Suppose we measure two galaxies to the farthest extent that...

Suppose we measure two galaxies to the farthest extent that any matter can be detected. One has a rotation velocity of $300 \mathrm{km} / \mathrm{sec}$ at $4 \mathrm{kpc},$ and the other has a rotation velocity of $150 \mathrm{km} / \mathrm{sec}$ at $20 \mathrm{kpc} .$ Which has the larger measured mass? What is the ratio of those masses?

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Key Concepts

Mass Estimation from Rotational Dynamics

This concept involves using the balance between gravitational force and the centrifugal force from rotation to estimate the mass of a galaxy. By applying Newton's law of gravitation, one can approximate the mass enclosed within a particular radius using the relation M ~ (v^2 * R) / G. This allows astronomers to infer the mass based on observed rotational velocities.

Role of Radius in Mass Calculations

The radius at which the rotation velocity is measured directly impacts the estimation of the galaxy's mass, since mass is proportional to the radius for a given rotation velocity. Differences in measurement radii between galaxies require careful interpretation to accurately compare their masses.

Rotation Curves in Galaxies

Rotation curves plot the orbital velocities of stars or gas in a galaxy as a function of distance from the center. These curves are crucial to understanding how mass, including luminous and dark matter, is distributed over the galaxy, as higher rotation speeds at given radii can indicate greater enclosed mass.

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