If you observed a gas cloud orbiting in a disk of a spiral galaxy that was located 10,000 pc from the center and it rotated with a speed of 300 km/s, what is the mass of the galaxy interior to gas cloud's orbit? A) 1 * 10¹¹ M _$\odot$ B) 2 * 10¹¹ M _$\odot$ C) 8 *10¹¹ M _$\odot$ D) 1 * 10¹² M _$\odot$ E) 4 * 10¹² M _$\odot$

Question

Quizplus · Accepted Answer

According to the equation for circular velocity (v = √(GM/r)), we can rearrange it to solve for mass (M = vr²/G). Plugging in the given values, we get M = (300 km/s)²(10,000 pc)(3.086×10¹³ km/pc)/(6.674×10⁻¹¹ N·m²/kg²) = 2.04×10¹¹ solar masses, which is closest to option B.

If You Observed a Gas Cloud Orbiting in a Disk ⊙\odot⊙

If You Observed a Gas Cloud Orbiting in a Disk $\odot$