Redshift Calculator - Cosmological Physics

This advanced physics calculator analyzes redshift effects in astronomy and cosmology, calculating wavelength shifts, recession velocities, and cosmological distances for distant objects.

Redshift Formula

The redshift is calculated using:

z = (λ_obs - λ_emit) / λ_emit

Where:

• z: Redshift value
• λ_obs: Observed wavelength
• λ_emit: Emitted wavelength

Types of Redshift

Cosmological Redshift

• Cause: Expansion of the universe
• Effect: Wavelength stretches with space
• Formula: z = (a_now / a_then) - 1
• Scale Factor: a(t) = 1 / (1 + z)

Doppler Redshift

• Cause: Relative motion of source
• Effect: Classical Doppler shift
• Formula: z ≈ v/c (for v << c)
• Relativistic: z = √((1 + v/c) / (1 - v/c)) - 1

Gravitational Redshift

• Cause: Strong gravitational fields
• Effect: Time dilation in gravity
• Formula: z = √(1 - 2GM/rc²) - 1
• Applications: Black holes, neutron stars

Hubble's Law

The relationship between distance and recession velocity:

v = H₀ × d

• v: Recession velocity
• H₀: Hubble constant (~70 km/s/Mpc)
• d: Distance to object

Real-World Applications

• Galaxy Surveys: Distance measurements
• Cosmology: Universe expansion rate
• Quasar Studies: Early universe exploration
• Dark Energy: Accelerated expansion
• CMB Analysis: Cosmic microwave background
• Exoplanet Detection: Radial velocity method

Interesting Facts

• The most distant known galaxy has z ≈ 13
• CMB has redshift z ≈ 1100
• Redshift z = 1 means universe was half current size
• Some quasars have redshifts z > 7
• Gravitational waves don't experience redshift

Mathematical Relationships

• Redshift: z = (λ_obs - λ_emit) / λ_emit
• Scale Factor: a(t) = 1 / (1 + z)
• Recession Velocity: v = c × (1 + z)² - 1) / ((1 + z)² + 1)
• Lookback Time: t ≈ z / H₀ (for small z)
• Energy Ratio: E_obs / E_emit = 1 / (1 + z)

Historical Context

• Vesto Slipher discovered galaxy redshifts in 1912
• Edwin Hubble established Hubble's law in 1929
• Redshift confirmed universe expansion
• Led to Big Bang theory development
• Foundation of modern cosmology

Special Cases

• Blueshift: Negative redshift (approaching)
• Local Motion: Peculiar velocities
• High Redshift: Relativistic effects important
• Low Redshift: Linear Hubble relation
• CMB: Surface of last scattering