   Chapter 34, Problem 16PE

Chapter
Section
Textbook Problem

Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.

To determine

To prove:

The velocity of a star which is orbiting its galaxy is inversely proportional to the square root of its orbital radius.

Explanation

Orbiting stars have uniform speed though form the derivation it is proved that orbital velocity decreases as the radius increases. The mass enclosed refers to the mass enclosed by the orbit rather than the mass of the orbiting star.

As per the Kepler's third law of relation:

The square of the period of the satellite in a circular orbit is proportional to the cube of its radius

P2 = a3

Substituting the gravitational constant parameters, we get:

P2 = (4π2/(G M(a) + m*

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 