J.C.MacSwell

"Be a cubical photon" for the win!

At the risk of sounding inane, "nothing", as we think we know it, may not be nothing after all. (or in this case before all, and possibly again after all) Turtles may be the best guess so far: "A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"" —Hawking, 1988

With apologies to Wolfang Pauli, it is NOT EVEN... ..."not even wrong"

For the Earth/Moon gravity, the force is the same, but opposite, on the Earth as it is on the Moon. The Barycenter is not a massive point effecting the GPEs For the Earth/Moon the changes in GPE are pretty close to proportional to displacement (marginal change in force over the distances discussed) If you jump in the air, the COM between you and the Earth stays in place (or on it's path), but of course (almost) all the energy of displacement goes to you. It is not split equally even though the mass displacement is equivalent (opposite) ...all because the Earth is so much more massive

The increase in GPE wrt distance to the barycenter. It is less for the Earth than the Moon.

WRT the barycenter the gain for the moon is much greater than that for the Earth.

OK, let's see how you approach this. Let us know any assumptions you make that you feel might not be obvious.

Ok. Obviously that is not steady, and much more complicated than what would start out as as a constant velocity horizontal flow. I think you have to start by making some simplifying assumptions. when you have hard corners, changing cross sectional area, and varying pressure head before you even get to the airfoil.

I have seen a number of links that claim that the planets orbit the SSB exactly and not the Sun. I think the logic is flawed. If Jupiter was set in stable orbit always further from the Sun, the SSB would move further from the Sun, and at the same time make Jupiter less of an influence on the orbits of the inner planets. If Jupiter was moved far enough, the SSB would have been moved entirely outside the orbit of Mercury. Unless one argued that the orbit of Mercury was hundreds of years rather than 88 days, it would be pretty clear that Mercury was in fact orbiting the Sun. I think they are taking the results of a two body problem and assuming it holds when more bodies are involved. Reasonable guess, but that wouldn't be correct.

In this case it is steady flow, so they are the same thing.

By stream I mean the flow bounded by two streamlines, or the airfoil surface and a streamline when no boundary later is present (as in the hypothetical of inviscid flow). Edit: trying to post an image but keep getting You are not allowed to use that image extension on this community.

It would look the same as when the streams divide at the stagnation point at the front. There is a point (same point in each stream) that comes to rest (wrt the airfoil) before reaccelerating on it's path/s. There is no boundary layer in this (inviscid) case, so "they" (the streams) meet at a point after going above or below the airfoil.

The way I understand it: I think that if the Euler Equations for inviscid flows are set (certain assumptions are made with regard to the wake, or division of flow at the trailing edge) up to allow lift, they invariably include a net drag force on the airfoil. You have circulation about the airfoil, with faster moving flow from above the wing converging with slower moving air from below. In all the set ups that have zero drag (D'alemberts paradox), there is no circulation and the flows converge at zero speed wrt the airfoil...they meet at a second stagnation point and there is no net lift force

There would be no drag, and no lift, if that was the case.

What is the definition of "orbit" that we are comfortable using here? The planets are not drawn gravitationally toward the SSB. At any one time one might be by coincidence, but for the most part the gravitational force vector does not favour that point.

For our Solar System, wouldn't the Solar System barycentric frame be the closest thing we have to an inertial frame? (closest and most permanent)

The SS barycenter orbits the Galaxy, but should otherwise be on a steady path.

That seems to be more about the Sun orbiting the barycenter, and each planets contribution to it. Moving Jupiter closer would move the barycenter closer to the Sun's centre. I agree with the bold, the period of orbit (or wobble) would get shorter

Agree, but that doesn't change the fact that I think the conclusions in the link are incorrect. I don't believe Mercury orbits the common mass of the Solar System, but more so the Sun itself.

It should shift only due to momentum and outside influences, but otherwise should be on a steady path. Conservation of momentum. I don't understand the claims in the link http://solarchords.com/solar-chord-science/astrophysicists-earth-orbit-sun-or-barycentre/ Why would the inner planets orbit the barycenter? As I stated in a different thread: "Taking the 3 body problem of Sun, Jupiter, and Mercury, If we placed Jupiter far enough away the barycenter would lie outside Mercury's orbit. I think Mercury would still be in stable orbit about the Sun in that case, though of course the Sun and Jupiter would still essentially orbit about the (new) barycenter." What am I missing? Surely having Jupiter further way would give it less influence on Mercury's orbit (during any one orbit period)

I think it is not uncommon to assume lift and associated (vortex inducing) drag for airfoils with inviscid flow, by making assumptions about the separation points and wake (which is outside of the potential flow and cannot be entrained with it, as there are no shear forces and no friction), for the purpose of analyzing the flow outside the boundary layer of a real airfoil in steady flow. The assumptions are necessary (for the reasons stated by Studiot, without them no drag and no lift), and with them you can get a pretty good approximation of the lift to induced drag, above a baseline of skin friction and form drag. When an airfoil is allowed to rise this reduces it's effective and apparent angle of attack (I prefer to take the no lift angle as zero, which is different from Zet's, but either can be used) Within normal range, until the stall point is approached, induced drag is close to linear correlation with lift and angle of attack. The problem is assuming no induced drag (no lift associated drag). That's free lunch. You are assuming energy conservation does not hold from the start, so of course energies won't balance...you can use turbines and propellors based on this and design perpetual motion machines...free lunch. Zet, for your L shaped thought experiment... Assuming you get lift and associated drag, but otherwise neglect skin friction and form drag: When the airfoil is constrained that is the highest lift case...and highest drag. The result is lower exit velocity of the flow, but higher kinetic energies remaining overall, due to vortices from the induced drag associated with the higher lift. When the airfoil is allowed to rise that is a lesser lift case...and lesser drag. The result is higher exit velocity of the flow, though less K.E. overall, due to less vortices from the reduced induced drag associated with lift... and the potential gained from raising the airfoil being the difference.

I was hoping to hear back from AJB, but I am fairly sure Earth (and Mercury, though I don't believe it is exactly the same point) orbit something much closer to the centre of the Sun than the centre of mass of the Solar System. Taking the 3 body problem of Sun, Jupiter, and Mercury, If we placed Jupiter far enough away the barycenter would lie outside Mercury's orbit. I think Mercury would still be in stable orbit about the Sun in that case, though of course the Sun and Jupiter would still essentially orbit about the (new) barycenter.

Why does it not occur anyway? (it occurs more so...but baby steps) The airfoil is slowing the wind. Drag is being created. What makes you think it slows the wind more by allowing it to rise? If I do a brake stand in my car, revving the engine at full power, and finally take my foot off the brake, are you going to ask "I wonder where the energy came from to accelerate the car?"

To AJB: My bolded is incorrect, as per Moontanmans link. Jupiter moves the center of mass close (outside) to the perimeter of the Sun...I don't believe Mercury orbits that point, but something much closer to the Sun's center of mass for reasons stated

Is this correct? Surely, say, Mercury is orbiting the Sun's centre more so than the collective centre of mass? Not that they (Sun's centre of mass vs solar system as a whole) would be very far apart(still near the centre of the Sun), and still influenced of course by the other planets but it would seem to me the inverse square law would reduce the influence of the more distant planets more than a linear mass balance, with the Sun.