Redshift Calculator

What Is Cosmological Redshift?

Redshift measures how much the wavelength of light from a distant object has stretched during its journey through expanding space. A positive redshift means the source is moving away from the observer. Astronomers use redshift to estimate distance and recession speed.

Redshift Formulas

Redshift from observed and emitted wavelengths:

$$z = \frac{\lambda_{\text{obs}} - \lambda_{\text{emit}}}{\lambda_{\text{emit}}}$$

For small redshifts, recessional velocity approximates:

$$v = c \times z$$

Hubble's law relates recession velocity to distance:

$$d = \frac{v}{H_0}$$

where $H_0$ is the Hubble constant, typically about 70 km/s/Mpc.

Applications in Astronomy

Spectral lines from galaxies shift toward longer wavelengths as space expands. Higher redshift means greater distance and younger light. The tool uses the non-relativistic approximation valid for $z \ll 1$.

Frequently Asked Questions

What does a redshift of 0.02 mean?

A redshift of 0.02 means the observed wavelength is 2% longer than the emitted wavelength. The recessional velocity is about 6000 km/s using v = c times z.

When is v = c times z valid?

This approximation works well for small redshifts (z less than about 0.1). At higher redshifts, relativistic corrections are needed for accurate velocity and distance.

What is the Hubble constant?

The Hubble constant H0 describes how fast the universe expands. A common value is 70 km/s/Mpc, meaning a galaxy 1 megaparsec away recedes at 70 km/s. This calculator uses 70 km/s/Mpc by default.

Can redshift be negative?

Yes. Negative redshift (blueshift) means the source moves toward the observer. Nearby galaxies in our local group can show blueshift due to gravitational interactions.

How do I convert redshift to distance?

First compute recessional velocity as v = c times z, then divide by the Hubble constant: d = v / H0. The result is in megaparsecs when H0 is in km/s/Mpc.

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What Is Cosmological Redshift?

Redshift Formulas

Applications in Astronomy

Frequently Asked Questions

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