Separate common calibration from scatter

Compare galaxy spectra, distance and expansion evidence

Fictional controlled comparisons · separate historical observations · Six original fictional records with artificial vacuum references. Low-redshift cz is a proxy, not an exact cosmological speed. Distance and peculiar-motion bounds are stipulated feasible ranges, not confidence intervals. A separate historical observed panel preserves all 24 raw Hubble 1929 Table 1 records. Neither fit is a current H0 estimate; Hubble time is not cosmic age.

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A galaxy is a gravitationally bound system of stars and other matter. Disk galaxies can include a central bulge and an extended halo; gas, dust and stellar populations need not share the same shape. Smooth elliptical and irregular appearances also occur. A viewing angle can change the appearance of one object without changing its physical identity. These schematic regions do not establish a galaxy's distance, age, stellar count or dark-matter distribution.

Try sketching the same disk from two directions, then list what a picture alone cannot determine. Morphological categories are not a universal evolutionary sequence. The NASA galaxy overview supplies background; the drawings here are original teaching constructions.

Controlled experiment: six fictional records

Selected D: Irregular. Appearance is supplied, not classified by the browser. All six records are original teaching cases. Selecting one highlights its evidence; it does not change the sample. The separate historical panel below supplies actual published observations.

The independent-method model distance is 40.00 Mpc and angular diameter is 15 arcseconds. With the small-angle local approximation, projected diameter is 2.90888 kpc. Mpc means million parsecs; kpc means thousand parsecs. One arcsecond is 1/3600 of a degree. These deliberately equal-size examples do not establish a real standard ruler.

Consistent virtual-line shifts under the selected calibration; fictional local approximation. Accepted common z: 0.010006923; accepted cz proxy: 3000.000 km/s. The 10⁻¹⁰ consistency tolerance suppresses arithmetic noise in exact constructed lines; it is not instrument precision or a confidence interval.

Descriptive slope H = 70.61856 km/s/Mpc. The calculation minimizes unweighted squared proxy residuals while forcing zero intercept. It is not an errors-in-variables analysis or a modern H₀ estimate. Wider bounds leave the central fit unchanged; multiplying all distances by 1.2 lowers the fitted slope by 1/1.2. A calibration change is not a new independent sample.

Connect the local approximation and conditional bounds

For each identified virtual feature, z = λused/λreference − 1. Multiplying by c = 299792.458 km/s expresses redshift as a proxy cz. The approximation cz ≈ Hd + u includes a prescribed line-of-sight peculiar-motion term u. It omits relativistic cross terms and distinctions between distance definitions. Neither cz as a speed nor cz/H as a distance is generally valid at high redshift without more cosmological assumptions.

The fitted slope is Σ(d × cz)/Σd²; Σ means add over all six records. The stated distance bounds and |u| ≤ 300 km/s give, for these positive proxies, Hlow = max(0, (cz − 300)/dhigh) and Hhigh = (cz + 300)/dlow. This is compatibility with rectangular assumptions and H ≥ 0, not a probability statement. No observational error bars are inferred from decimal precision.

Projected diameter in kpc ≈ 1000 × distance in Mpc × angular diameter in arcseconds / 206264.806. This uses the small-angle approximation and local angular-diameter distance. The distance and angular-size calculation remains available even when spectral inference fails.

For purely cosmological redshift of comoving sources, 1 + zcos = aobserve/aemit, where a is cosmic scale factor. A measured redshift may contain peculiar motion and other contributions, so this exercise's mixed proxy does not uniquely measure that scale-factor ratio.

Inspect how the fictional sample was constructed

The six central proxies were prescribed as 70 × distance plus offsets −300, +300, −300, +200, −200 and +200 km/s. These offsets are not random draws or population statistics. The model distances were supplied independently of the resulting proxies. Artificial references at 400, 500 and 600 nm are multiplied by 1 + z, then a +2 nm instrument offset is added. All six angular sizes were chosen to give the same nominal projected diameter. These choices teach controlled comparisons; they do not measure real expansion.

Observed reference: Hubble's 1929 Table 1

These 24 published historical distance–velocity pairs are observations, separate from the fictional calibration experiment. Its controls do not alter this panel. Distances use the obsolete historical calibration; velocities are the table's measured values before the fitted solar-motion correction used in the paper's Figure 1. These descriptive fits are neither a reproduction of that corrected figure nor a modern expansion measurement.

The full sample remains the default evidence. The four common-distance objects are not automatically four independent distance calibrations. The disclosed omission is a sensitivity comparison, not a way to choose a preferred result. Neither fit models distance error, sample selection or the author's solar-motion solution.

Reproduce the historical arithmetic and provenance

For distance r and velocity v, the through-origin descriptive slope is Σrv / Σr². Here n = 24, Σr = 21.873, Σv = 8955, Σr² = 29.517795 and Σrv = 12513.695. Each Σ means add over all rows. Dividing 12513.695 by 29.517795 gives about 423.9373. A free-intercept line also estimates where the line crosses the velocity axis; changing that assumption changes its slope.

Table 1 used stellar/luminosity distance criteria; Table 2 instead inferred distances from velocity and is excluded. Using the latter to verify the same velocity–distance relation would be circular. The table is not a random, volume-complete survey. Scatter and missing individual error estimates limit inference.

Primary scan, printed page 169 · Original paper DOI. Retrieved 2026-10-26. The numerical transcription preserves every row and sign; normalized identifiers replace historical typography. Local record SHA-256: c7d41a68838eec76e7bcb539c77f2db39a28aa304cd8d376b86abce84c746ff5.

Calculate Hubble time without claiming cosmic age

For a hypothetical present rate of 70 km/s/Mpc, 1/H corresponds to 13.96846 Gyr using 1 Mpc = 3.085677581491367 × 10¹⁹ km and a Julian year of 31557600 seconds. This is Hubble time, not the age of the universe. A present rate does not determine the past expansion history. Neither these six fictional cases nor the historical table establishes dark energy, a cosmic edge, a privileged center or the entire Big Bang model.

For scale-factor and distance definitions, see Hogg's redshift derivation. Bound galaxies and solar systems do not simply grow according to the background expansion relation.

Fictional six-record descriptive slope 70.6186 km/s/Mpc; selected galaxy D has z=0.0100069.

Consistent virtual-line shifts under the selected calibration; fictional local approximation. Independent-distance angular-size estimate 2.9089 kpc. Historical observations are a separate fixed dataset; uncertainty envelopes are conditional, not probabilities.