The modified Newtonian dynamics approach of Milgrom (1983, 1986, 1989,
1994, 1997, 2001) was an interesting alternative to the dark matter paradigm. The
objection of this fix has been that it is too ad hoc, without any underlying theory.
The author himself has been arguing over the years (Sidharth 2000, 2006a, b)
(cf. ref. Sidharth (2008) for a summary) that the gravitational constant G is not fixed
but varies slowly with time in a specific way. In fact this variation of the gravitational
constant has been postulated by Dirac, Hoyle and others from a different point of
view (cf. ref. Sidharth 2008; Narlikar 1993) which for various reasons including
inconsistencies have in the author’s scheme, exactly accounts for the galactic
rotation anomaly without resorting to dark matter or without contradictions.
Our starting point is the rather well known relation (Narlikar 1993).
G ¼ G o 1 À
t
t o
ð8:9Þ
where G o is the present value of G and t o is the present age of the Universe, while t is
the relatively small time elapsed from the present epoch. On this basis one could
correctly explain the gravitational bending of light, the precession of the equinoxes
of mercury, the shortening of the orbits of binary pulsars and even the anomalous
acceleration of the pioneer spacecrafts (cf. references given above).
Returning to the problem of the rotational velocities at the edges of galaxies, one
would expect these to fall off according to
v
2
%
GM
r
ð8:10Þ
However it is found that the velocities tend to a constant value,
v $ 300 km=s
ð8:11Þ
This, as noted, has led to the postulation of the as yet undetected additional matter
alluded to, the so called dark matter.(However for an alternative view point
cf. Sivaram and de Sabbata (1993).) We observe that from (8.9) it can be easily
deduced that (Sidharth 2001).
a € r o À € r
ð
Þ%
1
t o
t€ r o þ 2_ r o
ð
Þ%À 2
r o
t 2
o
ð8:12Þ
as we are considering infinitesimal intervals t and nearly circular orbits. Equation
(8.12) shows (cf. ref. Sidharth (2006a) also) that there is an anomalous inward
acceleration, as if there is an extra attractive force, or an additional central mass, a
la Zwicky’s dark matter.
So,
8 Dark Matter Anomaly
81
1994, 1997, 2001) was an interesting alternative to the dark matter paradigm. The
objection of this fix has been that it is too ad hoc, without any underlying theory.
The author himself has been arguing over the years (Sidharth 2000, 2006a, b)
(cf. ref. Sidharth (2008) for a summary) that the gravitational constant G is not fixed
but varies slowly with time in a specific way. In fact this variation of the gravitational
constant has been postulated by Dirac, Hoyle and others from a different point of
view (cf. ref. Sidharth 2008; Narlikar 1993) which for various reasons including
inconsistencies have in the author’s scheme, exactly accounts for the galactic
rotation anomaly without resorting to dark matter or without contradictions.
Our starting point is the rather well known relation (Narlikar 1993).
G ¼ G o 1 À
t
t o
ð8:9Þ
where G o is the present value of G and t o is the present age of the Universe, while t is
the relatively small time elapsed from the present epoch. On this basis one could
correctly explain the gravitational bending of light, the precession of the equinoxes
of mercury, the shortening of the orbits of binary pulsars and even the anomalous
acceleration of the pioneer spacecrafts (cf. references given above).
Returning to the problem of the rotational velocities at the edges of galaxies, one
would expect these to fall off according to
v
2
%
GM
r
ð8:10Þ
However it is found that the velocities tend to a constant value,
v $ 300 km=s
ð8:11Þ
This, as noted, has led to the postulation of the as yet undetected additional matter
alluded to, the so called dark matter.(However for an alternative view point
cf. Sivaram and de Sabbata (1993).) We observe that from (8.9) it can be easily
deduced that (Sidharth 2001).
a € r o À € r
ð
Þ%
1
t o
t€ r o þ 2_ r o
ð
Þ%À 2
r o
t 2
o
ð8:12Þ
as we are considering infinitesimal intervals t and nearly circular orbits. Equation
(8.12) shows (cf. ref. Sidharth (2006a) also) that there is an anomalous inward
acceleration, as if there is an extra attractive force, or an additional central mass, a
la Zwicky’s dark matter.
So,
8 Dark Matter Anomaly
81