Calculate redshift from velocity, wavelength, or frequency, and estimate cosmological distances and lookback time from redshift and Hubble constant.
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Redshift to Velocity Formula
The following equation is the low-speed approximation for radial Doppler velocity. The calculator also provides the relativistic Doppler relation; neither gives a general cosmological recession speed.
- Where V is the velocity (m/s)
- Z is the redshift ratio
- C is the speed of light in vacuum, exactly 299,792,458 m/s
For small radial Doppler shifts, multiply redshift by the speed of light. The exact radial Doppler relation is v/c = ((1+z)ยฒโ1)/((1+z)ยฒ+1). Cosmological distances instead depend on the selected cosmology.
| Redshift (z) | Velocity (km/s) |
|---|---|
| 0.0001 | 29.979 |
| 0.0005 | 149.896 |
| 0.001 | 299.792 |
| 0.002 | 599.585 |
| 0.003 | 899.377 |
| 0.005 | 1,498.962 |
| 0.0075 | 2,248.443 |
| 0.01 | 2,997.925 |
| 0.015 | 4,496.887 |
| 0.02 | 5,995.849 |
| 0.03 | 8,993.774 |
| 0.04 | 11,991.698 |
| 0.05 | 14,989.623 |
| 0.06 | 17,987.547 |
| 0.075 | 22,484.434 |
| 0.08 | 23,983.397 |
| 0.09 | 26,981.321 |
| 0.1 | 29,979.246 |
| 0.2 | 59,958.492 |
| 0.3 | 89,937.737 |
| Assumes electromagnetic waves in vacuum (c = 299,792.458 km/s) and the low-velocity approximation v โ zยทc. For larger radial Doppler shifts, use the relativistic relation. For cosmological redshift, use a cosmological model instead. | |
What is a Redshift?
Definition:
Redshift is the fractional wavelength change: z = observed wavelength / rest wavelength โ 1. Positive radial Doppler redshift corresponds to recession; negative z is blueshift. Cosmological expansion and gravity can also shift light.
How to Calculate Velocity From Redshift?
Example Problem:
The following example outlines the steps and information needed to calculate velocity from redshift.
First, determine the redshift ratio. In this example, the redshift ratio is 0.01 and the low-speed approximation is used.
Next, determine the speed of the wave. For light in vacuum, use c = 299,792,458 m/s.
Finally, calculate the velocity from redshift using the formula above:
V โ Z * C
V โ 0.01 ร 299,792,458 m/s
V โ 2,997,924.58 m/s
FAQ
What is the significance of the speed of light in redshift calculations?
The speed of light, denoted as C and valued at approximately 299,792,458 meters per second, is a fundamental constant in physics. In redshift calculations, it represents the speed at which light waves travel through a vacuum. This constant is crucial for determining the velocity of distant celestial objects moving away from us, as it helps in calculating the extent of their redshift, which is approximately proportional to radial Doppler velocity only for small shifts. Cosmological redshift does not generally follow the special-relativistic velocity relation.
How does redshift provide information about the universe's expansion?
Redshift is key observational evidence for the expansion of the universe. According to Hubble's Law, objects in the universe are moving away from each other at speeds proportional to their distances. This movement causes the light emitted by these objects to stretch into longer wavelengths, a phenomenon known as redshift. With an assumed cosmological model, measured redshift constrains distance and lookback time. This calculator uses a flat matter-plus-ฮ model with radiation omitted, so high-redshift estimates have limited physical accuracy.
Can redshift be used to determine the direction of an object's motion?
In a radial Doppler interpretation, a positive redshift indicates recession. Redshift measures wavelength change, and cosmological expansion or gravity can also contribute. Conversely, blueshift indicates that an object is moving closer, as the light waves are compressed into shorter wavelengths. Therefore, while redshift and blueshift can indicate the direction of motion (away or towards, respectively), they do not provide specific directional information (e.g., north, south, east, west).
