This has got to be one of most inept attempts made by YECists in showing the Sun and solar system are compatible with YEC time scales.
There are many examples of evidence which the show Sun and solar system are orbiting the galaxy's center and not spiralling towards it.
One such case goes back to the 18th century before astronomers even knew our Sun resides in a galaxy let alone a spiral.
William Herschel observed there is a point in space in the constellation Hercules where neighbouring stars are diverging indicating the Sun and solar system are moving towards that point known as the solar apex.
In the opposite direction 180 degrees apart there is a divergence in the constellation Columba known as the solar antapex in which the Sun and solar system are moving away from.
Astronomers subsequently found this observed relative motion was due to two factors, the proper motion of the neighbouring stars and the Sun and solar system's orbital motion around the galaxy's centre. Furthermore they found when using the galaxy centre frame of reference instead of the neighbouring star's frame of reference, they found the Sun and solar system are moving towards and way in the constellations of Cygnus and Vela/Puppis respectively.
Now if the Sun and solar system were instead spiralling towards the centre along with all other stars there would be no solar apex and solar antapex but using the galaxy centre frame of reference it would be moving towards the point where galaxy's centre is located in Sagittarius and away from a point in Auriga/Taurus.
Here is a table to summarize these points.
| Feature | Reality (Circular Orbit) | Hypothetical (Coherent Infall) |
|---|
| Primary motion | Nearly circular orbit around Galactic Centre | Radial spiral inward toward Galactic Centre |
| Sun’s motion relative to nearby stars (LSR) | Non-zero (~20 km/s) | Zero |
| Solar apex (relative to nearby stars) | Exists | Does not exist |
| Solar apex constellation | Hercules (near Vega) | N/A |
| Solar antapex constellation | Columba | N/A |
| Sun’s motion relative to Galactic Centre | Tangential (orbital) | Radial inward |
| Galactocentric apex (direction of motion) | Cygnus (approx.) | Sagittarius |
| Galactocentric antapex | Vela / Puppis (approx.) | Auriga / Taurus |
| Key implication | Apex measures peculiar motion | Solar apex disappears; only galactocentric direction remains |