A constraint on the distance dependence of the gravitational constant

Extended supergravity theories predict the existence of vector and scalar bosons, besides the graviton, which in the static limit couple to the mass. An example is the graviphoton, leading to antigravity. If these bosons have a small mass (?10^?4 eV), an observable Yukawa term would be present in the gravitational potential in the newtonian limit. This can be parametrized by a distance dependent effective gravitational “constant” G(r). Defining G₀ = G(10 cm) and G_c = G(10³ km), the comparison between theory and observations of the white dwarf Sirius B results in $\text{G}{}_{\mathrm{<mtext>c</mtext>}}\text{G}{}_0\text{= 0.98 ± 0.08}$.