Well, what is the definition of deductive reasoning? There are several, natch, but I will use a common definition.
Basically, a deductive reasoning is inference in which the conclusion is of the same generality as the premises, whereas inductive reasoning goes from the particular to the universal, and thus the conclusion is less likely than the premises.
Now, given the premises of 20th century physics, we can deduce the orbit of the sun. A sampling of these premises are: the universal constants are locally constant, Newtonian orbital mechanics is grossly correct (I simplify, we need to include relativity in general, but that hardly matters to figure out where the sun will be tomorrow morning), etc. There are more I haven't listed. But, from these premises we can deduce the position of the sun in the anon.
This is rather different from the Popper argument, as I understand it, which I simplify as "well, we saw the sun rise yesterday, and the day before, and the day before that; so, we can conclude inductively that it will rise tomorrow."
That's a horrific, and unfair simplication of Popper, but what can you do in 1 post? I anticipate that the rebuttal will be it's not so much the rising of the sun that we observe and draw inductive conclusions from, but the laws themselves - orbital mechanics and the such. And that's fair, but it's useful to sketch things out quickly to lay the groundwork, IMO.
I argue that we start with some premises - that it's a material world (we aren't living in the Matrix), that the laws of nature (theories, whatever the heck you want to call them, let's not quibble about dictionary terms) are consistant, and that our human makeup is also material, allowing us access to the 'external' material world, and the rest follows deductively.
I'm expecting an outcry at this point.

It's deserved. My reference to "20 years of thought" in this matter was obviously a tongue in cheek joke. I have been thinking about it that long, but not rigorously.
So what follows falls squarly in the 'speculation' category. But let me share my thinking/speculating.
Switch to math for me for a moment. Assume an infinite 2D plane, and I will start giving you data. For each data point, you are to predict the position of a point. (also assume the actual problem is more formally defined; as stated you couldn't actually make the predictions I say you can make. Again, only so much you can do in one post)
data point 1: the position of the point is 290 units from the origin +- 3 units, with 90% accuracy.
prediction: A donut, smeared on the edges, where the density at each point corresponds to the probability of the point lying there.
data point 2: the position of the point is 180 units from (100, 35), +- 20 units, with a 70% accuracy.
prediction: draw a second donut corresponding to the 2nd data point, and take the intersection with the first.
etc.
With enough data points, we can be very precise about the position of the point, and even give error bars for our estimates. We can introduce further complications: the "signal" for each data point can be noisy, there can be known and unknown failure modes, but in each case we can introduce math to handle that case. For example, if 4 out of 5 of the data points jibe, and one doesn't, well, we know probably there was a failure somewhere in the 5th.
This, of course, is how GPS works in the real world. Every time you get in a plane you trust your life to this math modelling. You basically triangulate on the data points, and account for possible data errors and equipment failures. Tracking things in the time domain allows you to figure out where the errors are: if sat 3 gives consistantly wrong data it's an equipment problem, whereas if it only gave wrong data once it was probably transmission related.
And this is the crux of my argument/speculation. We 'triangulate' (metaphorically) onto what is really happening when we observe by making observations by different means. We don't just observe and than make an inductive decision, usually (sometimes we do, and the result is provisional). Rather, we make observations, create a tenative hypothesis, test that with an entirely different set of observations, etc. We 'triangulate'.
So here comes my bald faced hand waving assertion.

This error elimination allows us to achieve certainty in our decisions,
within the limit of our premises. Yes, of course, if we are a brain in a vat, or some experimenter's computer program, they could change a parameter and all of our science would be invalidated. But it is our
premise that this is not true. Thus, some of our knowledge of the world is entirely deductive, and as certain to be true as are the
premises certain to be true. Remember, deduction does not require that the premises must be true, only that the conclusions be guaranteed to be true if the premises are true.
Okay, I proved nothing in that paragraph, and I don't have a solid proof in my head, I know it. Some issues I see: I blithely state we can make enough observations, from different 'angles' (metaphorically) to remove all possible errors from the observations, but I have hardly proved it. The question of whether to start from a reductive attitude or constructive attidude eludes me. By that I mean do we start by proving QM, and moving on from there, or at the macro scale (e.g. if I drop this iron ball in a vacuum it will fall at
g acceleration). Macro seems like the correct starting point, but then you have quite a few (putting it mildly) assumptions, or premises to make. Even if I deductively prove the behavior of that iron ball, a critic will point out that it is build on a mountain on inductive premises.
I could go on, but you get the idea. It's my pet theory, most of my pet theories have been proven to be wrong in the past, why would this one be any different? Yet, I was bolstered several years ago when I heard an interview on NPR where a prominant scientist (I forget his name) pronounced Popper's ideas as nonsense, as we clearly do acquire definitive knowledge. Perhaps that is the correct tact

. This computer I am typing on depends on the correctness of vast swarths of knowledge; any single one of those things being wrong would keep the computer from operating. At some point one has to become tired of saying "but we could be an elaborate experiment in a vat somewhere" and recognize we are truly generating sure knowledge about this world. Given that, challenge the Popperians: I don't know where your logical error lies, but there clearly is one, since your conclusions are in variance with emperical results. Yes, still a bit hand-wavy, but nontheless I find it satisfying.
So, that's what I think is likely to be true. I don't expect you to, and I'm not particularly interested in a typical 20 page JREF debate on the topic, though if someone gave me something to think about in relation to this it sure would be appreciated.
See, told you you didn't want me to address this.
ETA: Dang, about 2 sentence in there were taken
nearly verbatim from wikipedia, and I forgot to cite it. Basically I reworded their definition of deductive reasoning. Sorry, that was intellectually sloppy.