Final answer:
Variations in luminosity relate to the size of an object's emitting region because the rapidity of the change indicates how quickly light from the entire region can reach an observer. Thus, a quick change in a quasar's brightness suggests a compact emitting region, no larger than the distance light travels in the time frame of the change.
Step-by-step explanation:
Using variations in luminosity to set limits on the size of an object's emitting region involves understanding that the time it takes for a luminosity change to be observed corresponds to the size of the emitting region. For instance, if a quasar doubles its luminosity in 1 hour, it implies that the energy-emitting region must be compact enough that the light from all parts of it reaches us within that hour's time frame. Given that light travels at a speed of about 299,792 kilometers per second, the emitting region can be no larger than 1 light-hour in diameter. Otherwise, the light from more distant parts of the region would take longer to reach us, and the observed luminosity change would be more gradual rather than the rapid fluctuation observed.