Introduction.
The problem of missing matter in the galaxy generated
different approaches already and more approaches are possible. The
startling difference between the modern theory and experimental observation
comes from the observation of the deviation of the light by the mass – light
bending by galaxies, clusters of galaxies etc. The most general expression for
the gravity influence on light goes from Schwarzchild metric expression:
Z=GM/(c2R)
This Z value as observed is too
large for the measured distance, visible mass and known gravitational constant.
So the hypothesis are:
1.Missing matter – dark matter
approach – value M should be higher to account for Z
2.Gravitity law is changed at high
distance – combination of G and R should be reconsidered (MOND)
3.G value is wrong when away from
Earth – gravity enhancing field hypothesis, fifth force hypothesis (developed
in [1])
4.Speed of light is not constant
and if it is smaller between
galaxies the value of Z may be higher to account for the measured light
bending. The speed of light theoretically may be smaller away from gravitating
mass if the gravitation influences quantum vacuum much stronger than expected
now – in this case not only the G constant is smaller away from galaxy (the
hypothesis discussed above), but the vacuum permeability, responsible for speed
of light is larger, for example, due
to enhancement of positron-electron virtual pairs generation in the absence of
gravitational field
5.The geometry is not correct –
the value of R is wrong. For example, the Einstein’s idea that space is created
by the mass is even more important and between galaxies there is virtually less
space than inside galaxy – in this case the simple geometrical rules are not
applicable.
This
article is devoted to the fifth approach, claiming that the distances are
measured wrongly on galactic scales because the “ruler” is based on photons and
the space is more distorted than expected by the presence of the mass (energy
in more general terms).
Main part.
The idea proposed in [1] for
experimental observation of the discrepancies connected with gravitation is
rather simple: the Cavendish experiment should be performed away from
gravitating mass (away from the Sun, say beyond the Pluto orbit). Modern space
probes are already left the solar system, so this experiment is within the
reach of modern technology. However, the simple measurement of the deviation of
the expected force from the calculated one:
F=G*M1*M2/R2
May come not only from the
difference in G as it depends from mass but also from deviation of R as it is
measured away from gravitating body. If the probe is sent toward Sun, this is
expected effect (general relativity will reveal itself in such measurement
close to the Sun). But what if the space distorted by the presence of mass more
than general relativity teaches us? What if there is another, much larger scale
of influence of mass onto the space-time, in addition to Schwarzschild radius?
Application of “ruler” created near Earth to the galactic and intergalactic
distances than would generate the large error which is perceived as missing
matter. For example, if the space is more “diluted” away from gravitating
bodies (this is idea number 5 from [1]), than for stars on the outskirts of
galaxy both distance measured is larger than it is in reality (from graviton
point of view, for example, not from photons point of view) and the measured velocity is larger, too
(assuming in the first approximation that time is not touched) because v=dR/dt.
In this case the galaxy rotation curve may be modified toward the predicted shape.
(see the picture in [5])
How this idea would reveal itself
in other astronomical observations?
In this case the orbits of the
binary stars are not ellipses any more, rather distorted ellipse (ovoid).
Because the space is expected to be a little more “diluted” when two stars are
away from each other, the ellipsoid will be deformed. (see the picture in [5])
Indeed, the observation of the
binary stars which are nearby and were observed for full cycle demonstrated
that the best fit ellipse is different from the real orbit in exactly this
place (see the picture from [2] for Gamma Virginis, Porrima star), in [5]
It is clearly seen that the best
fit elliptical orbit is not passing through the middle or median of the
numerous points when the stars are especially far from each other (those points
have smaller errors because it is much easier to measure higher separation between stars than small separation when
start are almost overlap each other).
Simple mathematics may allow to
evaluate the degree of the “dilution” of space when the stars are separated.
For ellipse with parameters a and b
(a>b):
(x-a)2/a2+ y2/b2=1
For aphelion-perihelion line the
crossing points for y=0 are 0 and 2a.
Let the distance along x
axis is distorted: x → x*exp(-cx) where c<<1. This means that the space
is diluted with characteristic length of 1/c when the stars are apart compare
to when they nearby. In this case the shape of the figure is as follows:
(x*exp(-cx)-a)2/a2
+y2/b2=1
For y=0
(aphelion-perihelion line) the new crossing points would be determined from the
equation:
(x*exp(-cx)-a)2=a2
x*exp(-cx)-a=-a
Or x*exp(-cx)-a =a
The first point is still
x=0 and the second point is determined from the equation: x*exp(-cx)=2a
Because c<<1 we have
exp(-cx)~1-cx
and substituting into
equation x*exp(-cx)=2a
we have: x*(1-cx)=2a
or: -cx2+x-2a=0
The root of this quadratic
equation is:
x1=[-1+sqrt(1-8ac)]/(-2c)
The second root has no
physical meaning.
Because c<<1 the
value of 8ac<<1 and using the Maclaurin formula:
(1+x)1/2=1+1/2*x-1/8*x2
+ … we have
(1-8ac)1/2=
1-4ac-8a2c2+ …
Than x1=[-1+sqrt(1-8ac)]/(-2c)=[1/(-2c)]*(-1+1-4ac-8a2c2)=2a+4a2c
The difference between the
real path of the star and the pure ellipse is Δ=4a2c. The relative
shift of the ellipse is Δ/2a=2ac
This relative shift is
possible to see from the Fig.3. It is approximately 3/80.
For Gamma Virginis the
parallax is 0.0856 and semi-major axis in arc seconds is 3.662 [3]
Then the semimajor axis in
astronomical units is 3.662/0.0856=42.8 a.u.
The value of 2a=85.6
a.u.=1.28*1013 m
The value of
c=3/80*1/(2a)=2.9*10-15 1/m
The characteristic length
would be ξ=1/c=3.4*1014 m (0.036 light year), what correlates with
the value of the decay length of the gravity deduced in [1,4] from the
mass-luminosity curves analysis: 3.2*1014 m. Because the gravity law
has inverse squares of distance in
Newton formula it means that the characteristic length of space dilution should
be twice small compare to the decay of the gravity to lead to the same numerical
value of force.
Conclusion.
For the advancements in
understanding of gravity and how it leads to the rotation curves of the
galaxies, in addition to the attempts to detect the dark matter more accurate
measurements of the binary stars orbits are necessary. The deviations in the
gravity laws, easily visible on the galactic scale must reveal itself in the
dynamic of smaller objects, like binary stars, despite possibly in tiny
amounts. From historic perspective the analysis of simple object like binary
star (but performed with high accuracy) may lead to the crucial discoveries
faster than the analysis of much more visible phenomena on galaxy or Universe
scale because of the extreme complexities associated with larger objects. Described
here analysis may be performed by professional astrophysicists for much broader
range of binaries to find the possible deviations from pure elliptical orbits.
References.
1.D.S.Tipikin “The quest for new
physics: an experimentalist approach”// https://vixra.org/pdf/2011.0172v1.pdf
2. http://stars.astro.illinois.edu/sow/porrima.html
3. https://en.wikipedia.org/wiki/Gamma_Virginis
4.D.S.Tipikin “Analysis of slope
of mass-luminosity curves for different subsets of binaries – dark matter, MOND
or something else governs the accelerated rotation of galaxies?” //
https://vixra.org/pdf/2008.0217v1.pdf
5.D.S.Tipikin "Careful analysis of the binary stars orbits may reveal the
space-time distortions on medium scale."
https://vixra.org/pdf/2012.0180v1.pdf
or:
https://vixra.org/abs/2012.018