The Sun lies at 8 kpc from the centre of the Milky Way (MW), where it...

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The Sun lies at 8 kpc from the centre of the Milky Way (MW), where it orbits with a circular velocity of 220 km s-¹. (a): Calculate the total mass of the MW enclosed within 8 kpc from its centre, under the assumption that the Sun obeys Keplerian rotation. [3 marks] (b): Knowing that all the stars enclosed within 8 kpc emit a total luminosity of 4 x 10¹0 Lo show that the MW must contain a form of dark matter. For this calculation, assume that all the stars have the same mass and luminosity of the Sun. [2 marks] (c): Consider a globular cluster with absolute visual magnitude My = -8 mag. Using the distance modulus, calculate the apparent V magnitude of the cluster at the distance of the MW centre. [2 marks] (d): Due to the presence of dust, 80% of the cluster's light is absorbed by dust. Calculate the distance modulus between the Sun and the MW centre that an observer would incorrectly infer when neglecting dust. [2 marks] The Sun lies at 8 kpc from the centre of the Milky Way (MW), where it orbits with a circular velocity of 220 km s-¹. (a): Calculate the total mass of the MW enclosed within 8 kpc from its centre, under the assumption that the Sun obeys Keplerian rotation. [3 marks] (b): Knowing that all the stars enclosed within 8 kpc emit a total luminosity of 4 x 10¹0 Lo show that the MW must contain a form of dark matter. For this calculation, assume that all the stars have the same mass and luminosity of the Sun. [2 marks] (c): Consider a globular cluster with absolute visual magnitude My = -8 mag. Using the distance modulus, calculate the apparent V magnitude of the cluster at the distance of the MW centre. [2 marks] (d): Due to the presence of dust, 80% of the cluster's light is absorbed by dust. Calculate the distance modulus between the Sun and the MW centre that an observer would incorrectly infer when neglecting dust. [2 marks]