The Andromeda galaxy is at a distance of 2.1 X 10^22 m from our Galaxy. The mass
ID: 2123928 • Letter: T
Question
The Andromeda galaxy is at a distance of 2.1 X 10^22 m from our Galaxy. The mass of Andromeda is 6 X 10^41 kg and the mass of our Galaxy is 4 X 10^41 kg.
(b) The speed of Andromeda relative to our Galaxy is 266 km/s. What is the speed of Andromeda and what is the speed of our Galaxy relative to the center of mass of the two galaxies?
(c)What is the kinetic energy of each galaxy relative to the center of mass? What is the total energy (kinetic and potential) of the system of the two galaxies? Will the two galaxies eventually escape from each other?
Explanation / Answer
we know from the relation
v1 x r1 = v2 x r2
where v1 and v2 are the velocities and r1 and r2 are the orbital ditances
or v2 = (v1 x r1/r2)
the kinetic energy of our galaxy is
K1 = (1/2)m1 x v1^2
where m1 is mass of our galaxy
the kinetic energy of Andromeda galaxy is
K2 = (1/2)m2 x v2^2
where m2 is mass of Andromeda galaxy
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