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Redshift is a lengthening of wavelengths, e.g., of spectral lines, due to Doppler effects of radial motion of the radiation-source away from the observer (i.e., its recessional velocity). Given the expansion of the universe, which effectively results in higher recessional velocity at further distances, redshift is used as a measure of distance and time, and a redshift due to this is called a cosmological redshift.
Redshifts and blue shifts (for the analogous shortening of the wavelength from sources moving toward the observer) are also measured to determine radial velocity in studies of peculiar velocity and of objects orbiting stars such as extra-solar planets and binary star companions. Measurements using the highest-precision high resolution spectrography (HRS) can determine radial velocity differences as small as 1 meter per second.
The redshift parameter (often just called redshift) z is:
observed wavelength - rest wavelength z = ————————————————————————————————————— rest wavelength
The relationship between z and the recessional velocity is:
1 + v/c 1 + z = sqrt( ——————— ) 1 - v/c
Transverse motion and gravity also produce/affect redshift.
Redshift derived from absorption lines is termed absorption redshift (zabs) and from emission lines is termed emission redshift (zem). A difference between the two implies distance and/or velocity differences between the emitting and absorbing material, and can motivate some analysis to determine the "true" cosmological redshift.
If a body's redshift is determined, assuming the redshift is cosmological, a distance estimate can be calculated using the redshift and the Hubble constant (70 km/s/Mpc). Below are some calculated values. "Linear" was calculated using a simple linear approximation (workable for z less than 0.1) and "Relativistic" taking special relativity into account (the above formula), suitable for more redshifts (though for the largest redshifts, corresponding distances and times are further affected by the universe's density, calculated to be a little smaller than shown below). "Gyears" (for gigayears) is how far in the past we're viewing the body and is also its distance in billions of light-years.
z | Velocity Mpc Gyears | Velocity Mpc Gyears | excess |
0.01 | 2998km/s 43Mpc 0.1Gy | 2983km/s 43Mpc 0.1Gy | 0.50% |
0.02 | 5996km/s 86Mpc 0.3Gy | 5936km/s 85Mpc 0.3Gy | 1.01% |
0.03 | 8994km/s 128Mpc 0.4Gy | 8859km/s 127Mpc 0.4Gy | 1.52% |
0.04 | 11992km/s 171Mpc 0.6Gy | 11752km/s 168Mpc 0.5Gy | 2.04% |
0.05 | 14990km/s 214Mpc 0.7Gy | 14615km/s 209Mpc 0.7Gy | 2.56% |
0.06 | 17988km/s 257Mpc 0.8Gy | 17449km/s 249Mpc 0.8Gy | 3.09% |
0.07 | 20985km/s 300Mpc 1.0Gy | 20253km/s 289Mpc 0.9Gy | 3.62% |
0.08 | 23983km/s 343Mpc 1.1Gy | 23027km/s 329Mpc 1.1Gy | 4.15% |
0.09 | 26981km/s 385Mpc 1.3Gy | 25772km/s 368Mpc 1.2Gy | 4.69% |
0.1 | 29979km/s 428Mpc 1.4Gy | 28487km/s 407Mpc 1.3Gy | 5.24% |
0.2 | 59958km/s 857Mpc 2.8Gy | 54061km/s 772Mpc 2.5Gy | 10.91% |
0.3 | 89938km/s 1285Mpc 4.2Gy | 76898km/s 1099Mpc 3.6Gy | 16.96% |
0.4 | 119917km/s 1713Mpc 5.6Gy | 97230km/s 1389Mpc 4.5Gy | 23.33% |
0.5 | 149896km/s 2141Mpc 7.0Gy | 115305km/s 1647Mpc 5.4Gy | 30.00% |
0.6 | 179875km/s 2570Mpc 8.4Gy | 131370km/s 1877Mpc 6.1Gy | 36.92% |
0.7 | 209855km/s 2998Mpc 9.8Gy | 145658km/s 2081Mpc 6.8Gy | 44.07% |
0.8 | 239834km/s 3426Mpc 11.2Gy | 158381km/s 2263Mpc 7.4Gy | 51.43% |
0.9 | 269813km/s 3854Mpc 12.6Gy | 169731km/s 2425Mpc 7.9Gy | 58.97% |
1 | 299792km/s 4283Mpc 14.0Gy | 179875km/s 2570Mpc 8.4Gy | 66.67% |
1.5 | 449689km/s 6424Mpc 21.0Gy | 217091km/s 3101Mpc 10.1Gy | 107.14% |
2 | 599585km/s 8565Mpc 27.9Gy | 239834km/s 3426Mpc 11.2Gy | 150.00% |
3 | 899377km/s 12848Mpc 41.9Gy | 264523km/s 3779Mpc 12.3Gy | 240.00% |
4 | 1199170km/s 17131Mpc 55.9Gy | 276731km/s 3953Mpc 12.9Gy | 333.33% |
5 | 1498962km/s 21414Mpc 69.8Gy | 283587km/s 4051Mpc 13.2Gy | 428.57% |
6 | 1798755km/s 25696Mpc 83.8Gy | 287801km/s 4111Mpc 13.4Gy | 525.00% |
7 | 2098547km/s 29979Mpc 97.8Gy | 290568km/s 4151Mpc 13.5Gy | 622.22% |
8 | 2398340km/s 34262Mpc 111.7Gy | 292480km/s 4178Mpc 13.6Gy | 720.00% |
9 | 2698132km/s 38545Mpc 125.7Gy | 293856km/s 4198Mpc 13.7Gy | 818.18% |
10 | 2997925km/s 42827Mpc 139.7Gy | 294878km/s 4213Mpc 13.7Gy | 916.67% |
11 | 3297717km/s 47110Mpc 153.7Gy | 295657km/s 4224Mpc 13.8Gy | 1015.38% |
12 | 3597509km/s 51393Mpc 167.6Gy | 296265km/s 4232Mpc 13.8Gy | 1114.29% |
13 | 3897302km/s 55676Mpc 181.6Gy | 296749km/s 4239Mpc 13.8Gy | 1213.33% |
14 | 4197094km/s 59958Mpc 195.6Gy | 297139km/s 4245Mpc 13.8Gy | 1312.50% |
15 | 4496887km/s 64241Mpc 209.5Gy | 297459km/s 4249Mpc 13.9Gy | 1411.76% |
100 | 29979246km/s 428275Mpc 1396.8Gy | 299734km/s 4282Mpc 14.0Gy | 9901.96% |
1090 | 326773779km/s 4668197Mpc 15225.6Gy | 299792km/s 4283Mpc 14.0Gy | 108900.18% |
See "Distances table" for redshifts/distances to example astronomical objects and times since astronomical events.