Chapter 34, Problem 16PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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

â€ƒâ€ƒP2Â =Â a3

Substituting the gravitational constant parameters, we get:

â€ƒâ€ƒP2Â =Â (4Ï€2/(GÂ M(a)Â +Â m*

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