The Virgo Galaxy Cluster has a mass of 1014Modot and its centre is 16Mpc from Earth. The large elliptical galaxy M87 lies at the centre of the Virgo cluster. M87 has a supermassive black hole at it's centre with an estimated mass of 6times109Modot. Take Hubble's constant to be H0=70kms−1Mpc−1.
Taking the Virgo cluster to be spherically symmetric with a radial density profile given by
rho(r)=rho0(fracr1Mpc)−2,
Determine the value of the constant rho0 is S.I units assuming the radius of the Virgo cluster is 1Mpc.
I am confused with how to approach this question,
I know that density rho=fracMfrac43pir3, when I substitute it into the given radial density profile, the r variable doesn't cancel, should I substitute the radius of the cluster into r? Is it really that straight forward?
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