Question

Suppose a blazar at a redshift z = 1.0 is observed to have a brightness fluctuation on a timescale of 5 hours as seen from Earth. (a) At what speed does the blazar seem to be moving away from us? (b)_ Using the idea of time dilation, determine how long this fluctuation lasted as measured by an astronomer in the blazar's host galaxy. (c) What is the maximum size (in AU) of the region from which the blazar emits energy that we observe?

I got answers for parts A and B but don't know how to start and solve part C.

A) 1.8x10^8 m/s

B) 6.25 hrs

C)?

Answer 1

Part C is pretty simple, once you get the idea.

Assume that the blazar is rotating at a circular path.

We have found the speed at which it is moving as well as the time taken for one complete rotation.

Assume a circular path with radius R.

So, the distance for one complete revolution is

The time taken = 6.25 hours = 6.25*3600 = 22500 seconds.

speed of motion = 1.8*10^8 m/s

So, using distance,

d = speed*time,

d = 22500*1.8*10^8 = 4.05*10^12 m

R = d/(2*3.14) = 6.449*10^11 m

SInce 1 AU = 1.496*10^+11 m,

R = 4.31 AU

Now, the size of the blazar is ofted said as diameter and not radius.

So, diameter, D = 2*4.31 = 8.62 AU