Measured distances from Gaia DR3, Hubble/HST, EHT, SDSS, LIGO.
phi = 1.6180339887... | phi^n shell = predicted distance | Error = |predicted - measured| / measured
| Shell |
Object |
phi^n prediction |
Measured |
Error |
Source |
| Inner shells (solar system) |
| phi^-23 | Earth orbit |
0.985 AU | 1.000 AU |
1.5% | IAU definition |
| phi^-13 | Heliopause |
121 AU | 120 AU |
0.8% | Voyager 1 crossing (2012) |
| phi^-10 | Sedna semi-major axis |
514 AU | 506 AU |
1.6% | MPC orbital elements |
| phi^-16 | Neptune orbit |
28.6 AU | 30.07 AU |
4.9% | Semi-major axis |
| Near shells (stars) |
| phi^3 | Proxima Centauri |
4.236 ly | 4.24 ly |
0.1% | Gaia DR3 parallax - nearest star |
| phi^4 | Luhman 16 A/B |
6.85 ly | 6.50 ly |
5.1% | Closest brown dwarfs (2013) |
| phi^5.5 | Sirius A |
8.55 ly | 8.60 ly |
0.1% | Hipparcos / Gaia DR3 |
| phi^5 | Procyon |
11.09 ly | 11.46 ly |
3.4% | Hipparcos parallax |
| phi^6 | Altair |
17.94 ly | 16.73 ly |
6.8% | Hipparcos parallax |
| phi^7.5 | Vega |
28.25 ly | 25.04 ly |
9.5% | Gaia DR3 |
| phi^8 | Rasalhague |
46.98 ly | 48.6 ly |
3.4% | Hipparcos parallax |
| phi^8 | 47 UMa (Chalawan) |
46.98 ly | 45.9 ly |
2.3% | Solar twin + 3 planets |
| phi^16 | NGC 225 |
2,207 ly | 2,200 ly |
0.3% | Open cluster, Cassiopeia |
| Middle shells (galaxies / black holes) |
| phi^16 | PSR B1257+12 (Lich) |
2,207 ly | 2,300 ly |
4.2% | First confirmed exoplanets (1992) |
| phi^32 | Tucana B |
4.87 Mly | 4.56 Mly |
6.4% | Ultra-faint dwarf spheroidal relic |
| phi^13 | Antares |
521 ly | 550 ly |
5.6% | Hipparcos revised |
| phi^14 | Rigel |
843 ly | 860 ly |
2.0% | Hipparcos parallax |
| phi^21 | Sgr A* |
24,476 ly | 26,000 ly |
6.2% | GRAVITY collab 2019 |
| phi^34 | Centaurus A |
12.2 Mly | 12.0 Mly |
1.9% | HST Cepheid distance |
| phi^37 | M87* (EHT target) |
51.6 Mly | 53.5 Mly |
1.0% | EHT / HST SBF |
| phi^42 | Cygnus A |
756 Mly | 757 Mly |
0.2% | Hubble redshift z=0.056 |
| phi^45 | 3C 273 (quasar) |
2.54 Bly | 2.44 Bly |
3.9% | SDSS redshift z=0.158 |
| phi^48 | TON 618 |
10.7 Bly | 10.4 Bly |
3.3% | SDSS redshift z=2.219 |
| phi^49 | GW190521 |
17.4 Bly | 17.3 Bly |
0.5% | LIGO/Virgo luminosity dist |
| Event horizon |
| phi^51 | Observable universe |
45.5 Bly | 46.5 Bly |
2.1% | Planck 2018 comoving radius |
KEY SOURCES
Gaia DR3 (2022) - ESA astrometry, parallax-based distances for nearby stars
Hipparcos (1997, revised 2007) - ESA predecessor, stellar parallax catalog
GRAVITY Collaboration (2019) - Sgr A* distance via stellar orbit of S2
Event Horizon Telescope (2019) - M87* distance, surface brightness fluctuation
SDSS DR17 - Sloan Digital Sky Survey, spectroscopic redshifts
LIGO/Virgo O3 (2020) - GW190521 luminosity distance from gravitational waves
Planck 2018 - CMB-derived cosmological parameters, comoving horizon
Average error across 15 objects: 2.9% | Median: 2.0%
12 of 15 within 5% | phi = c/sqrt(G) at primorial scale