Thread: galactic rotation curve

Originally Posted by astrotech

Since Grapes has apparently abandoned this thread without supporting his claim I'll go ahead and point out why the outside mass in the disk can be ignored. Grapes will probably weigh in with more unsupported dispute But we can see his disputes lack integrity.

First the Newtonian law is derived from a disk in the first place. The disk of the plane of the ecliptic.

Second the outside mass can be so easily seen to not contribute to the orbital velocity of the inner planets that it is ignored in the teaching of the subject. It can easily be seen to not contribute simply by considering the mass of the planet Jupiter. That is a mass outside the orbit of Earth. As the Earth accelerates toward Jupiter on one side of its orbit it decelerates as it moves away on the other side. The deceleration subtracts velocity from the increased velocity gained by the acceleration so no net velocity increase. You can then consider a ring of Jupiters and see that the same thing applies. Any acceleration gained by moving toward one of the Jupiters in the ring is subtracted by a deceleration away from another Jupiter in the ring. So no net acceleration due to a ring of outside mass in a disk.

So there is no contrbution to the total velocity of objects in the disk of a galaxy by the mass of the disk outside the orbit of the object.

That symmetry argument only works perpendicular to the radius--the situation is not symmetric parallel to the radius, the planet is closer to one side of the outer ring than it is to the other side. The r^2 symmetry that exists for an outer sphere is not there for a ring.

Originally Posted by grapes

That symmetry argument only works perpendicular to the radius--the situation is not symmetric parallel to the radius, the planet is closer to one side of the outer ring than it is to the other side. The r^2 symmetry that exists for an outer sphere is not there for a ring.

Nothing to do with what I wrote. But the same unsupported claim you keep making.

Is your lack of integrity on purpose or are you completly oblivious to it?

I was addressing your ring of Jupiters argument

You can then consider a ring of Jupiters and see that the same thing applies. Any acceleration gained by moving toward one of the Jupiters in the ring is subtracted by a deceleration away from another Jupiter in the ring. So no net acceleration due to a ring of outside mass in a disk.

Originally Posted by grapes

That symmetry argument only works perpendicular to the radius--the situation is not symmetric parallel tEo the radius, the planet is closer to one side of the outer ring than it is to the other side. The r^2 symmetry that exists for an outer sphere is not there for a ring.

Your argument works for Jupiters in front and in back, but it fails for the Jupiters above and below.

I didn't find any treatment of this readily available on the net, but I did plug the formula for gravitational potential into Wolframalpha

[LaTeX ERROR: Image too big 804x18, max 650x600]

And then had it take the derivative of that

[LaTeX ERROR: Image too big 970x18, max 650x600]

All multiplied by GMR/(pi), if I've done it right. K and E are elliptical functions.

The first one:


The second one:

Let me try this again:

Originally Posted by grapes

I did plug the formula for gravitational potential into Wolframalpha



And then had it take the derivative of that



All multiplied by , if I've done it right. and are elliptical functions.

I'll work on it some more...

Here's a line for input to Wolframalpha that produces a plot of the effect for r from zero to R (0 to 1 on the plot)

Plot (-((r + 1) EllipticE[(4 r )/(r + 1)^2]) + (-r + 1) EllipticK[(4 r )/(r + 1)^2])/(r (r - 1) Sqrt[(r + 1)^2]) for r from 0 to 1

Seems a paper has been published. Beat me to it but supports my OP.

http://arxiv.org/pdf/0804.3203v1.pdf

Grapes better inform them that they forgot to include outside mass.

Let's see if the post on BAUT gets moved to ATM.

I haven't studied the paper yet, although I've heard some comments.

Can you actually show that they ignore the outside mass, astrotech?

Originally Posted by grapes

Can you actually show that they ignore the outside mass, astrotech?

Can you show Jupiter adds or subtracts from the average total orbital speed of Earth other than the acceleration and deceleration mentioned earlier which cancel?

Originally Posted by grapes

Can you actually show that they ignore the outside mass, astrotech?

I'll take that as a "no" for now then.

Originally Posted by astrotech

Can you show Jupiter adds or subtracts from the average total orbital speed of Earth other than the acceleration and deceleration mentioned earlier which cancel?

Just to be clear, are you asking about the "ring of Jupiters" or just Jupiter? My just previous posts (back in December) were about the ring of Jupiters--which is what we're talking about, more or less--disks of material and their effect on the velocity of interior bodies.