See the section "The Rotation Curves of Low Surface Brightness Galaxies" in attached first link. And also the last link. That has loads of data you looking for.

Other option is to look for articles and wikipedia and extract the data points manually or use some online available tools. I have attached multiple links below.

https://www.astro.umd.edu/~ssm/data/

https://en.wikipedia.org/wiki/Galaxy_rotation_curve#/media/File:M33_rotation_curve_HI.gif

http://arxiv.org/pdf/astro-ph/0506370.pdf

http://astro.u-strasbg.fr/~koppen/Haystack/rotation.html

http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/main_BACK.html

http://www.ioa.s.u-tokyo.ac.jp/~sofue/h-rot.htm

Thank you Vikash, this will be most helpful.

I also came across the issue of prograde and retrograde motion..

https://www.researchgate.net/profile/Steven_Sesselmann/publication/292984048_Possible_Reasons_for_Differences_in_the_Velocity_Measurements_of_Orbiting_Celestial_Bodies/links/56b3c71808ae61c480581120.pdf?ev=pub_int_doc_dl&origin=publication_list&inViewer=true

Article Possible Reason for Differences in the Velocity Measurements...

Here is something direct

http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/courteau/www/courteau_help.html

and here is an ancient compilation (> 20 years) that shows the power of rotation curvey analysis

http://adsabs.harvard.edu/abs/1993AJ....105...97S

and for 2D velocity fields, consult this

http://adsabs.harvard.edu/abs/2001ApJS..136...41B

Stephen, do you realise that your use of "prograde" and "retrograde" is very non-standard. It's likely to cause a lot of confusion.

@ George: Yes I realise it is non standard, but I believe it is necessary to assign a vector to any orbital motion which does not return to the same point in space. 

Any body with respect to an observer can only be in one of three states, moving towards, moving away or at rest, meaning the velocity vector is positive, negative or zero.

Measurements confirm distances between heavenly bodies is generally increasing, therefore I call most orbitals retrograde as the bodies are spiralling away from us. 

SS: Any body with respect to an observer can only be in one of three states, moving towards, moving away or at rest, ..

Those describe radial motion only. The terms are used to describe clockwise versus anticlockwise motion around a centre. For us near the edge of the galaxy, both would be moving away for about half the orbit but towards for the other half.

Orbits within galaxies are also mostly circular (at least for the thin disk) so at constant radius. Cosmological expansion only applies between galaxies, not within.

@GD: Orbits are not circular, bodies do not return the the same coordinates in space-time, instead they follow a helical path. Radial motion is just the extreme case of perpendicular motion, take for example the moon, the radius has been measured to increase by around 1" per year, which means it is in a retrograde orbit.

Think of the orbit as grooves on a vinyl record, when the record is playing prograde the needle eventually moves to the centre, but when you play it retrograde the needle moves to the rim.

The path in this case is helical.

Your illustration would indeed be helical but in the case of stars within the galaxy, the orbits are not helical, radii don't increase. In fact gravitational radiation means they will generally be decreasing but by an undetectable amount. Orbits in the thin disc are close to circular, those in the thick disc layers are more elliptical. Of course there are minor perturbations where stars pass close to each other but those only add random elements and such close encounters are rare, and most stars also have an oscillatory motion perpendicular to the plane of the disc which is more rapid than the orbit.

Even if they were helices, a helix could either wind clockwise or anticlockwise. Retrograde would mean a particular star's helix wound the opposite way to all the other stars, that was the point I was noting, your use of that term is unusual.

 @GD

In your first paragraph you state that stars orbit in closed orbits, then you say they decrease by undetectable amounts, so lets agree it's ambiguous, and statistically very unlikely or near impossible that the orbits can be closed.

In your second paragraph it seems you may not fully understand what is meant by v and -v , as it has nothing to do with what it looks like. When I state that the moon is moving in a retrograde orbit, I am not suggesting it should rise in the west.

What changes direction is the arrow of time, and there is a simple test to prove this, I call it the string test. If you hold a roll of string and tie one end to the moon when it is directly above your head, and hold the rope tight, does the string wind or unwind on the roll?

I rest my case.

https://www.youtube.com/watch?v=Zi6FkABFcQY

SS: In your first paragraph you state that stars orbit in closed orbits, ..

If you read it carefully, you'll see I never said the orbits were closed.

SS: then you say they decrease by undetectable amounts, ..

That is correct but it is really a tiny amount.

SS: .. so lets agree it's ambiguous, ..

No, but ..

SS: and statistically very unlikely or near impossible that the orbits can be closed.

Yes, we agree on that. Specifically the displacement above and below the disc is unlikely to be an exact fraction of an orbit so stars won't return to the same place each time. See the first link.

SS: When I state that the moon is moving in a retrograde orbit, I am not suggesting it should rise in the west.

Quite right. Imagine looking down on the Earth/Moon system from the North pole. The Moon appears to rise in the east because the Earth is spinning anti-clockwise from that point of view. The Moon also orbits anticlockwise once a month so it appears to rise about an hour later each night (53 minutes). If the moon orbited clockwise, that would be called a retrograde orbit and it would rise earlier each night.

See the second link for an illustration.

SS: If you hold a roll of string and tie one end to the moon when it is directly above your head, and hold the rope tight, does the string wind or unwind on the roll?

I presume you are standing at the pole so the string doesn't wrap round the Earth. The answer then is both ways, you have to wind for two weeks then unwind for two weeks because the orbit is elliptical, but that only measures radius which is irrelevant. Retrograde would mean the string moved west compared to a Foucault Pendulum, prograde means it would move east, regardless of the variation of the radius. That's why I said you were using the term in an unconventional and confusing manner.

The Wikipedia link below should make it clearer.

http://www.astro.utu.fi/~cflynn/galdyn/lecture9.html

https://en.wikipedia.org/wiki/Retrograde_and_prograde_motion

https://en.wikipedia.org/wiki/Retrograde_and_prograde_motion#/media/File:Retrogradeorbit.gif

@GD  

Quote WIKI "In the Solar System, all of the planets and most of the other objects that orbit the Sun, with the exception of many comets, do so in the "prograde" direction,"

The above statement is false yet they show a correct animation of retrograde motion and it is similar to the planetary system.

It all comes down to the point of reference, so if you assume the fixed background stars to be your point of reference everything is prograde, but if as I suggest the observer is the point of reference the direction changes. 

If you imagine the earth and the moon as two rotating discs of the same radius, one with an orbital of 1 day and the other with an orbital of 28 days it's easy to see that the moon disc is moving retrograde with respect to the earth disc.

SS: The above statement is false

No, the statement is true as is the rest of the page, it is your understanding of the meaning of the word that is flawed. That's what I was pointing out.

SS: It all comes down to the point of reference, so if you assume the fixed background stars to be your point of reference everything is prograde, but if as I suggest the observer is the point of reference the direction changes.

It is neither, the point of reference is the central object. In the case of the Earth and Moon, the reference is the Earth. In your quote from the Wiki page, the reference is the Sun. It says the planets orbit around the Sun in the same direction that the Sun rotates.

SS: If you imagine the earth and the moon as two rotating discs of the same radius, one with an orbital of 1 day and the other with an orbital of 28 days it's easy to see that the moon disc is moving retrograde with respect to the earth disc.

If the discs are rotating in the same direction, that's prograde. If the Earth rotates anticlockwise while the Moon rotates clockwise, that's retrograde. If the disc of the Moon orbits anticlockwise round the Earth (it does), that's prograde but if it orbited clockwise that would be retrograde.

The speed of rotation is not involved in the term.

@GD 

Our way of thinking about space-time differs. you are suggesting there is some kind of absolute space in which the events of the world take place, I say this after reading your above comment

[Quote GD] "If the discs are rotating in the same direction, that's prograde" [/quote]

How are you defining direction ? If one only has two discs there is no way to tell, all one can say is they have relative rotation, but if we introduce a third disc we can say something about any two of the discs with respect to the third.

We can now substitute the three discs with, a) the sun b) the earth c) the fixed stars and say with respect to the fixed stars the Sun and the Earth are moving in a prograde direction, I don't disagree with this.

What is unconventional with my thinking is to use the observer as the fixed reference point, and the reason I am doing this is because galaxy rotation curves are measured by doppler shift "from earth" and not by Keplers method using the fixed background stars. 

If you can find a way to measure galaxy rotation with respect to the fixed background stars you can perfectly well use Keplers law to work it out, but I can't think of an easy way to do that. 

So astronomers only need to flip the sign in front of the vector to see the correct rotation curve, instead they go off on a tangent and invent dark matter (a unicorn) to fix the problem. 

Substituting an unknown with a fictional substance is lousy science, yet scientists are getting away with it time and time again. What these unicorns have in common are strange names and properties that make them impossible (or very expensive) to observe.

SS: If you can find a way to measure galaxy rotation with respect to the fixed background stars you can perfectly well use Keplers law to work it out, but I can't think of an easy way to do that.

That is done using VLBI against "fixed" quasar references. It confirms that the Solar System has a velocity of roughly 240km/s in a circular orbit (with the minor variations we discussed earlier) within our own galaxy.

SS: galaxy rotation curves are measured by doppler shift "from earth"

True, so see the first attached graphic. Suppose that Doppler is used to measure the speeds at C and D and the results are +300km/s at C and -200km/s at D. The speed of the galaxy as a whole relative to Earth (the black arrow) is the average hence +50km/s, and the rotation speed of stars at the radius of the green circle is the absolute value of half the difference or 250km/s.

Now repeat for stars at A and B typical of all those at the radius of the red circle. The values turn out to be the same, +300km/s at A and -200km/s at B so the rotation speed is also 250km/s at that larger radius.

How would "flipping the sign" makes the rotation speed on the red circle less than that at the green circle?

Regarding the language definition, in the first diagram, both stars are rotating the same way. If all the stars in the galaxy were rotating round its centre the same way (green arrows at C and D) apart from one rogue star (red arrows at A and B) as shown in the second diagram, that star would be described as moving retrograde but I don't see what relevance that has to the measured speeds, the signs would be reversed for that one star but the average and rotation values would be the same. Note also, we cannot generally measure single stars that way, only the bulk motion of the disc.

George, I think you have just confirmed my case...

A body in circular motion within a system moving away from you the observer is tracing out a helix in space, 

Think of the space between you and the galaxy as a long screw, the distance to a star in the galaxy, following the thread is increasing, which means negative velocity with respect to the observer.

We needs to stop thinking of the world as a static stage on which celestial mechanics take place like some kind of gear box, this is not how it works, stars do not rotate in perfect circles like gears on ball bearings, everything is tracing out helixes.

https://youtu.be/0jHsq36_NTU

SS: I think you have just confirmed my case

No, I've shown why it's wrong.

SS: A body in circular motion within a system moving away from you the observer is tracing out a helix in space

No, it traces a prolate cycloid.

SS: Think of the space between you and the galaxy as a long screw,..

That would be the case if we saw it face on, but the orbital velocity can't be measured by Doppler in that case. The illustration I drew shows the distant galaxy edge on, you've got the orientation wrong by 90 degrees.

http://mathworld.wolfram.com/ProlateCycloid.html

 George, all that matters is that the distance along path is increasing, it doesn't make one iota of difference weather I call it a helix or a prolate cycloid. I honestly don't think you have given this much thought, it shouldn't be that hard to comprehend. 

Sometimes we have to unlearn the misinformation we have been taught. 

I can't add any more..

SS: all that matters is that the distance along path is increasing,

The common motion of the galaxy as a whole is subtracted from the rotational measurement so what you are talking about is already taken into account, it's really quite trivial.

SS: it doesn't make one iota of difference weather I call it a helix or a prolate cycloid.

Names don't matter but the angle we see the galaxy does. You've got that completely wrong.

SS: I can't add any more.

No, probably not, but you can sit down quietly and think about what I've said, it will save you a lot of embarrassment.

 So you bend the laws of physics to fit your theory?

Who told you to subtract the motion of the galaxy?

Absolute relative velocity is measured along the path connecting you the observer and the star there is no third party involved here.

PS: When I use the term "you" it is not meant to be personal, I mean "you" as in all the qualified astronomers who believe Kepler's inverse square law is correct, as opposed to me, the crank who insist planets orbit backwards.

SS: So you bend the laws of physics to fit your theory?

No, they are applied accurately. You seem to be failing to correct for the motion of the observer.

SS: Who told you to subtract the motion of the galaxy?

Newton's inverse square law relates a force to the distance between the bodies

f = GMm/r2

When considering a planet orbiting round the Sun, the value for "r" is the distance between the planet and the Sun. If you wanted to apply Kepler's Laws to Mercury for example, you use the orbit of Mercury as measured from the Sun, not from the Earth. Since our measurements are from the Earth however, you need to convert those to measurements relative to the Sun.

For a star orbiting round the centre of a distant galaxy, the value of "r" is the distance between the star and the centre of that galaxy. That speed is also related to Kepler's Third Law which relates the period of the orbit to the radius, and the period is the circumference divided by the speed of course. That's the speed relative to the centre of the distant galaxy, not relative to Earth.

That means subtracting the galaxy's mean velocity vector from the observed vectors.

SS: Absolute relative velocity is measured along the path connecting you the observer and the star there is no third party involved here.

The "third party" is the centre of the galaxy around which the star is orbiting.

PS: When I use the term "you" it is not meant to be personal, I mean "you" as in all the qualified astronomers who believe Kepler's inverse square law is correct, as opposed to me, the crank who insist planets orbit backwards.

No problem, I understand it's nothing personal.

@GD: There is no doubt that you and everyone else are applying Newtons laws correctly to orbital motion, and I have no problem understanding how the laws are being applied and why they give the results they do and I am not suggesting for a minute that you should apply Newtons laws in any other way.

I have been trying to share some new insight I have had with respect to observing bodies at higher vs lower potential. It would probably be easier to understand if you had quick read through my GPT paper (unless you have already done this). 

To my surprise GPT predicted relative velocity between an observer on earth and a body orbiting above earth ought to increase with increasing height (radius), this of course contradicted Keplers law, so it became an issue for me and my theory.

An issue until I realised how planets orbit with retrograde motion, so as the radius increased bodies moved faster backwards. When you think of it this makes sense, because when you want to move a satelite to a higher orbit you need to apply more energy to accellerate it i.e. make it move faster backwards.

To understand my point of view you need to accept how I have flipped the world around and postulated the observer at rest, this was a necessary move and a consequence of GPT absolute potential. 

Please give GPT a chance as a stand alone theory without trying to mould it to classical physics, it won't work, it's like trying to put a left hand thread nut on a right hand thread bolt.

GPT provides a simple solution to the dark matter problem which does not require the invention of any new unicorns, like dark matter, so why not consider it?

Research Ground Potential Theory

SS: as the radius increased bodies moved faster backwards.

They don't, they continue to move forwards but slower. It's easy to check this, just look at some real life examples. The first link below allows you to track the International Space Station, it's just about to fly west to east across Canada as I type (image attached) and you can see the screen update in real time. This is a low radius prograde orbit so it moves faster forward than the Earth turns hence it "rises" in the west.

If you watch TV via satellite, your antenna will point at a fixed point in the sky. To do that, the satellites are in a "geosynchronous" orbit which takes 23 hours, 56 minutes. To do that, they orbit slower but still in the prograde direction, completing one orbit in the same time as the Earth rotates so they are at higher altitude.

The third example is the Moon. It has an even higher altitude so it moves slower, taking a month to complete an orbit. The Earth spins faster so the Moon 'rises' in the East, however the orbit is still prograde so it rises 53  minutes later on consecutive nights.

If a satellite orbited retrograde, it would rise in the East but do so earlier each night.

SS: GPT provides a simple solution to the dark matter problem ... so why not consider it?

Why not? Because you haven't addressed the evidence for dark matter at all so you offer nothing to consider:

• I drew you a graphic showing how velocities are measured but you haven't replied to that at all.
• You thought the orbits were helices but that would apply to galaxies seen face on which couldn't have their velocities measured by Doppler, the correct orientation is close to edge on and the motion is a cycloid.
• You didn't know you had to subtract the mean velocity of the galaxy to get the orbital velocity of the stars which is secondary school vector subtraction.
• You haven't explained why the orbital velocity of stars in galaxies is constant while that of satellites and planets decreases with altitude.

Basically, you don't have the faintest idea of what is being measured, never mind what it implies.

http://www.isstracker.com/

http://www.esa.int/Our_Activities/Human_Spaceflight/International_Space_Station/Where_is_the_International_Space_Station

• [GD}I drew you a graphic showing how velocities are measured but you haven't replied to that at all.

I thought it was trivial and as I already said above I am not disputing your method and how you apply classical mechanics to this problem. The classical approach will give the classical answer. thousands of astronomers cant be wrong right?

• [GD]You thought the orbits were helices but that would apply to galaxies seen face on which couldn't have their velocities measured by Doppler, the correct orientation is close to edge on and the motion is a cycloid.

Of course I understood that, I also understand that the orbital direction can't change simply by rotating the orientation of a galaxy.

• [GD]You didn't know you had to subtract the mean velocity of the galaxy to get the orbital velocity of the stars which is secondary school vector subtraction.

Of course I knew that, I was merely pointing out hoe this operation was necessary to make the observation agree with classical mechanics. In the system I propose where velocity is a direct consequence of potential this operation is superfluous.

• [GD]You haven't explained why the orbital velocity of stars in galaxies is constant while that of satellites and planets decreases with altitude.

Yes I did, because when you flip the sign and sum consecutive negative velocities you get a flat curve. 

• [GD]Basically, you don't have the faintest idea of what is being measured, never mind what it implies.

I never claimed to be an astronomer, but I do understand how rotation curves are measured calculated and plotted, and I can clearly see how and why it is giving the wrong result. Made a reasonable attempt to explain it to you, but you seem either unable or unwilling to understand me.

In my GPT paper I show in a series of logical steps how absolute velocity is a function of absolute potential, which when applied to orbitals come out with a negative sign.

As for the international space station it's most likely in a prograde orbit, because it will finally crash to ground not move further and further away like the moon. As I stated before it all depends on weather the orbiting body is getting closer and closer to the centre of rotation (prograde) or further and further away (retrograde).

Thanks for the links, very interesting..

http://groundpotential.org/forum/viewtopic.php?f=11&t=40

@ GD, To help you grasp the concept of prograde vs retrograde orbitals, I have made a diagram to show both prograde and retrograde orbits. As you can see it depicts two identical systems both with a similar mass orbiting at the same radius and (according to classical Newtonian standards)  in the same direction, yet as you can clearly see these orbitals are inverse.

In the case of the international space station friction with the upper atmosphere causes it to loose speed, and without the occasional rocket boost it would be in a natural prograde orbit, however this is not the case with the moon and other naturally orbiting bodies, they are all in retrograde orbits. 

Hope that settles the debate ;)

SS: To help you grasp the concept of prograde vs retrograde orbitals, I have made a diagram to show both prograde and retrograde orbits

Thank you Steven, that's immensely helpful, I now understand what you mean.

I've copied your diagram and added arrows to indicate the rotation of the central bodies, A and B. I've kept the systems identical so both are rotating the same way. That means both orbits are prograde. I've also duplicated the drawing beneath but this time with both central bodies orbiting the other way. For this pair, both diagrams illustrate "retrograde".

Since prograde and retrograde describe the direction of rotation independent of the radius, I've added text to all four to include that aspect.

SS: this is not the case with the moon and other naturally orbiting bodies, they are all in retrograde orbits.

The planets have decreasing radii so in your terms they would be prograde while the Moon is very unusual, it is dragged by the Earth's ocean tides so the radius is increasing so it would be what you call retrograde. Unfortunately you are using the term incorrectly. Your diagram on the right represents the Moon orbiting the Earth and as you can see in my version version where the arrow on A represents the rotation of the Earth, that should be described as prograde.

SS: Hope that settles the debate ;)

I hope so too, my extended version shows all four possibilities with the definitions astronomers use. Remember you can always check my diagram against the Wikipedia page.

Now if that clears up the terminology, we can go back to your claim about "flipping the sign" removing the need for dark matter.

@GD 

Nice we are getting closer, but I have to object to your illustration above on the grounds that one can NOT define a direction for both bodies without a third reference point. All that can be said about a systems of two bodies is that they are in a mutual orbit. 

You need to think about this system more carefully. Imagine the smaller body spinning extremely rapidly around the central body, and imagine you were able to slowly turn the central body clockwise and then counter clockwise with a velocity much less than the orbiting body, it should be clear to you that this does not in any way change the orbital direction, it merely changes the orbital speed slightly.

So basically that little arrow you added changes nothing, the only thing that matters is weather the orbiting body is getting closer or further away

GD: "The planets have decreasing radii" 

Do you mean that the radius between the planets and the sun are decreasing?

Have you found a reference to this?

According to GPT this ought not to be the case, unless there is some kind of atmospheric drag causing the planets to lose energy.

The stars in a galaxy should all be in retrograde spiral orbits when  observed from earth. 

Now that we are on the same page we can start looking closer at how to plot the rotation curve.

SS: Nice we are getting closer, but I have to object to your illustration above on the grounds that one can NOT define a direction for both bodies without a third reference point.

Traditionally that would be the "fixed stars" when considering the Solar system although in our case the Sun is sufficient unless you want to go back to the pre-Copernican idea of the Sun orbiting around the Earth. However, modern technology can measure rotation well enough to show even the stars are not really "fixed".

The way to understand it is to use a gyroscope. Take it to the North Pole, align the axle horizontally and start it spinning. You can now measure the rotation of the Earth relative to the gyroscope. The Earth will take 23h 56m to complete one rotation of 360 degrees relative to the gyroscope and it turns anticlockwise, that's the "sidereal day". The moon will take 27d 7h 43m to orbit once round the Earth and it too rotates anticlockwise, that's the "sidereal month". That corresponds to the top left diagram in my image.

Since both rotate anticlockwise relative to the gyroscope, the Moon's motion is called prograde. That is how the term is used.

SS: Now that we are on the same page ...

Not quite yet. We know the Earth rotates because the Sun rises and sets, my added arrows (top pair) show the direction as seen from above the North pole which correspond to the Sun rising in the East. Once you grasp that, we'll be on the same page. The diagram is how astronomers use the term and if you adopt that, much of the confusion will disappear.

For stars in a galaxy, the central object is the core of that galaxy, not the Earth of course.

GD: "The planets have decreasing radii" 

SS: Do you mean that the radius between the planets and the sun are decreasing?

Yes, I did, although in hindsight I can see it could be read as the planets shrinking. That was never the intent.

SS: Have you found a reference to this?

No, I doubt it's been measured. It would be due to drag of the Solar Wind, the Poynting-Robertson effect and gravitational radiation but all of those are tiny for a planet. Essentially, the radii are nearly constant. The same is true of stars in a galaxy.

https://en.wikipedia.org/wiki/Poynting%E2%80%93Robertson_effect

@GD

By now we should agree there are two different definitions.

• relative rotation
• absolute rotation

Absolute rotation is what you talking about and relative rotation is what I am talking about. See Machs Principle for absolute rotation.

Two bodies can be in a state of relative rotation without a strict definition of the centre of rotation, the center of rotation can be anywhere on a line connecting the two bodies. Where on this line will generally be a function of their relative masses. 

Relative rotation may take on one of three possible states.

• spiralling outwards (negative velocity)
• steady state (no relative velocity)
• spiralling inwards (positive velocity)

The difference between negative and positive velocity can obviously be very subtle.

We know planets around the Sun have been orbiting for a very long time which means they must be very close to a steady state and the slightest drag from collissions with particles of dust and gas could send them spiralling inwards. 

On a large scale the Universe seems to be expanding (Hubble redshift) so I am pretty sure far distant objects ought to be spiralling away from us.

We can agree that Keplers method of calculating orbital velocity was based on absolute rotation because his mate Tycho Brahe plotted planetary movements against the background stars. 

Whereas the method of doppler spectroscopy measures relative velocity. I understand that astronomers adjust for the hubble expansion in order to correct the numbers, but I believe this method is fundamentally flawed.

Subtracting a real velocity between the observer and the measured galaxy upsets the relative velocity measurement and should be considered an illegal operation one can  compare this to a one sided entry in an accounting book. 

Absolute velocity measurements work fine on a small scale, so Newtons planets are not in any imediate danger of falling out of the sky, but on a large scale we cant use absolute measurements in the same way. Hubbles constant can't simply be adjusted awayto make classical physics work, it has to be left in. 

I didn't make the rules that govern the Universe, but I know if I agree with you we will both be wrong ;)

https://en.wikipedia.org/wiki/Mach%27s_principle

SS: Absolute rotation is what you talking about and relative rotation is what I am talking about.

No, what we are talking about is how "prograde" is distinguished from "retrograde" in the English language. Your diagram was very helpful, it showed that the way you are using the words is not what they mean in English. I've corrected your diagram, you just need to correct your use of the terms, and check a dictionary or the Wikipedia article if you think I'm wrong.

SS: See Machs Principle for absolute rotation.

Mach's Principle probably isn't right but you have to think about what it means in reality anyway. His idea was that the reference for rotation isn't absolute but is set by the mean rotation of all the matter in the universe. These days we use a set of distant quasars to determine the reference frame and if the universe is rotating, that reference set is sufficiently large to identify the correct reference motion according to Mach's Principle. It removes the error caused by the rotation of our galaxy which would result from using visible stars.

In other words, measuring relative to the ICRF is valid either way.

SS: On a large scale the Universe seems to be expanding (Hubble redshift) so I am pretty sure far distant objects ought to be spiralling away from us.

The Andromeda galaxy and many others nearby are moving towards us, however that is irrelevant. More distant galaxies are all moving away.

The key point you need to grasp is that since the Andromeda galaxy is 2.54 million light years away, it would have to move at 5.83 billion times the speed of light to rotate around us in a day.

Other than minor peculiar motions, the distant galaxies are moving radially

SS: We can agree that Keplers method of calculating orbital velocity was based on absolute rotation because his mate Tycho Brahe plotted planetary movements against the background stars.

Yes, and we should be able to agree that galaxies don't orbit round the Earth at billions of times the speed of light so that technique is correct.

SS: I understand that astronomers adjust for the hubble expansion in order to correct the numbers, but I believe this method is fundamentally flawed.

You need to think about it more carefully.

SS: Subtracting a real velocity between the observer and the measured galaxy upsets the relative velocity measurement and should be considered an illegal operation one can  compare this to a one sided entry in an accounting book.

No, subtracting the same number from both sides of a subtraction has no impact on the result. That's true in accounting and all other maths.

SS: Absolute velocity measurements work fine on a small scale, so Newtons planets are not in any imediate danger of falling out of the sky, but on a large scale we cant use absolute measurements in the same way. Hubbles constant can't simply be adjusted awayto make classical physics work, it has to be left in.

You could do that if you wished, but the end result will not change, when you subtract the opposing side, it cancels along with the motion of the galaxy.

SS: I didn't make the rules that govern the Universe, but I know if I agree with you we will both be wrong ;)

The problem is you're not using Mach's Principle, you are trying to use the Earth as a non-rotating reference and that goes back to the Aristotelian model of the universe, a precursor to the Ptolemaic system. You should read up on a chap called Copernicus and his model at least. ;-)

http://csep10.phys.utk.edu/astr161/lect/retrograde/aristotle.html

http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html

@GD:

If the main sticking point here is the definition of prograde and retrograde, let's agree to use other words to describe the phenomenon, how about spiralling away and spiralling towards?

I am not sure that measuring relative to ICRF hold for very distant objects, the relativistic effects become larger with distance.

Consider shining a laser beam perpendicular to the surface of the earth somewhere near equator, the laser beam will sweep around in a 24 hour period, but if we were to follow the beam out to a large radius we would get to a point where the angular velocity is equal to the speed of light and at that point the beam would move side ways 1 meter for every meter it moves forwards. Taking this to the limit we see that the radius approaches an asymptote where the beam cheses its own tail around the orbit.

The point I am trying to make here is that distance distorts measurements so using the ICRF as a reference might not hold.

If you read my GPT paper you see that the relative velocity equation is already relativistic, and needs no further adjustment to be accurate, if you know how something moves you know what its potential is and vis versa.

Regarding Aristoteles and Copernicus, there is no wrong and right, only a choice of preference. Aristoteles method is closer to my GPT it gives preference to the observers state, as GPT places the observer at the origin of space and time.

Can we agree that a body spiralling away from the observer has the opposite velocity vector to a body spiralling towards the observer?

That would be a good outcome ;)

SS: If the main sticking point here is the definition of prograde and retrograde, let's agree to use other words to describe the phenomenon, how about spiralling away and spiralling towards?

It's not really a sticking point but if you are going to use technical terms, you should use them correctly. If you can't do that for some reason then it's best not to use them at all. Those phrases would be fine, they convey what you mean.

SS: I am not sure that measuring relative to ICRF hold for very distant objects, the relativistic effects become larger with distance.

The ICRF is defined by objects at very large distances so it works fine.

SS: Consider shining a laser beam perpendicular to the surface of the earth somewhere near equator, the laser beam will sweep around in a 24 hour period, but if we were to follow the beam out to a large radius we would get to a point where the angular velocity is equal to the speed of light and at that point the beam would move side ways 1 meter for every meter it moves forwards.

Exactly, so we don't do that. Instead we make measurements that take account of the rotation of the Earth (and its orbital motion) so that the laser would shine in a straight line. That removes the errors.

SS: The point I am trying to make here is that distance distorts measurements ..

Not if you correct for the rotation and motion of the Earth, which of course we do (there are still relativistic effects of course). Bear in mind also that many observations are from the Hubble Telescope which isn't even on the Earth. They too are corrected for the telescope's orbital motion. Astronomers aren't idiots as you seem to be suggesting, these aspects are glaringly obvious.

SS: Aristoteles method is closer to my GPT it gives preference to the observers state, as GPT places the observer at the origin of space and time.

That's the root cause of your problem, you are using a naive 2000 year old religious model that was shown to be wrong nearly 500 years ago.

SS: Can we agree that a body spiralling away from the observer has the opposite velocity vector to a body spiralling towards the observer? That would be a good outcome ;)

No, but we could agree that once you take account of the rotation of the Earth, distant objects move radially, not in spirals, with lateral motions less than the speed of light. (If you try to resurrect the Aristotelian model, you'll be laughed out of court.)

Then we could agree that those that move away from us would have the opposite sign from those that move towards us. :-)

@GD

What makes you think that one can arbitrarily make modifications such as stopping the earth from rotating and stopping the universe from expanding while making your measurements?

That's akin to stopping a racing car in along the track to measure its velocity, and then concluding that it's standing still. 

Velocity is what it is and should be measured as such.

The inertial observer is the only object at rest, everything else moves. What I discovered in GPT is a direct linear relationship between surface potential and velocity. 

ICRF is a false model, which we should have guessed by it's name starting with I for "International", making it sound as if it was defined by politicians. 

SS: What makes you think that one can arbitrarily make modifications such as stopping the earth from rotating ..

You rotate the telescope the opposite way so that it points in a fixed direction.

SS: That's akin to stopping a racing car in along the track to measure its velocity, and then concluding that it's standing still.

No, it's like someone at the centre of a slowly turning playground roundabout trying to measure the speed of a car moving on a straight road directly towards or away from them. If they don't compensate for the roundabout's rotation by turning themselves, their radar gun won't even keep pointing at the car, but if they do compensate, they get an accurate speed measurement.

SS: The inertial observer is the only object at rest

An observer on the Earth is not inertial. I think you need to look up the definition of that word too.

http://playquestadventureplay.co.uk/images/Roundabout2.jpg

@GD

You are tragically wrong, but it's not your fault it's the institution that rewards its members when they comply nicely with the rules. 

You can't simply compensate for the rotation of the playground roundabout, and the rotation of the earth and the rotation of the solar system and the rotation of the galaxy because it will never end, the only real option we have it to take things as they are.

Ground potential Theory does exactly this, it sets an absolute velocity function.

Absolute velocity v = c[U/Ø] where U the floating potential and Ø is the absolute potential and c is of course the speed of light. 

So to find the absolute velocity of ground potential we can pop in the real numbers here:

Absolute velocity at ground potential = v = c[930MV/938MV] = 297,235,593 m / s

This is the speed you would arrive at if you added up all the speeds from the playground roundabout and everything else. As you can see it's 99% the speed of light.

Classical physics in the form you preach is dead.

SS: You can't simply compensate for the rotation of the playground roundabout, and the rotation of the earth and the rotation of the solar system and the rotation of the galaxy because it will never end,

Of course you can. You compensate the rotation of the Earth by rotating the telescope, if you don't, it won't even stay in the field of view. Over the period of a few hours of an observation (while the target is above the horizon), there is a small velocity change because the telescope isn't at the pole but as long as we know its longitude, latitude and altitude, correcting for that is trivial too. All the other motions add only a constant to the measured velocities so we don't even need to bother with them for calculating the rotation curves of distant galaxies, they cancel automatically when calculating the rotation of the target.

SS: the only real option we have it to take things as they are.

That's what astronomers do.

SS: This is the speed you would arrive at if you added up all the speeds from the playground roundabout and everything else. As you can see it's 99% the speed of light.

Your number is wrong, the correct speed is 368±2 km/s. That's the speed of the Solar System determined from the dipole component of the CMBR due to Doppler shift so takes account of every contribution other than the orbital motion of the Earth which depends on the time of year.

The galaxy as a whole is moving at about 2% which is typical of the range you get for peculiar motion in general, galaxies move at a few percent of the speed of light at most relative to the local Hubble flow.

SS: Classical physics in the form you preach is dead.

Common sense isn't, you should try it. You haven't even got the right answer with your approach.

[edit] Oh, and p.s., at speeds of 99% of the speed of light, galaxies would have more than 13 thousand times as much kinetic energy as at 3% so you would need 13 thousand times more dark matter to get the deeper potential required to hold clusters together. That would have collapsed the universe into a "big crunch" as soon as it formed ;-)

https://ned.ipac.caltech.edu/level5/March05/Scott/Scott2.html

@GD

I don't think we are comparing apples to apples. the absolute velocity I quoted above is  the velocity required to maintain the centripetal force between matter and antimatter at ground potential. This is not the same as velocity between here and our horizon. 

If I was to make a guess, I would say that the velocity of the observer with respect the CMB ought to be zero, but this might be distorted by the fact that we are in a state of constant acceleration here on the earths surface.

According to GPT all what we see around us is at ground potential unless it is moving with respect to the observer, and when it is moving it's potential follows;

∆v = c[∆U/Ø]

At present ∆v between baryons should be limited to artound 8 MV this is the potential of Hydrogen when ionised at ground potential and corresponds to a velocity of;

c[-8MV/938MV) = -2558 km/s

We shouln't measure any red shifts larger than this.

GPT works differently to classical mechanics and I am still learning how to apply it with common sense of course.

Steven

SS: I don't think we are comparing apples to apples.

You're right there, I was addressing your original question.

SS: the absolute velocity I quoted above is the velocity required to maintain the centripetal force between matter and antimatter at ground potential.

I'm taking about gravitational potential in relation to galaxy velocity rotation curves and intra-cluster velocities which is related to dark matter, not electrostatic potential applied to sub-atomic particles which would be a completely unrelated subject.

SS: According to GPT all what we see around us is at ground potential unless it is moving with respect to the observer, and when it is moving it's potential follows;

I have no idea what you are talking about but it isn't "gravitational potential" in the sense that controls the orbital speed of stars in a galaxy (or galaxies in a cluster) which is what your original question asked about:

• "Where can I find raw data to model galaxy rotation curves? I am specifically looking for mass distribution and observed angular velocity of as many galaxies as possible."

SS: ... -2558 km/s We shouln't measure any red shifts larger than this.

In astronomical terms, redshift is usually given the symbol z which is the fractional increase in wavelength, thus "z=0.1" means the wavelength is 10% longer as we see it than it would be as measured by an observer at the source and not moving relative to it. For your figure

z = 2558/c = 0.008533

That is a very small redshift, corresponding to a Hubble distance of just 36MPc. The highest observed value for a galaxy is z=11.09 (GN-z11, see the links) and values up to z=2 or 3 are common. The vast majority of galaxies are at higher redshift than your number.

https://www.spacetelescope.org/news/heic1604/

http://arxiv.org/abs/1603.00461

Okay that's really interesting, a redshift of 11.09 is 98% of c is that right?

In that case my last interpretation is way off, I need to rethink what the equations are telling me. I apologise for going off topic, give me a couple of days to get this thread back on topic, I need to plot some rotation curves. 

You have to be very careful with high redshifts in an expanding universe. At the time the light left the galaxy, GN-z11 was receding by 4.32 light years per year. You cannot analyze these numbers with special relativity obviously ;-)

There's a useful calculator linked below, just enter your desired redshift and press the calculate button. The "cosmocalc" program is quite widely available and tells you lots of basic values.

http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2013.htm

@GD Thanks for the resource, it will come in handy. 

For rotation curve modelling we need mass distribution data which has not been modified to include dark matter, is this what is referred to as luminous mass, or is there some other terminology I should look for?

SS: is this what is referred to as luminous mass

Yes, that's right. The speeds of galaxies within clusters are a bit higher than your "upper limit" but only by a factor of 5 or so. The same method works for galaxies but speeds are lower by about a factor of 10 and you need to take account of the shape, a thin disc doesn't have the same potential well as a roughly spherical cluster.

Expansion creates much higher redshifts as I mentioned but you can't describe that through a potential. That's comes out when you subtract the common motion of the system though so speeds relative to the centre of mass of the system will work.

@GD 

I seem to have no problem finding data for rotation curves, but I am struggling to find anything on the luminous mass of galaxies, and if I do find some data it has been corrupted by someones idea of dark matter.

I found some databases like like http://simbad.u-strasbg.fr/simbad/ 

These seem a bit to advanced for what I need initially which is just radial measurements of angular velocity and corresponding luminous mass, and of course the overall redshift of the galaxy so I can plot the actual vs expected curve.

I think I know what's going on, but I need to do some modelling to see if it makes sense first. 

If you want raw data then sources like Simbad are where you will find it, but of course it will be unprocessed, that's what you want.

I Googled rotation curves and there are many example so I picked one at random, the first link. Then I looked for "luminous mass NGC 3198" and I got several relevant hits. Your best bet is to look at the papers that derive dark matter mass for such an example and extract their analysis of only the luminous component. The dark part would be the remainder but you can ignore that part of their work and apply your own attempt.

I would say just look around that way until you find a galaxy for which the data you need is made available part processed. (NGC 3198 is probably not the best, just the first I came across). The references in the papers will lead you back to the source data for rotation curves too.

http://w.astro.berkeley.edu/~mwhite/darkmatter/rotcurve.html

http://iopscience.iop.org/article/10.1088/1742-6596/566/1/012008/pdf

@GD

The more I investigated the mass distribution of galaxies the more obvious it became that no one has any idea and it's all a lot of guess work. So I decided to take a simple approach and make up something myself. 

First I downloaded a good image of the Andromeda galaxy, opened it in photoshop and desaturated the colours making it monochrome and blurred, then I used the pixel colour tool to read the grey scale along the radius of the galaxy, this gave me point readings from zero to 255

From the pixel colour I calculated the disc area value and derived the mass inside the radius from the sum of the rings and normalised it to solar masses.

Considering the crude method I used my rotation curve came out looking similar to the published ones.  

In the case of the Andromeda galaxy my retrograde rotation curve was not a good fit, but I think it may have something to do with the abnormal blueshift of Andromeda, it is approaching us at 300 km/s.

This means somewhere in the receding half of the galaxy one star is standing still relative to us.

I am still thinking about this one. 

Nice, but what you described is the light profile only, not the velocity profile. For that you need a file with Doppler information.

The Universe Today article gives some links that might be helpful.

Steven, investigate the FITS file standard, many images in databases are stored in that and you can read out lots of data from it. I've added a link.

https://en.wikipedia.org/wiki/FITS

http://www.universetoday.com/75164/m31s-odd-rotation-curve/

[quote] Nice, but what you described is the light profile only, not the velocity profile. For that you need a file with Doppler information. [/quote]

You are jumping to conclusions, these are rotation curves calculated from luminous mass, see attached spreadsheet.

The article you linked to confirms my theory, namely that rotation curves should go up not down. 

The software you suggested looks interesting, but what I fid with photoshop has the same function.

OK, I thought you wanted actual rotation curves from your question, I guess you just wanted the light distribution.

Incidentally I note on your diagrams that you're still using "prograde" and "retrograde" incorrectly, you really should replace those with meaningful terms.

The light green plot is the measured rotation curve, I didn't make that one up.

Instead of prograde and retrograde I could use forwards and backwards, but that's as good as it gets. 

I think you have decided not to understand the GPT concept and I don't even think you have read the paper, so it's very hard to communicate my idea. 

SS: Instead of prograde and retrograde I could use forwards and backwards, but that's as good as it gets.

In the disc of a galaxy all the stars rotate in the same direction, so "forwards" could mean chosen to describe that direction but no stars then move "backwards". The terms "clockwise" or "anticlockwise" when specified from a point on the axis (north or south pole) are clearer but I think that's not what you mean.

Anyway, whether a galaxy rotates clockwise or anticlockwise will make no change whatsoever to the link between potential and speed.

SS: I think you have decided not to understand the GPT concept

The concept of the potential well of a galaxy is well understood and often used, that's nothing new.

SS: I don't even think you have read the paper, so it's very hard to communicate my idea.

I started reading it but when you use terms like "retrograde" or even "forwards" in a way that only you understand and contrary to its usual meaning, you cannot expect anyone else to follow you. I'm trying to get you to learn what the words really mean so that you can describe your idea in terms other can follow. The only reason I joined the thread was because I could see others struggling with the same problem. I'm not prepared to spend my time trying to work out what you are trying to say, making the paper understandable is your job.

That's not the paper I was referring to, I would like you to read Ground Potential, then you will understand something about the world you never realised.

I had a quick look, the description is "A theory describing the asymmetric and absolute field potential between electrons and protons." What has that got to do with galaxy rotation curves? If it's about particle physics, I'm not your man, I'm studying cosmology.

Aha..but physics is everything, the velocity equation derived in the second half of the paper says "velocity increases with increasing potential" which contradicts Kepler, and law and behold Kepler was wrong, because the planets are moving backwards with "increasing" velocity not forwards with "decreasing" velocity. 

I trust my equation :)

SS: velocity increases with increasing potential" which contradicts Kepler,

No, that's the same as Kepler (assuming you are talking about magnitudes).

Kepler's Laws are correct (other than small relativistic corrections), that is easily confirmed just by looking at the speeds of the planets around the Sun so if your equation differs from that, it is wrong.

@GD

Does potential increase with height above ground?

Does orbital velocity increase with height above ground?

Yes and yes, Kepler got it wrong, the planets orbit backwards, mercury orbits backwards slowest with respect to the sun, then comes Venus which moves backwards a little faster then Earth and then Mars and so on.

you add a negative sign in front of the Mercury velocity, then take the difference in velocity between venus and mercury and subract that, so it becomes

-v1 - v2 - v3 -v4 etc 

...elementary my dear George..

SS: Does potential increase with height above ground?

That can be ambiguous, it increases in the sense that it becomes more positive, but since the value is negative, its magnitude decreases.

SS: Does orbital velocity increase with height above ground?

No, it decreases. A TV satellite is in a high orbit, altitude 35786km, and orbits at 3.07km/s which is about half the speed of the ISS for example which is in a low orbit at an altitude around 403km and moves at 7.66km/s.

SS: Yes and yes, Kepler got it wrong, the planets orbit backwards,

Backwards compared to what? The Earth rotates clockwise and orbits the Sun clockwise so I guess that's "forwards" in most people's language.

SS: mercury orbits backwards slowest with respect to the sun, then comes Venus which moves backwards a little faster

Mercury orbits once in 88 days while Venus orbits once in 224.7 days. The orbit of Venus has a diameter roughly twice that of Mercury but it takes 3 times longer per orbit  so obviously Venus moves slower than Mercury, your basic facts are wrong.

I've linked a table of planetary parameters.

You might also note in the table that the Rotation Period numbers for Venus and Uranus are negative, those are therefore retrograde, the rest are all prograde.

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

https://en.wikipedia.org/wiki/Geostationary_orbit

http://www.heavens-above.com/IssHeight.aspx

http://www.kshitij-iitjee.com/gravitational-potential-energy-function

@GD

Doesn't it bother you that the ISS have to fire their booster rockets to slow down the spacecraft ?

SS: fire their booster rockets to slow down the spacecraft ?

I guess you didn't look at the link I gave you.

From the previous post:

SS: Does orbital velocity increase with height above ground?

GD: No, it decreases.

Look at the link Steven, you can easily see where the engines were used as stated in the caption. The increase in altitude causes the near vertical upward lines on the graph with the slow decay from atmospheric drag producing the gentler downward slopes. They fire the engine to raise the orbit to higher altitude which results in it moving more slowly as I said.

http://www.heavens-above.com/IssHeight.aspx

GD: They fire the engine to raise the orbit to higher altitude which results in it moving more slowly

In which direction do they fire the thrusters, upwards or tangentially?

It's easiest to explain as two separate short burns though in practice it may be one longer firing. That is called a Hohmann Transfer.

They fire the engine tangentially in the same direction that they are moving which increases the speed. The orbit becomes elliptical with the first firing at perigee so the radius starts increasing. As the radius increases, the speed decreases (by too much). When it reaches apogee, half an orbit later, they fire the engine again in the same direction. That increases the speed to put it back into a circular orbit. The altitude is now higher and the final speed is lower than it was before the manoeuvre.

The two examples I gave you before were the ISS versus a geostationary orbit. The linked Wikipedia page gives a transfer from 300km to geostationary so you can see the calculations and numbers for that example. Obviously the altitude adjustments for the ISS are only a few km but the principle is the same.

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit#Example

GD:They fire the engine tangentially in the same direction that they are moving which increases the speed. The orbit becomes elliptical with the first firing at perigee so the radius starts increasing. As the radius increases the speed decreases;

Think carefully about what you just wrote here. 

1) They fire the engine tangentially 

2) Increasing the speed in the direction of motion

3) As radius increases speed decreases. 

Point 3 is an illusion, the velocity is negative all the time, and when they increase the negative velocity the orbit increases.

The velocity in a circular orbit is continually changing. Do you understand the difference between velocity and speed?

What we are talking about is the tangential speed. Speed is the magnitude of the vector so it is always positive. Firing the engine in the same direction increases the speed, increasing the radius decreases the speed.

I guess you didn't read the link again.

George we could argue forever about this, especially when it is always possible to turn the argument one way or the other. I am familiar with the concept of speed, but if you adopt my backwards thinking it would not be necessary to fiddle the outcome by calling velocity for speed and converting what really is a negative velocity into a positive speed. 

Science has found ways to deal with all the stuff that isn't understood, and teach it again and again until it becomes accepted, even if it is imaginary. 

The observers world is the only world and therefore there is no such thing as speed, only poorly understood velocity.

GD said: I guess you didn't read the link again.

I read everything through a filter, I look for imaginary unicorns in the text and try to ignore ignore them, because I feel it's important to find the truth.

We can't accept everything written in WIKI or printed in peer reviewed journals as being "True" all we can say is it agrees with commonly accepted beliefs. 

Widely accepted statements such as "Gravitation is a force of attraction between all objects in the universe" is a classic case of a unicorn, it has an intangible object with an invented name, which can't be isolated or proved by a scientist andy more than God can be proved by a priest.

Now if you go through an accepted physics text book and underline the Unicorns in red I think you will end up looking like a failed exam.

We need a simple theory about our world which does not rely on imaginary stuff.

MFCW

SS: I am familiar with the concept of speed, but if you adopt my backwards thinking it would not be necessary to fiddle the outcome by calling velocity for speed and converting what really is a negative velocity into a positive speed.

I think you miss the point. Speed doesn't have a sign associated with it. If I drive a car at 30mph in a straight line, it means I'll be 30 miles from where I started after an hour. That tells me nothing about the direction. If you want to change the sign convention and say I'm moving at -30mph, it won't make the slightest difference to where I end up, I'll still be 30 miles away.

If I apply my brakes, my speed might decrease from 30mph to 25mph, you would say it changed from -30mph to -25mph and it's then ambiguous whether you call that an increase or a decrease but that's only words, the effect of applying the brakes is that after an hour, you will only have travelled 25 miles.

The bottom lines is that changing the sign has absolutely no effect on the physics whatsoever.

SS: We can't accept everything written in WIKI or printed in peer reviewed journals as being "True" all we can say is it agrees with commonly accepted beliefs.

No, and I've corrected details in a few poor pages myself, but that page is giving you the basic rules of space flight that have been proven on every space mission ever flown. When the ISS engines are fired to raise the orbit, the craft passes over the sites used to communicate slightly later each orbit so we know it is travelling fewer km in an hour than before the manoeuvre. Whether you call it positive or negative makes no difference, in a given time, it travels a smaller distance.

From your previous post:

GD: 3) As radius increases speed decreases. 

SS: Point 3 is an illusion, the velocity is negative all the time, and when they increase the negative velocity the orbit increases.

No, point 3 is proven fact. If you want to call the velocity negative in the direction of the orbit, then increasing the orbit radius makes it a smaller (negative) number. That is, the negative velocity decreases.

I guess the way I think, the velocity vector points in the direction of least resistance, so when a rocket takes off it moves up up and away from the observer and never really turns around. 

The vector in this case follows a bessier curve much in the same way as a ribbon flows.

https://youtu.be/iVFRjNll3ds

I am happy to acknowledge that classical Euclidean geometry disagrees with this, but I see no practical reason why velocity vectors should be straight lines. 

SS: .. so when a rocket takes off it moves up up and away from the observer and never really turns around.

Yes, and you add the vector of the launch site to find the total for the craft, but we're talking about craft already in orbit rather than take-off.

Take the example I gave before. Suppose the ISS orbits at an altitude of 401km. Add that to the radius of the Earth (6378.137km at the equator) and you have the radius of the orbit, 6,779.137km. Now just multiply that by 2 pi to get the circumference, 42594574km and that orbit is completed in 5554.85s so the speed is 7668m/s. Note that dividing the circumference by the time to get the speed doesn't involve a vector or a direction hence the number doesn't have a sign, it's just distance over time.

Repeat that for an altitude of 404.5km (that corresponds roughly to the boost they did last November). The orbital radius has increased to 6782.637km, the circumference has increased to 42616.565km, the time for each orbit is increased to 5559.16s and the speed has therefore fallen to 7666 m/s.

As the radius increases, the speed decreases, we know that for a fact.

SS: I see no practical reason why velocity vectors should be straight lines.

A vector is a magnitude and a direction at a point, it isn't a path at all but remember we aren't talking about vectors at all, only speeds which have no direction.

http://www.heavens-above.com/IssHeight.aspx

p.s. Compare the ISS figures with those for a geostationary satellite (e.g. TV).

ISS:

Altitude 401 km

Radius 6779.137 km

Circumference 42594.574 km

Orbital period 5554.853 s

Speed 7667.993 m/s

Geostationary:

Altitude 35786 km

Radius 42164.17 km

Circumference 264925.3 km

Orbital period 86164.1 s

Speed 3074.66 m/s

Note that at the much higher altitude, the speed of a geostationary satellite is less than half of that for the ISS.

George, by now it should be obvious to you that we are talking about two different ways of measuring, of course everyone who completed year 12 at school knows Keplers law and how it is measured, and we know that the geostationary orbit is approximately at a 36,000 km radius.

But we are measuring speed the wrong way, instead of measuring speed against some imaginary euclidean plane imagine if we used the sum of kinetic, potential and mass energy to determine the speed i.e relativistic mass/momentum you will see that it is higher for the geostationary orbit. 

I think the confusion comes about when we attribute reality to empty space, when indeed there is none. One can not construct euclidean geometry on a non existent plane, therefore to say a body is moving with respect such a non existent plane is nonsense.

Instead every moving body traces its past trajectory to a line of least resistance (as in the ribbon dancers ribbon) and when we consider the speed along this path we see that velocity does indeed increase. 

This brings us right back to the completely naive understanding that boosting the engine thrusters of a rocket increases it's speed, and the occupants in the rocket will all agree on this.

Steven

SS: George, by now it should be obvious to you that we are talking about two different ways of measuring

Not really, you have only said that you want to reverse the sign of the speed, it still has to be measured the same way, distance travelled divided by time taken. I wondered at one point if you meant angular velocity instead of speed but that falls too so I think we both mean tangential speed and you are just wrong about it, sorry.

SS: of course everyone who completed year 12 at school knows Keplers law and how it is measured, and we know that the geostationary orbit is approximately at a 36,000 km radius.

Good, we can always use agreed points as a basis for the discussion.

SS: But we are measuring speed the wrong way, instead of measuring speed against some imaginary euclidean plane ...

Well rather than Euclidean geometry, we should be using the Schwarzschild metric  but in that, the relationship that the circumference of the orbit is 2 pi times the radius is still accurate.

SS: ... imagine if we used the sum of kinetic, potential and mass energy to determine the speed i.e relativistic mass/momentum you will see that it is higher for the geostationary orbit.

The mass of the craft doesn't change so we can ignore that. There is a simple relationship between potential and kinetic energy:

PE = -2 * KE

If we add an amount E to the craft's total orbital energy, the potential energy increases (i.e. becomes less negative) by 2E while the kinetic energy (which is positive) decreases by E.

Total = potential + kinetic

E = 2E + (-E)

Because the kinetic energy decreases, the craft speed reduces as the radius increases. The two methods are completely consistent.

SS: I think the confusion comes about when we attribute reality to empty space, when indeed there is none.

A lot of people do try to do that, the philosophy is even called "substantivalism" because it is so common, but strict GR doesn't do that, it only recognises the fact that the rules of (Reimann) geometry apply to the measured distances and times within that manifold. It's a subtle point but an important one. However, for our purposes, we don't need to get into such philosophical discussions. All we need to know is that the circumference of an circular orbit is 2 pi time the radius. Divide the circumference by the orbital period and the get the linear speed. That speed is lower for greater altitude.

SS: Instead every moving body traces its past trajectory to a line of least resistance (as in the ribbon dancers ribbon) and when we consider the speed along this path we see that velocity does indeed increase.

No, whether you measure the speed as circumference over period or from the kinetic energy as v=sqrt(2E/m), the speed decreases as altitude is increased.

SS: This brings us right back to the completely naive understanding that boosting the engine thrusters of a rocket increases it's speed, and the occupants in the rocket will all agree on this.

The occupants are weightless, they feel no speed, only a brief acceleration during each engine burn, but the control stations on the ground will see that the orbital speed increases on each burn. It is the half-ellipse while the craft transfers between the lower and higher orbit when the speed drops as the altitude increases. Again, the Wikipedia page gives a clear and accurate account of what actually happens.

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

@GD

Neat gif animation..

https://66.media.tumblr.com/4e881a0340b323bcdfa3797001ca1c6c/tumblr_o9ua2xrMW11qiz5q7o1_540.gif

Nice example, it illustrates the key points.

• The Earth, Jupiter and Juno are all shown moving anticlockwise round the Sun so all are moving prograde.
• After its boost by the flyby of Earth, as the Juno craft moves out towards Jupiter, it slows down (as is required to conserve angular momentum).

Yes we agree on this when using the fixed background stars as a reference, but if you trace the path of the craft right back to its origin following the white line, you will see how the craft speed is actually increasing with respect to the origin. 

SS: Yes we agree on this when using the fixed background stars as a reference

Reference to distant stars is not required (though they would give the same answer), the direction of rotation is anti-clockwise referred to a simple gyroscope.

SS: but if you trace the path of the craft right back to its origin following the white line, you will see how the craft speed is actually increasing.

The speed I am talking is measured along the line as you describe, and it decreases as the distance from the Sun increases. You can see that just by eye in the animation.

Here's another from the Wikipedia page, can you not see that the green dot move downwards on the left hand side faster than it moves upwards on the right hand side?

https://en.wikipedia.org/wiki/Elliptic_orbit#/media/File:Elliptic_orbit.gif

Please find the link - http://www.ioa.s.u-tokyo.ac.jp/~sofue/htdocs/2021rcMW/RC-innerMW-dR100pc.dat

or used this text file

Manoj Sithara , Thanks for the reference source. I haven't worked on this project for a while, but since dark matter is turning into a new religion, I suppose I should revisit this science one day. 😊

Perhaps there is no sucha thing as darck matter . However, the Darck Matters assumed as asame as you believed Myths belong to supper natural things like God. However , I have been modeling such a model, seems the experimental datas will mached with my theoretical model. Please find my graph attched in bellow.

Manoj Sithara , What assumptions are you making in your theoretical model?

I have been formulate the rotational speeds at a radial distance ,using existing laws of physics. If you are help me to check my final formula with few Galatical measures ,I can gives my final formula to you . I will be grateful if you can check its consitancy . But I can't tells you all the steps in the derivation. You like?

Manoj Sithara , I am not an expert in the field, but feel free to share your method I like to see how you derived it. :)

Basic assmuption is there is no such a thing as dark matter !!. I will send you a copy of my work in future. I am sill been compleating my final assesments of its consitancy to real world.