I present a simple scheme for the treatment of gravitational interactions on galactic scales. In anal- ogy with known mechanisms of quantum field theory, I assume ad hoc that gravitation is mediated by virtual exchange particles – gravitons – with very small but non-zero masses. The resulting den- sity and mass profiles are proportional to the mass of the gravitating body. The mass profile scales with the centripetal acceleration experienced by a test particle orbiting the central mass, but this comes at the cost of postulating a universal characteristic acceleration a0 ≈ 4.3 × 10−12msec−2 (or 8πa0 ≈ 1.1×10−10msec−2). The scheme predicts the asymptotic flattening of galactic rotation curves, the Tully-Fisher/Faber-Jackson relations, the mass discrepancy–acceleration relation of galaxies, the surface brightness–acceleration relation of galaxies, the kinematics of galaxy clusters, and “Renzo’s rule” correctly; additional (dark) mass components are not required. Given that it is based on various ad-hoc assumptions and given further limitations, the scheme I present is not yet a consistent theory of gravitation; rather, it is a “toy model” providing a convenient scaling law that simplifies the description of gravity on galactic scales.

ABSTRACT
1. INTRODUCTION
2. GRAVITATIONAL INTERACTION
    2.1 Fundamental Assumptions
    2.2 Consequences
3. TESTS
    3.1 Galactic Rotation Curves
    3.2 Tully-Fisher/Faber-Jackson Relations
    3.3 Mass Discrepancy–Acceleration Relation
    3.4 Surface Brightness vs. Acceleration
    3.5 Galaxy Clusters
    3.6 “Renzo’s Rule”
4. DISCUSSION
    Dynamical friction.
    Collisions of galaxy clusters.
    Gravitational lensing.
    Cosmology.
5. CONCLUSIONS
REFERENCES

• SASCHA TRIPPE(Department of Physics and Astronomy, Seoul National University)