Investigations of the orbital velocities of stars and gas clouds in disk galaxie

Question

Investigations of the orbital velocities of stars and gas clouds in disk galaxies show that virtually all galaxies have huge amounts of dark matter. This dark matter represents around 90% of the mass of a galaxy and is distributed in a halo that extends to distances that are many times the size of the observable galaxy. Explain how dark matter is detected in disk galaxies.

a. The orbital velocity of an object depends on the amount of mass generating the gravitational force and the distance from the object to the mass. The closer an object is to the mass the faster it orbits. In a galaxy the gravitational force comes from the mass that is interior to an object’s orbit. This is because the mass exterior to the orbit pulls in two different directions and therefore provides a net force of zero. Near the luminous edge of the disk of a galaxy we would expect nearly all the mass of the galaxy to be interior to the object’s orbit. For objects farther still from the center, the interior mass should not be changing and therefore the orbital velocity should decrease due to the increase in distance. Instead what is seen is a constant orbital velocity for objects far from the luminous mass. This can only happen if more interior mass is being added as the distance increases. This added unseen mass is called dark matter.

Explanation / Answer

The facts presented by option "b" are correct. Hence true explanation is as given in option "b".

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