Le 05/11/2017 =C3=A0 09:05, Jos Bergervoet a =C3=A9crit=C2=A0:
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.
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.
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.
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]]