==Is astronomy a historical science or an empirical science?
It’s both.
==We can make measurements today on light that is the result of events that occured billions of years before our planet even existed.
You are assuming what must be proved.
==We can essentially make predictions about what light patterns we will see in the future related to events that happened in the distant past.
Could you provide some specific examples?
==Maybe there is not such a big distinction between the two kinds of science as the essayist suggests.
There is a huge distinction, in that operational/experimental science deals with the observable and the repeatable, whereas histrorical science deals with the (mostly) unobservable, unrepeatable past.
What astronomers are trying to prove are things like what is dark matter and dark energy? How exactly do stars form? How is it that the universe is "clumpy", i.e. clusters of galaxies rather than an even distribution.
If/when we get answers to those questions it will almost certainly be based on the solid assumptions that the speed of light is a constant, that the speed of light has been constant throughout the history of the universe, and that the stars are close to being the distances away from us that we currently believe they are.
None of this is absolutely certain, because it is all based on inductive knowledge. However, we have good reason to believe that all of these theories will hold true for now and into the forseeable foture.
As far as making predictions about what we'll see in the future based on past events: if we see a supernova exploding, we may be able to predict how the explosion will proceed and what the resulting product will be, even though the explosion occured billions of years ago. Also, we can predict what pictures the Mars rovers will send us even though the pictures were taken ~20 minutes before we get a chance to view them.
There is not a huge distinction between historical and empirical science: both types of science make hypothesis based on information gathered to that point: abduction. Both collect lots of evidence to support or undermine that hypothesis: induction. Both draw logical conclusions from the data they collect: deduction.
If someone measured the speed of light yesterday, am I no longer allowed to use it for empirical research because that measurement is now historical data?