ASTR 420 Lecture 02: Relativistic Redshift and Distance

Terms Developed in Context

These terms form the lecture's reasoning chain from observable through model to a bounded physical conclusion.

Doppler redshift

A wavelength shift produced by relative motion through spacetime between emitter and observer. In this lecture it supports the evidence-to-model chain for special-relativistic redshift and cosmological distance measures.

Use and relationship: Read it together with Distance duality and Cosmological redshift. The governing relation \(1+z=\\sqrt{(1+\\beta)/(1-\\beta)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The difference is about 1.5%; cosmological redshift is not generally a simple Doppler velocity. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Cosmological redshift

A wavelength stretch accumulated as light propagates while the cosmic scale factor grows. In this lecture it supports the evidence-to-model chain for special-relativistic redshift and cosmological distance measures.

Use and relationship: Read it together with Doppler redshift and Luminosity distance. The governing relation \(1+z=\\sqrt{(1+\\beta)/(1-\\beta)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The difference is about 1.5%; cosmological redshift is not generally a simple Doppler velocity. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Luminosity distance

The distance defined by the inverse-square relation between intrinsic luminosity and observed flux. In this lecture it supports the evidence-to-model chain for special-relativistic redshift and cosmological distance measures.

Use and relationship: Read it together with Cosmological redshift and Angular-diameter distance. The governing relation \(1+z=\\sqrt{(1+\\beta)/(1-\\beta)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The difference is about 1.5%; cosmological redshift is not generally a simple Doppler velocity. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Angular-diameter distance

The distance defined by the ratio of an object's physical transverse size to its observed angular size. In this lecture it supports the evidence-to-model chain for special-relativistic redshift and cosmological distance measures.

Use and relationship: Read it together with Luminosity distance and Distance duality. The governing relation \(1+z=\\sqrt{(1+\\beta)/(1-\\beta)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The difference is about 1.5%; cosmological redshift is not generally a simple Doppler velocity. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Distance duality

The relation D_L=(1+z)^2 D_A that connects luminosity and angular-diameter distances when photons are conserved. In this lecture it supports the evidence-to-model chain for special-relativistic redshift and cosmological distance measures.

Use and relationship: Read it together with Angular-diameter distance and Doppler redshift. The governing relation \(1+z=\\sqrt{(1+\\beta)/(1-\\beta)}\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: The difference is about 1.5%; cosmological redshift is not generally a simple Doppler velocity. This caveat prevents the term from being treated as a unique explanation or a context-free number.