solar masses. (Hint: Use the formula for circular velocity, V. = VS"; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 x 101º m.) solar masses (M)

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Among the globular clusters orbiting a distant galaxy, one is moving at 417 km/s and is located 16 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? Convert your answer to
solar masses. (Hint: Use the formula for circular velocity, V, = V
GM
; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 x 1016 m.)
solar masses (M.)
Transcribed Image Text:Among the globular clusters orbiting a distant galaxy, one is moving at 417 km/s and is located 16 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? Convert your answer to solar masses. (Hint: Use the formula for circular velocity, V, = V GM ; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 x 1016 m.) solar masses (M.)
Expert Solution
Step 1

Given Data:

The orbital velocity of a globular cluster is, ve=417 km/s

The distance from the centre of a galaxy is, r=16 kpc

 

The expression for the orbital velocity is given as,

ve=GMr................(1)

Here, G is the Universal gravitational constant, M is the mass of a galaxy, and r is the distance. 

 

Conversion of distance from kpc to m,

we know that,

1 kpc=103 pc1 pc=3.1×1016 m

Hence,

r=16 kpc×103 pc1 kpc×3.1×1016 m1 pcr=4.96×1020 m

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