Measuring the Transverse Velocity of a Galaxy

[fishlens]

Homework Statement

In the figure below we see a component of a jet of a galactic nucleus which is moving away from its nucleus. The distance to the galactic nucleus is D. What is the observed apparent transverse velocity? And what is the value of the Lorentz factor needed to explain this motion?

Figure : https://imgur.com/a/t0m7kCr

Relevant Equations

gamma = 1/sqrt(1-(v/c)^2) (gamma - Lorentz factor, v - velocity, c - speed of light)

See the attached figure.

I understand that we look for the apparent transverse velocity v , for example through v = d/t (d - distance, t - time). The distance to the galactic nucleus is known as D. Though I am not sure how to read off the time from this figure.

 

[mfb]

The numbers next to the images are (decimal) years. The first image is from mid 1977, the last from mid 1980.

 

[fishlens]

Hi, thanks for the reply @m

The numbers next to the images are (decimal) years. The first image is from mid 1977, the last from mid 1980.

Thanks for the reply!

Yes, I assumed that it was the time in years. Though, I am not sure if we should take the time span to be the whole time difference between mid 1977 to mid 1980. Why should we do this? I am confused about this. Also, are we not supposed to use the x-axis in some way? Sorry for maybe dumb questions.

 

[mfb]

The best approach is to find the separation between galaxy and jet in all 5 images and to make a linear fit. For a homework problem it should be acceptable to just take the first and last image.That's the distance between us and the galaxy, not the distance between jet and galaxy.