A small satellite galaxy is moving in a circular orbit around a much more massiv

Question

A small satellite galaxy is moving in a circular orbit around a much more massive (parent) galaxy, and just happens to be moving exactly parallel to the line of sight as seen from the Earth. The recession velocities of the satellite and the parent galaxy are measured to be 6450 km s-1 and 6500 km s-1, 3 respectively, and the two galaxies are separated by an angular distance = 0.1o as seen from the Earth. Assuming that the Hubble constant is H0 = 65 km s-1 Mpc-1, calculate the mass of the parent galaxy.

Explanation / Answer

Solution:

Let the mass of the small galaxy be m and that of the bigger one be M.

Since the small galaxy is moving in a circular orbit around the bigger galaxy, there is sentripetal force given by mv^2/ R, where R is the distance between the two galaxies;

Also there is a gravitational force of attraction between them which is GMm/R^2

For the two galaxies to be in equilibrium , these forces must be balanced.

GMm/R^2 = mv^2/R

=> M= mass of the bigger galaxy = v^2 R / G

To calculate the distance between the two galaxies , Hubble's law is used.

Ho X distance =Recessional velocity v

Ho = Hubble's constant = 65 km/s/MPc

Distance = v / Ho   = 6500 km/s / [65km/s/MPc] = 100 MPc = 3.086 x 10^24 meters.=R

M = v^2 R/G = (6500 x 10^3)^2 (3.086 x 10^24) / (6.67 x10^-11) = 1.95 x 10^48 kg

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