According to Newtonian mechanics, planets move around stars due to the centripetal force provided by the host star's gravitational pull. But in light of what Einstein said (i.e. relativity), the case is quite different. A massive object like a star distorts and curve space, and so it's the curved space around the star that is responsible for moving the planets around their parent star.

I understand all this perfectly. However, after thinking about it a bit more deeply, I'm left at a disadvantage. I mean, is it correct to say that curved space is what moves planets around stars, or around the Sun in the particular case of our Solar System? Or is it still the centripetal force that is caused by the Sun?

I hope this is clear enough for you, guys. Thank you.

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

It's curved spacetime which does the job. In fact, for the planets of the solar system, the temporal part of the curvature (gravitational time dilation) is more important in determining orbits. Only rapidly-moving objects sample the space curvature to any great extent: hence the deviation from Newton we see in the orbit of Mercury, for instance.
Or so says Bernard Schutz, director of the division of Astrophysical Relativity at the Max Planck Institute, in his book Gravity: From The Ground Up. His Chapter 17 on spacetime geometry has two successive sections entitled Newtonian gravity as the curvature of time and Do the planets follow the geodesics of this time-curvature?. In these two sections he uses a metric which has Schwarzschild's time coordinates in flat space, and demonstrates that it generates a Newtonian gravitational redshift and Newtonian orbits.
As to whether spacetime curvature or gravitational force holds the planets in their orbits: under GR it's the spacetime curvature which modifies the path of a freefalling object into a closed curve; the object accelerates as if subjected to a force. Whether you can say that spacetime curvature is what really causes the deviation from straight-line movement is a philosophical point that I think has been debated on BAUT quite recently.

Grant Hutchison

So, Grant, which would be the correct (the better?) way to explain planetary motion? Centripetal force or curved spacetime?

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

As grant mentioned, "Whether you can say that spacetime curvature is what really causes the deviation from straight-line movement is a philosophical point that I think has been debated on BAUT quite recently."

I do not believe gravity is a force at all, as F=ma, and yet gravity works in a finite manner on massless particles such as photons, thereby creating an apparent discontinuity via indeterminency. Yet GR's equations describe the effects on both particles with mass, as well as massless particles, with aplomb. We know spacetime curvature is real, the equations work, so I propose we stick with that framework instead of working out conceptual ways of shoehorning Newtonian mechanics into the a relativistic framework.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

I know; I just felt compelled to ask the question.

You know, what's funny is that in schools they teach these things mostly in accordance with Newtonian mechanics. Actually, I don't think spacetime is even taught in colleges (not for undergraduates at least). But anyway.

Thank you both for your answers. Any more comments are most welcome.

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

For many reasons you may be correct since down at the unification scale only the weak, electromagnetic and strong forces appear to have the same magnitude but then at the planck scale gravity joins the fray. So I am not sure if gravity is or isn't a force.

And Newtonian gravity works very, very well indeed: for many purposes one can dispense with the fiddliness of GR and stick with Newton.
If you believe that science's job is to tell us what the Universe really does, then you're going to go with GR as our current best approximation to the truth. If you believe that science's job is to make useful predictions about the behaviour of the Universe, then you'll pick whichever tool is best suited (in ease and accuracy) to the job at hand.

Grant Hutchison

Well, I do believe the school job is to tell us the best approximation to the truth. I really don´t get why the basic school sticks to pseudo-forces concepts. I think it´s time to bring GR to the basic school [or at least to the middle one].

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What brings us together is stronger than what pulls us apart

Indeed, you make the important point that the theories we choose are indeed choices, and that is always true in every scientific paper ever written. This I feel is a very important and common misconception about science-- many people think that the theories of science are handed to us, and we have no choice in them. But that isn't how it works in practice-- everyone who ever wrote a scientific analysis of some phenomenon always started out, in every case, by making an array of choices in how they would do that. So it is undeniably clear that the act of doing science gives an important role to making choices, that are not completely arbitrary, but are flexible to the goals at hand, as you say.

Toward that end, I think it is quite important to avoid language that tends to further the misconception that any aspect of science is devoid of such choices. So I think we should be careful when saying "If you believe that science's job is to tell us what the Universe really does", because I would say that anyone who believes that is much more like a creationist than they would care to admit-- in that they are holding to beliefs that are patently refuted by scads of evidence to the contrary. But I think I know what you intended by that, which perhaps is closer to "If you believe the ultimate goal of science is to expand our understanding, and create models that are in some sense 'closer and closer' to what is really happening." If that's our goal, we will never be content with a theory that we know is less accurate than some other one. But still the first step is doing science always pretty much boils down to "choose your poison." And as someone once said, "it's the dose that makes the poison", so I don't mean that this is in any way a futile or unproductive choice to have to make.

Well, I'm happy enough with your "third way", here, but it certainly wasn't what I intended to say. I intended exactly the stance you lampoon as being close to creationism; it's a stance we've seen on BAUT often enough.

Grant Hutchison

Probably depends on the school. I took a one semester course on gravitational physics as an undergrad.

I agree. It's pretty strange, if you think about it.

I see. I was probably over-reacting a little in my statement. What I said remains true to an extent, though. I think all schools in general should pay a lot more attention to modern physical theories/concepts along with SR and GR, both for undergraduates and graduates. I'm a beginner astronomy-physics major myself, and apparently I'll be studying a rather considerable amount of physics courses in later years. I hope the majority of them will be on modern physics.

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

It was not my intent to lampoon anything anyone said, merely to point out that every era of science, throughout the ages, has always characterized its current best theory as the correct description of what the universe is really doing. So we clearly have two possibilities here: 1) it's actually true this time, with GR, say, or 2) it isn't true this time either, so the fact that many people are happy to imagine that GR is what the universe is "really doing" can then be viewed as a kind of problem worth commenting on.

I think we agree completely.
Perhaps you think because I didn't comment I was in some way being supportive of that stance? On the contrary, I think it's worth lampooning.

Grant Hutchison

Then forgive me, often in the past you've used that word to object to a straw-man argument against something you said, but evidently not this time. And I also was not suggesting you didn't realize all this-- it is more about what happens to our words when seen by people who already have a tendency to think scientists have the universe all figured out! What a terrible affront to science that would be, so as you know, I never miss an opportunity to point it out...

Different "-oon".
Another way of thinking of a straw-man argument is as cartoon: simply drawn, brightly coloured, and overblown.
Whereas on this occasion I suggested you were indulging in a lampoon. I was accusing you of being satirical, not simplistic.

Grant Hutchison

I'll have to pay more attention to your "oon" selections.