Question

1. You observe an AGN where you measure the MgII line (λ₀ = 280 nm) at an observed wavelength of λ_obs = 336 nm. Assuming a Hubble constant of 70 km s⁻¹ Mpc⁻¹ , what is the distance of this AGN in Mpc?

2. Jupiter has a mass of 2 × 10²⁷ kg. If the Jupiter would collapse into a black hole, what would be its Schwarzschild radius?

3. You measured the redshift of a galaxy to be z= 0.35. Assuming a Hubble constant of 70 km s⁻¹ Mpc⁻¹ , what is the distance in Mpc to this galaxy?

Useful Units:

• Gravitational Constant G = 6.67×10⁻¹¹ m³ s−2 kg⁻¹

• Speed of Light c = 3×10⁵ km s⁻¹ , or c = 3×10⁸ m s⁻¹

Answer 1

1. From the concept of redshift we have

where z is the redshift parameter

Given that and

Thus we have

From the concept of relativistic Doppler effect we have

In this case, we have

from Hubble's law, we have

where D - the distance in Mpc

H0 - Hubble's constant = 70 km/sec/Mpc

2. The expression for Schwarzschild Radius is given by

where G - universal gravitational constant =

Mass of Jupiter =M =

Thus

3. Here given that

z = 0.35

From the concept of relativistic Doppler effect we have

In this case, we have

from Hubble's law, we have

where D - the distance in Mpc

H0 - Hubble's constant = 70 km/sec/Mpc