Near the center of the Milky Way, the rotation speed climbs...

Name: Problem 3, Chapter 73: Pathways to Astronomy
Uploaded: 2020-10-22T19:24:24-08:00
Duration: 1 min 17 s
Channel: Zachary Warner
Description: Near the center of the Milky Way, the rotation speed climbs in proportion to the radius; so at 400 pc from the center, the speed is twice as fast as at 200 pc from the center. a. What does this imply about the mass within 400 pc versus the mass within 200 pc? b. Is there any differential rotation in this region? Explain.

Near the center of the Milky Way, the rotation speed climbs in proportion to the radius; so at 400 pc from the center, the speed is twice as fast as at 200 pc from the center. a. What does this imply about the mass within 400 pc versus the mass within 200 pc? b. Is there any differential rotation in this region? Explain.

Near the center of the Milky Way, the rotation speed climbs in proportion to the radius; so at 400 pc from the center, the speed is twice as fast as at 200 pc from the center.
a. What does this imply about the mass within 400 pc versus the mass within 200 pc?
b. Is there any differential rotation in this region? Explain.

Key Concepts

Solid-Body Rotation

Solid-body rotation occurs when every part of an object rotates at the same angular speed, meaning the linear velocity is directly proportional to the distance from the rotation axis. The observation that the rotation speed increases linearly with radius (i.e., twice the speed at 400 pc compared to 200 pc) implies that the region is undergoing solid-body rotation. In such a scenario, there is no differential rotation since all parts share the same angular velocity.

Mass Distribution

The relationship between rotation speed and radius can be used to infer the mass enclosed within a given radius. In this problem, having the speed double when moving from 200 pc to 400 pc implies that the mass enclosed within 400 pc is greater than that within 200 pc. The gravitational force that provides the centripetal acceleration for the circular motion is directly related to the total mass within that radius, suggesting a continual increase in mass with increasing radius.

Rotation Curve

The rotation curve of a galaxy shows how the orbital velocity of stars or gas changes with distance from the galactic center. In this context, an increase in speed that is directly proportional to radius indicates a rising rotation curve, which is characteristic of the inner regions of a galaxy. This behavior provides insight into the gravitational potential and the distribution of mass within those regions.

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