Any examples of this in the history of science? I’m thinking that possibly some of the early eclipse prediction projections which were pretty dead on despite being wrong as to the fundamental mechanism might fall into this category.
Eclipses are exactly what I thought of when I saw the thread title.
Any reason you don’t find that to be an adequate answer? Maybe what you meant to ask was if there are any other examples.
flipping a coin will give you the right answer half the time…
I remember my physics teacher in HS telling us that all of the motions of the planets, stars, and moon can be explained just as well with a “Geo-centric” theory as they can with a “Helio-centric” theory.
Bode’s Law. It even “predicted” the location of Uranus before the planet was discovered.
The theory that Apollo races around the sky every day does a pretty good job explaining the sun rising. The theory that “Americans want a black guy for President” did a pretty good job explaining Obama’s victory. etc, etc.
Newton’s theories (which were proved wrong by Einstein) predicted just about everything we care about just about correctly for hundreds of years and continues to do so.
Bad theories are usually disproved by the cumulative weight of evidence against them. That implies that until there is enough “weight” against them, they’ve done a good job of predicting.
Pretty much any theory that hung around for more than a couple of decades, did so because it gave good agreement with experiment. Ptolemaic astronomy, the phlogiston theory of heat, Aristotelian motion…
It might be better to ask whether there are any good examples of theories that hung around for a long time despite having no predictive power. (Scientific theories, that is… obviously our species has a penchant for keeping nonscientific, nonpredictive theories around for thousands of years past their sell-by date)
If a theory always gives correct predictions, how can it be ‘wrong’?
Science doesn’t care if a guy came up with a set of equations by imagining fairies and gnomes pushing atoms around or by casting the horoscopes of different molecules; if the equations make predictions that can be tested and are always right, then they’re correct.
Many would argue that if it has no predictive power, it is inherently un-scientific. See the debate about string theory, or the physical scientists scorn of anthropology, history, and other soft sciences. Many don’t consider them sciences at all.
(I assume you are automatically excluding things like astrology, ESP, etc. ?)
As several people have mentioned, Ptolemaic astronomy was extraordinarily accurate in predicating the movement of the heavenly bodies. But it put the Earth at the center of the universe; it used circles instead of ellipses for the motions of planets; and incorporated a number of other errors. To ‘correct’ for this, it had to use a number of highly complicated mathematical techniques like epicycles and deferents, equants, etc., etc. But it was still accurate enough for most any purpose. In fact, AIUI Copernicus’ system wasn’t more accurate (at least not right away); it was just more elegant.
Back when I was teaching and introducing the concept of scientific theories, I mentioned an alternative theory for why things fall down: the Earth sucks.
Always good for a laugh, but the theory does not really hold up when tested. 
Anyway, this brings up the idea of what it means for a theory to be “wrong.” Isaac Asimov wrote an essay on this topic years ago entitled The Relativity of Wrong. The essay can be read here.
As Asimov writes, “…when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.”
In other words, a theory can be wrong, yet still make good predictions. The theory that the Earth is flat is clearly wrong, yet this is the assumption that architects and engineers use for most human-scale projects, because the curvature of the Earth need not be taken into account for most building-sized projects.
The theory that the Earth is spherical is less wrong but still wrong. (The Earth is actually an oblate spheroid.) The spherical Earth theory, though wrong, nevertheless works just fine for most navigation needs. However, the spherical Earth theory does not work as well when launching satellites–you need to take the Earth’s equatorial bulge into account.
And so on. What makes a theory “wrong”?
Another example–Newtonian physics. Einstein showed that Newtonian physics was wrong. Nevertheless, it works just fine for most purposes. It does not work well at speeds near the speed of light or under high gravitational fields.
It could give correct predictions in one set of circumstances, but fail in a different one. For example, Newtonian physics works pretty well to predict the motion of an object, as long as the speed of that object is not a significant percentage of the speed of light (and some other conditions are met).
“Matter cannot be created or destroyed” would be another example. It works pretty well, as long as you stay away from the high-energy conditions where things like nuclear fusion can take place.
If you’re working with ordinary chemical reactions and stable isotopes, “one element cannot change into another” works pretty well.
Plenty of theories work in some places and not others - Newtonian physics is just fine at people-sized scales on Earth.
As has been mentioned in the two posts prior to yours… 
Your comment about theories working in some places and not others can be misconstrued, however.
It’s not that Newtonian physics is correct under ordinary conditions, and not under others.
Newtonian physics is actually “wrong” even under ordinary conditions. However, the difference in results from using Newtonian physics and relativistic equations is not measurable, at least under ordinary conditions.
Similarly, mass is technically not conserved even in chemical reactions. However, the difference in mass is not measurable. So technically speaking, the theory of conservation of mass is also wrong, even for chemical reactions.
What often happens is that scientists find that an accepted theory breaks down under different conditions. Scientists then strive to come up with a new theory (which is often a refinement of the original theory) that works for both the new conditions as well as the old.
In some cases it is found that no one theory works for all conditions. An example of this is general relativity, which breaks down under very short scales; and quantum theory, which breaks down under relativistic conditions. So really, both of these theories are “wrong.” One goal of modern physics is to reconcile these theories, and come up with a single theory that works under all conditions.
I wouldn’t so much say that Newtonian physics is wrong, as that it’s an approximation which is sometimes not very good. As an example of the fact that it’s always only an approximation, the electrons in a wire have an average speed of millimeters per hour or so (certainly far less than the speed of light), and yet the relativistic effects of their movement at that speed are measurable with a simple compass.
Technically speaking, mass is always conserved in all closed systems, even when you’ve got things like nuclear reactions and antimatter involved. It’s just that when talking about things like nuclear reactions and antimatter, people have a distressing tendancy to prefer to work with non-closed systems.
I have a very superficial understanding of Special and General Relativity, but aren’t the geo-centric and helio-centric models correct, but taking different reference frames into account? The orbits of the planets can be explained much more simply by the helio-centric model, but using the reference frame of the earth, the very complicated geo-centric theories do an adequate job?
Looking forward to having my ignorance overcome as necessary. Be kind.
Science does care, because it’s curious about whether it’s really fairies or forces doing the pushing. You are confusing the difference between “useful” and “correct” I think; a theory can be useful, even if it’s wrong, if it makes correct predictions within a known range of situations.
I’m having a hard time with this statement, Chronos. Can you elaborate on this? Even in a closed system, it is my understanding that mass-energy is conserved, but not mass.
Is what we are talking about here related to how medieval alchemists used to believe in transmutation, but despite their basic theory being wrong, it still led to advances in chemistry?
I would think a whole class of theories would fit here—when people correlate two things and infer causation.
An example of a spurious relationship can be illuminated examining a city’s ice cream sales. These sales are highest when the rate of drownings in city swimming pools is highest. To allege that ice cream sales cause drowning, or vice-versa, would be to imply a spurious relationship between the two. In reality, a heat wave may have caused both. The heat wave is an example of a hidden or unseen variable.