Le 08/11/2017 à 20:33, jacobnavia a écrit :
Le 05/11/2017 Ã 09:05, Jos Bergervoet wrote:
So you have information as to whether it is strong enough at the
relatively short distances of our environment, as mentioned above?

Suppose some star S at 60 thousand light years from the center of the
galaxy. A normal star whose mass can be accurately determined.

Its speed can be measured, and its mass is known. Then, we subtract
gravity effects and we obtain the force that is necessary to accelerate
that star to its observed speed at 60000 light years from the center.

Supposing a roughly linear decay, here at only 30000 light years from
the center we should have half of that.

Looks simple but can't be that simple. I am surely missing something,
but what?

[[Mod. note -- There are a couple of things:
1. A solar-type star at a distance of 60,000 light-years has an
apparent magnitude of around 21, which is faint enough that
getting a good spectrum will take a lot of big-telescope time.

We have big scopes now. Or just choose a nearer one. The farther you go,
the more the discrepancyy between gravity and its observed speed should
be, as we read from the speed charts of stars around the center.

The difference is bigger when you get away from the galaxy, at the
outskirts.

2. Once you get that spectrum you get the star's radial velocity
(its velocity along our line-of-sight to the star).
But if you want all 3 components of its vector velocity you
also need to measure its velocity perpendicular to our line-of-sight.

Mmm the galaxy has a plane of rotation. Th center of the galaxy, that
star and we are rotating around the same central object, the galaxy, in
a plane.

The center, we, and that star are in the same plane. Are those
corrections really necessary?

That means doing high-precision astrometry to measure how its
position gradually drifts relative to other more distant objects,
with corrections for the Earth's motion around the center of our
own galaxy. (This will be on the order of micro-arcseconds/year.)
This star is too faint for Gaia to give good data (Gaia's error
bars are up to 200 microarcseconds/year at magnitude 20), in
fact I can't think of any current telescope/detector that could
do relative astrometry at that accuracy level on an object that
faint in a reasonable amount of telescope time.

We can use stars nearer of course. For instance at mag 20 if that is the
limit of Gaia. That would be a good start.

3. Suppose we somehow managed to measure all 3 components of the
star's vector *velocity*. That doesn't tell us anything about the
star's gravitational *acceleration* (we don't know that it's moving
in a circular orbit about the center of our galaxy!), which is the
quantity which is actually influenced by dark matter/modified gravity.
-- jt]]


"We don't know that is moving in a circular orbit"... wow, I always
thought that they are doing so, and that the "arms" we see are density
waves in the disc of stars circling the center.

The stars must be doing "some" kind of circle around the center since
the form of the galaxy (a rotating plane of stars ) indicates so. I even
thought that the sun was rotating about 1 rotation per 250 million
years, so it is around 20 galactic years old. I thought that the orbit
was a circle. Is that not correct?

If we approximate the orbit by some kind of circle, we approximate the
milky way to a center of gravity around the black hole in the central
buldge, we can calculate the gravity exerced by the (I suppose known)
mass of the galaxy and the speed that a star should have isn't it?

Very roughly. A more sophisticated thing would take into account the
form of the buldge, the mass of the plane inside the orbit, etc.

Dark matter scenarios suppose some form of invisible matter outside and
propose a vector that is in the opposite direction pulling the stars.
The force the stars feel would come from outside the galaxy in some kind
of halo.

Maybe we could look in the other direction. And if the force came from
the galaxy itself?

A second star we could use of course, is the nearest one, the sun. The
sun's orbit could tell us about the force effects here. Here we have
more data and less problems than with the star's far away. We know very
precisely the distance to the center, and the mass between us and the
center, so the effects of gravity could be calculated much more easily.

Is there any delta?
Has anyone done this calculations?