Mysteries of the Universe : Current angular precision is about 1 milli-arcsecond

The current state of the art in angle measurement cannot even be used to measure the distance of most of the stars within our own galaxy! So astronomers have used Type 1A Supernova as standard candles to estimate distances. They then conjured up whole cosmologies around these estimated distances on the assumption that all of these stars exploded in exactly the same way. Now with many other techniques yielding diverse results, it might be because the distance estimates are largely incorrect. If they had better parallax measuring devices, they would gotten it right the first time. We would then have more confidence in their cosmological ideas.

The distance to a galaxy 14 billion light years away is taken to be the radius of a circle. Doubling it gives the diameter, and multiplying it by Pi gives the circumference. If we take the diameter of Earth's orbit to be the base of an equilateral triangle whose apex is also at the distant galaxy, then the base of this triangle can be treated as a portion of the circumference of the circle. The angle swept by the diameter of the Earth's orbit is then a fraction of the full 360 degree circle. This first swept angle a = 2.335934E-10 arc-seconds.

For a second galaxy located 100,000 light years closer, the swept angle b = 2.335950E-10 arc-seconds.

To resolve these two objects (as having different distances) requires a precision equal to the difference between the two swept angles, or 1.668536E-15 arc-seconds...

One femto-arcsecond is the required angular precision.

If they put as much effort into developing better instruments, as they have into hypothetical cosmologies, they would have better measurements by now.