๐ Physical Cosmology & Metric Expansion of Space
Cosmological Redshift & Hubble's Law Calculator
Compute galactic recession velocity ($v = H_0 d$), relativistic cosmological redshift ($z$), scale factor ($a = \frac{1}{1+z}$), and lookback cosmic time for deep sky objects.
๐ Virgo Cluster ($z = 0.0038$)
๐ Coma Galaxy Cluster ($z = 0.023$)
โก Quasar 3C 273 ($z = 0.158$)
๐ญ Deep Space ($z = 1.0$)
โจ JWST Earliest Galaxy ($z = 14.3$)
Cosmological Parameters
km/s / Mpc
Planck 2018 โ 67.4, SH0ES HST โ 73.0, Standard = 70.0
Recession Velocity (v)
14,625 km/s (0.0488 c)
Scale Factor ($a$)
0.9524
a = 1 / (1 + z)
Lookback Time
678 Million Yrs
Wavelength Stretch
+5.00% Longer
๐ก Relativistic Doppler Conversion:
$$v = c \frac{(1+z)^2 - 1}{(1+z)^2 + 1} = 14,625\text{ km/s} \implies d = \frac{v}{H_0} = \frac{14625}{70} = 208.9\text{ Mpc}$$
Hubble's Law & The Expanding Universe
Edwin Hubble discovered that galaxies recede with velocities proportional to distance:
- Linear Hubble Law: $$v = H_0 \cdot d$$
- Relativistic Velocity from Redshift: $$v = c \cdot \frac{(1+z)^2 - 1}{(1+z)^2 + 1}$$
- Cosmic Scale Factor ($a$): $$a(t) = \frac{1}{1 + z}$$ (At $z = 1$, the universe was half its current physical size).