If the rotational speed of the gas in the disk of a spiral galaxy is 200 km/s at a distance of 80,000 light-years 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_$\odot$

Question

Quizplus · Accepted Answer

We can use the equation for circular velocity in a galaxy at a given radius:

v = sqrt(GM/r)

where 
v = rotational speed = 200 km/s 
G = gravitational constant 
M = mass enclosed within radius r 
r = radius = 80,000 light-years = 7.59 x 10^17 km

Squaring both sides and rearranging gives:

M = v^2 r/G

Plugging in the given values:

M = (200 km/s)^2 x 7.59 x 10^17 km / (6.6743 x 10^-11 N m^2/kg^2)

M = 2.30 x 10^12 solar masses = 230 billion MF☉

Therefore, the correct answer is D.

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

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