Dark Matter and Orbital Velocity
Classical Mechanics
Level
2
Which of the following correctly describes the behavior of the orbital velocity of stars in spiral galaxies as a function of radius, including the effects of dark matter?
Grows linearly in the galactic bulge and falls off like
outside the bulge
Grows linearly in the galactic bulge and falls off exponentially outside the bulge
Grows linearly in the galactic bulge and is constant outside the bulge
Falls off exponentially everywhere
Is constant in the galactic bulge and grows linearly outside the bulge
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1 solution
Inside the galactic bulge, the high surface density of matter causes the orbital velocity of stars to grow linearly as the amount of matter centripetally accelerating these stars via gravitation increases rapidly. Outside the bulge, the Newtonian prediction says that the orbital velocity should fall off like r − 1 / 2 . The experimental fact that it does not but is instead constant is what constitutes evidence for dark matter , some unseen source of gravitation.