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 _$\odot$ B) 18 billion M _$\odot$ C) 70 billion M _$\odot$ D) 230 billion M _$\odot$ E) 400 billion M _$\odot$

Question

Quizplus · Accepted Answer

The rotational speed of gas, v, is related to the mass enclosed within a certain radius, r, by the formula:

v = sqrt(GM/r)

where G is the gravitational constant.

Rearranging the formula, we get:

M = v^2r/G

Plugging in the given values, we get:

M = (200 km/s)^2 x (25,000 pc) x (3.086×10^13 km/pc) / (6.67430(±0.00015) × 10^-11 N m^2 kg^-2)

M = 2.3 x 10^11 solar masses (rounded to two significant figures)

Therefore, the mass enclosed within a radius of 25,000 pc is approximately 230 billion solar masses. The correct answer is D.

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If the Rotational Speed of the Gas in the Disk $\odot$