these near stars showing annual parallax could be measured for certain. Using a non-proven heliocentric parallax, angles can be measured. This way, they say, the distance between the earth and a near star can be calculated geometrically. The 149.5 times 1,000,000 km semimajor axis of the Earth’s orbit provides a base line for trigonometrically determining the distance of these near stars. This method, they claim, can measure stars up to 400 light years away. In the geocentric system, with the rotating universe showing stellar parallax, there are no such angles with the sun to calculate distances. So, only if a heliocentric solar-system was proven could we say the up to 400 light-year distances of stars can be known.
As for the distance of further stars, well, here is what the experts tell us:
‘There is no direct method currently available to measure the distance to stars farther than [their unproven parallax] 400 light years from Earth, so astronomers instead use brightness measurements. It turns out that a star's color spectrum is a good indication of its actual brightness. The relationship between color and brightness was proven using the several thousand stars close enough to earth to have their distances measured directly. Astronomers can therefore look at a distant star and determine its color spectrum. From the color, they can determine the star’s actual brightness. By knowing the actual brightness and comparing it to the apparent brightness seen from Earth they can determine the distance to the star.’ --- (Howstuffworks website)
Star distances then remain unproven, a fact that makes Einstein’s space-time as a scientific fact redundant before he was born. Here again we have a case of trying to confirm something from a consequent when there are different movements that can cause such a consequent. That is like saying because an eclipse of the sun causes dark streets, then dark streets prove there is an eclipse of the sun.
The search for stellar parallax also assumes astronomers can tell whether a star is a near star or a far star. Now search as much as you like and you will not find anything specific. It seems modern cosmologists decide such nearness and farness by using yet another assumption; that near stars are brighter than far stars, which I suppose will be correct in most cases. The possibility that their brighter near-stars are actually far-stars that are intrinsically bigger and more brilliantly lit, and that their fainter far-stars are actually nearer stars that are intrinsically smaller or less illuminated seems not to have bothered them. What, just for argument’s sake, if many visible stars reside at around the same distance from Earth, bright ones and faint ones together, just like different wattage bulbs attached to the roof of a large dark theatre? There are many possibilities that could explain why some bright stars and faint stars are not near stars or far stars. We throw this in just to show how presumptuous this science can be.