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D. F. Bartlett (University of Colorado at Boulder)
The evidence for dark matter (and dark energy) is powerful, but not yet overwhelming. I propose an alternative that - like Yukawa's potential - allows scalar gravity to obey a second order linear differential equation. Consider the sinusoidal potential \phi(r)=-(GM/r) cos(kr). Here \lambda=2\pi/k is a universal wave length which -- judging from evidence both from within the Galaxy and without -- is Ro/20 or about 425 pc. For r = 1 AU, cos(kr) differs from 1 by only 10-14, too small a difference to have been detected in the motion of the planets. Alternatively, if kr>1, the sinusoidal potential provides both a gravitational force and a tidal force which diminish only as 1/r. The slow decline in force can explain the flat rotation curves of stars in disk galaxies.
It is, however, the very strong tidal forces that provide the real evidence. There is unexplained modulation (of period \lambda) in our Galaxy. This is seen in both Burton's (1988) profile of the H I layer and in the study of CO velocities by Clemens (1985). Closer to home, Matese and Whitmire (1997) have found that the perihelia of long-period comets are influenced by the galactic tidal force to a surprisingly large extent. The surprise can be removed if the tidal force is kRo = 120 times greater than expected. Strong tidal forces also appear to be responsible for the hierarchy of galactic structures: bar, extreme disk, thin disk, thick disk, and halo.
I will also answer general questions such as: Why do disk galaxies resemble spirals rather than Saturn's rings? Is there a link with quantized red shifts? Can the proposed potential predict which galaxies have central black holes?
The author(s) of this abstract have provided an email address for comments about the abstract: David.Bartlett@Colorado.edu