Chapter 12, Problem 39A

We believe our galaxy was formed from a huge cloud of gas. The original cloud was far larger than the present size of the galaxy, more or less spherical, and rotating very much more slowly than the galaxy is now. In this sketch we see the original cloud and the galaxy as it is now (seen edgewise). Explain how the law of gravitation and the conservation of angular momentum contribute to the galaxy’s present shape and why it rotates faster now than when it was a larger, spherical cloud.

To determine

To explain: The contribution of law of gravitation and the conservation of angular momentum to the galaxy’s present shape and the reason for current rate of rotation.

Answer to Problem 39A

Due to gravity and momentum, the particles of the cloud of gas came together and became denser than the former.

Explanation of Solution

Introduction:

Decreasing the rotational inertia imparts rotational kinetic energy to the particles of the dust cloud.

Denser the mass particle/ body, exerts more gravitational force on the small surrounding particles/ bodies. Now, the denser particle/ body is rotating on angular velocity, it would try to maintain its angular momentum and impart a gravitational force on the surrounding moving particles. Due to their angular velocity, smaller particles would be moving in a revolution around the denser one. With time and their angular momentum, smaller particles will assimilate in the denser one creating it denser. Thus, cloud dust would come closer and the surrounding particles/ bodies will have greater angular velocity around the denser ones in the center.

Conclusion:

Thus, as the gravitation force between the particles increases. So, their angular velocity increases. Due to the angular momentum of the cloud of the galaxy, particles come closer and become denser. That makes the larger cloud compact and spherical, and due to the increase in angular velocity, the rotation of the galaxy increases.