J.C.MacSwell

So is the flow increasing at 9.81 mps² at that point? The ocean analogy would have increasing flow toward the centre, but constant speed at each point (this is why I assumed some kind of drag was at work)

Ok. I guess I took your ocean analogy as how it might work. So the inflow of space somehow affects an object in free fall, but there is no resistance otherwise?

You haven't answered anything with regard to where the analogy clearly breaks down. Try explaining a simple orbit. In Relativity or Newton Gravity it's free fall. In this it is plowing along tangentially against the medium of the flow. Explain why there is no drag in the tangential direction.

OK. So you are required to resist the flow/gravity to stay stationary on the Earth's surface (presumably electromagnetic forces at play), and there appears to be a radial inverse square law effect, but how is there no drag tangentially, for orbits? Also, what is the inflow velocity of the flow near the Earth's surface that would interact with matter to produce the 9.81 m/s2 acceleration? If something was already free falling at that speed would it then accelerate much less, only to match the inflow velocity gradient?

Is this a constant flow? That would be consistent with feeling a constant force while resisting gravity at the surface (like my butt in my chair right now), but if something was dropped would it not get up to flow speed and therefore stop accelerating? (even in a vacuum) Or is it constantly accelerating flow, requiring more and more space to ingest, and why is my butt not feeling a constantly increasing pressure?

It is an equation

For homogenous spheres it makes no difference if integrated over the complete sphere, or simply calculated assuming r is at the centre point. The result is exactly the same, at any distance, whether using the basic formula or doing the calculus. The "inefficiencies" of the mass off the resultant vector line are exactly compensated by the "extra efficiencies" of the mass that is closer than r being a greater effect than the inefficiencies of the mass further away than r. At greater distances these inefficiencies become less significant, but it is not relevant except when non spheres or varying densities are present since they otherwise cancel out at any distance.

Really only enough information to answer "time required to react before getting eaten"

Not sure what you mean exactly. What was your result?

does it seem reasonable? If that is the final velocity the average would be half that...around 35m/s...and it would have taken about a seventh of a second to get to 70.71m/s You might want to double check the decimal place of your result...

It can effect the amount of dark matter required but obviously not enough to try to explain it otherwise. My main point was that much of the data is less accurate generally than implied by the error ranges given. Much of it for reasons unique to Cosmology.

Assuming I'm thinking it through correctly: Not for doppler shift measurements, no (Hubble effects aside). Wouldn't it exacerbate a problem if it did, rather than cancel? Allowing for Hubble at greater distances would not cancel either. If say you overestimated the distances and you then overestimate the speeds, these both lead to looking for more dark matter. You should however get some cancelling from overestimating mass (thus looking for less dark matter) (by radial velocity here you aren't referring to radial velocities within the galaxy, are you, but radial velocities wrt Earth used to calculate the tangential velocities at radial points, thus rotation curves, of the distant galaxy? )

The size, brightness, and most particularly distances from the galaxy centres are directly related to the distance away and therefore the rotation curves. M33 is in the Local Group (where one would expect some of the more accurate estimates) Velocity measurements from redshift effects based on distance (Hubble effects) would become significant much further away.

Using the galaxy rotation curves for M33 as an example: How do you think you can get such small error bars for velocities and positions on a galaxy where you are not even sure if it is 2,380,000 ly or 3,070,000 ly away? You base it on assumptions (pick somewhere in the middle that you believe most likely correct?) and then account only for further plausible errors inherent in your observations based on an estimate of what those further errors might be.

The error bars are based on a number of assumptions, none of which are (of course) at a confidence level of 100%. I understand you have to base these things on something, but this is not taken into account in the error bars. Assuming they are the most reasonable set of assumptions we have to work with it might also be reasonable to exclude proposed solutions that don't fit...but it is a much further stretch to exclude modified gravity entirely as a potential solution.

From Wiki on the M33 galaxy that rotation curve refers to (it's part of the local group): The disk of Triangulum has an estimated mass of (3–6) × 109 solar masses, while the gas component is about 3.2 × 109 solar masses. Thus the combined mass of all baryonic matter in the galaxy may be 1010 solar masses. The contribution of the dark matter component out to a radius of 55×103 ly (17 kpc) is equivalent to about 5 × 1010 solar masses. Estimates of the distance to the Triangulum galaxy range from 2,380×103 to 3,070×103 ly (730 to 940 kpc) (or 2.38 to 3.07 Mly), with most estimates since the year 2000 lying in the middle portion of this range,[3

For the bold: Right. So it seems something is needed. For the rest. What makes you even suspect this might be true?

Not at all required. If the noise was on par with the discrepancy neither dark matter or modified gravity would be needed.

Observations of normal matter are far from precise, and much of he accuracy is questionable. I think we know that it has to be dark matter or modifications to gravity theory since the discrepancies are so high. As we get more and better data some genius may recognize a pattern amidst the noise and then plausibly come up with a modified gravity approach, with or without dark or extra-normal matter...or maybe someone figures out what dark matter is and modified gravity is not required. I understand the idea...not working, give it up already...I think that time might have come for many or most, but to suggest that physics as a whole should give up on it completely is IMO premature. "We haven't succeeded yet" was true of every concept at one point in time, including ones that lead to current theories.

Except 16000 is allowable as you used initially, not 14000 (which would have allowed about 49kg not 11.21 by your method, which is sound otherwise, but with 16000 it is around 228 kg) Otherwise the difference was just that you used 9.81 for g and FrankP used 9.8

So 1428.57 kg maximum on cable accelerating upward. Capacity would be that - the mass of the empty elevator or 228.57kg.

I think I read it as you intended...my point was implying that since we are not at that point it would be premature to give up on all attempts at modifying gravity. Obviously there are judgement calls to be made. A researcher has to have strong reasons to believe in the plausibility of it, not simply "lets see if we can find an equation that fits all the observations" (much of which is "noisy")

Those are specific models. I'm not suggesting every line of inquiry for modified gravity should be kept open. Certain lines of thought have been more or less shown to be inadequate. Modified gravity as a concept has not IMO. Proof of dark matter may put it to bed, but in the mean time it will no doubt remain open. We are not at that point yet.

I agree. But seems less ad hoc is still far from proof. It just means it seems more plausible at this time. Some form of modified gravity is the second most likely explanation. Why should all of science completely abandon it? A shared explanation between the two ideas is also a possibility.

I thought it was more complicated than that, and it could be tough to find a fit for the dark matter in many cases. Not that the theory/hypothesis was ever proven wrong, but assumptions of the details in particular cases were very much subject to change as more observations were made.