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The Arches cluster is located in the Galactic Center, about 8.1 kpc away from Earth. The observed angular diameter of the cluster is 0.5 (arcmin).

The Arches cluster is located in the Galactic Center, about 8.1 kpc away from Earth. The observed angular diameter of the cluster is 0.5’ (arcmin). The time-averaged velocity of stars in the cluster is about 7 km s^-1 .

(a) What is the physical size (radius) of the Arches cluster in pc?

(b) Assuming that the cluster is gravitationally bound and in virial equilibrium, what is the total mass of the cluster?

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