If the rotational speed of the gas in the disk of a spiral galaxy is 200 km/s at a distance of 25,000 pc from its center,then what is the mass enclosed within this radius? A)7.5 billion M_⨀ B)18 billion M_⨀ C)70 billion M_⨀ D)230 billion M_⨀ E)400 billion M_⨀

Question

Quizplus · Accepted Answer

The rotational speed of the gas in the disk of a spiral galaxy is given by the expression:

v = (GM/r)^0.5

Where G is the gravitational constant, M is the mass enclosed within radius r, and v is the rotational velocity at radius r.

Rearrange the equation to get:

M = v^2 * r / G

Substituting the given values:

M = (200 km/s)^2 * 25,000 pc * 3.086e+13 km/pc / (6.67e-11 m^3/kg/s^2 * 1.989e+30 kg/Msun)

M = 2.3e+11 Msun

Therefore, the mass enclosed within the given radius is 230 billion Msun. The closest option is D.

If the Rotational Speed of the Gas in the Disk