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Relative Velocity in Two Dimensions

Relative Velocity in Two Dimensions

Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing vector...

Relating Angular And Linear Quantities - I

Relating Angular And Linear Quantities - I

If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and three dimensions, we can observe a mapping of the linear variables to the rotational ones.
When comparing the linear and rotational variables individually, the linear variable of position has physical units of meters, whereas the angular position variable has dimensionless units of radians, as it is the ratio of two lengths. The linear velocity...

Relating Angular And Linear Quantities - II

Relating Angular And Linear Quantities - II

In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the relation:

Space-Time Curvature and the General Theory of Relativity

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
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Distance Problem

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Updated: Jul 18, 2026

Echo Particle Image Velocimetry

Echo Particle Image Velocimetry

Published on: December 27, 2012

Is the velocity-distance relation for galaxies linear?

S van den Bergh¹

¹Dominion Astrophysical Observatory, National Research Council, Victoria, Canada.

Proceedings of the National Academy of Sciences of the United States of America

|June 1, 1993

Summary

Supergiant ScI galaxies and Type Ia supernovae are unsuitable as cosmic distance yardsticks. First-ranked cluster galaxies show minimal luminosity dispersion, suggesting a linear velocity-distance relationship with limited deviations.

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Area of Science:

Astronomy and Astrophysics
Cosmology

Background:

Investigating the velocity-distance relationship is crucial for understanding cosmic expansion.
Standard candles and yardsticks are essential tools for cosmological measurements.

Purpose of the Study:

To evaluate ScI galaxies, Type Ia supernovae, and first-ranked cluster galaxies as potential standard candles for the velocity-distance relationship.
To determine the suitability of these objects for accurate cosmological distance measurements.

Main Methods:

Analysis of the diameters of ScI galaxies.
Examination of the luminosities of Type Ia supernovae at maximum light.
Assessment of the brightness of central galaxies in rich clusters.

Main Results:

Supergiant ScI galaxies exhibit significant luminosity variations, rendering them unsuitable.
Type Ia supernovae show luminosity differences up to a factor of 10, limiting their use as precise standard candles.
First-ranked cluster galaxies display a remarkably small luminosity dispersion, suggesting potential as reliable distance indicators.

Conclusions:

Neither ScI galaxies nor Type Ia supernovae are ideal for precise velocity-distance relationship studies.
First-ranked cluster galaxies offer a promising avenue for studying the velocity-distance relationship with minimal deviations (approx. 20%) up to redshifts of 40,000 km/s.