Hi! I just need help with the part circled in red. Thank you! A globular cluster contains an RR Lyrae star with an observed pulsation period of 16 hours and an average apparent magnitude of 17.2.What is the distance (in kpc) to the globular cluster?If you measure the angular diameter to be 20 arc minutes, what is the linear diameter (in pc)?Part 1 of 2To determine the distance to the globular cluster, you need to use the magnitude-distance formula:D = 10(m-M+5)/5We can use the figure below to estimate the absolute magnitude of the RR Lyrae star. Absolute magnitude-7-650432-10Based on the figure,M =0.3& Cephel-kpcType(classical)CepheidsType IICepheidsRR Lyrae stars1 3Pulsation period (days)10 3010410310²100Luminosity, L/LUse the given average apparent magnitude to solve for the distance (in kpc).D = 10(m- - M+5)/5D =

Given, The pulsation period, P=16hrP=1624daysP=0.67days Angular distance,θ=20arc minθ=20×60206265arc…

Absolute magnitude 7 -6 5 4 3 2 7 0 Based on the figure, M = 0.3 & Cephel- kpc Type (classical) Cepheids Type II Cepheids RR Lyrae stars 1 3 10 Pulsation period (days) 30 104 103 10² 100 Luminosity, L/L Use the given average apparent magnitude to solve for the distance (in kpc). D = 10(m- (m-M+5)/5

Absolute magnitude 7 -6 5 4 3 2 7 0 Based on the figure, M = 0.3 & Cephel- kpc Type (classical) Cepheids Type II Cepheids RR Lyrae stars 1 3 10 Pulsation period (days) 30 104 103 10² 100 Luminosity, L/L Use the given average apparent magnitude to solve for the distance (in kpc). D = 10(m- (m-M+5)/5

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