The brightest galaxy in the Bootes cluster of galaxies is found to have a redshift of 0.13. (Assume the speed of light, c, is 3.0 × 10 8 m s−1.)
Assuming the Hubble constant, H0, is 70 km s−1 Mpc−1 to two significant figures, calculate the distance to this galaxy. Express your answer to two significant figures and in Mpc.
The wavelength of a particular spectral line is 589 nm in the laboratory. Use your knowledge of the definition of the redshift to calculate the wavelength of this line in the spectrum of the brightest galaxy in the Bootes cluster
A hypothetical object is observed within the field of view of another galaxy cluster, which is known to be at a distance of 700 Mpc. The wavelength of the spectral feature observed in part (a) at 589 nm in the laboratory is found to be 919 nm for this object, rather than at 683 nm for the other objects in this cluster.
Without doing any calculations, explain why we can state with confidence that this object is not part of this cluster, and is actually more distant
The object is observed to have an apparent brightness of
1.2 × 10−11 W m−2. Calculate its apparent brightness if it were actually part of the cluster

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