Observing the Light Intensity of M31
You know that the apparent brightness of an object changes as its distance
changes, so you should be able to see how much the galaxy M31 moves by
observing its change in brightness over a given time period. Finding its
velocity is then just a matter of dividing this distance by the time
interval. A snap. You can use a light curve of M31 to discern how the
galaxy's brightness changes over time.
The function that describes how apparent brightness changes with distance is
given by the relationship:
The intensity of the light varies as the inverse square of the separation
from the light source (r).