We deal with the effects induced on the orbit of a test particle revolving around a central body by putative spatial variations of dimensionless fundamental coupling constants ζ. In particular, we assume a dipole gradient for along a generic direction in space. We analytically work out the long-term variations of all the six standard osculating Keplerian orbital elements parameterizing the orbit of a test particle in a gravitationally bound two-body system. Apart from the semimajor axis a, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericentre ϖ and the mean anomaly undergo non-zero long-term changes. By using the usual decomposition along the radial (R), transverse (T) and normal (N) directions, we also analytically work out the long-term changes ΔR, ΔT, ΔN and ΔvR, ΔvT, ΔvN experienced by the position and the velocity vectors r and v of the test particle. Apart from ΔN, all the other five shifts do not vanish over one full orbital revolution. In the calculation we do not use a priori simplifying assumptions concerning e and I. Thus, our results are valid for a generic orbital geometry; moreover, they hold for any gradient direction . We compare our predictions to the latest observational results for some of the major bodies of the solar system. The largest predicted planetary perihelion precessions occur for the rocky planets, amounting to some 10−2–10−3 mas per century. Apart from the Earth, they are 2 − 3 orders of magnitude smaller than the present-day accuracy in empirically determining the corrections to the standard Newtonian–Einsteinian planetary perihelion rates. Numerically integrated time-series of the interplanetary range for some Earth–planet pairs yield Stark-like signatures as large as 0.1–10 mm; future planned planetary laser ranging facilities should be accurate at a cm level. The long-term variations of the lunar eccentricity and perigee are of the order of 10−14 yr−1 and 10−4 mas yr−1, respectively, while the change ΔR in the radial component of the Moon’s geocentric orbit is as large as 0.8 μm per orbit. A numerically calculated geocentric lunar range time-series has a maximum nominal peak-to-peak amplitude of just a few mm, with an average of 0.3 μm over 30 yr. The present-day accuracies in determining and for the Moon are 10−12 yr−1 and 10−1 mas yr−1, respectively. The Apollo facility should be able to determine on a continuous basis of the Earth–Moon range with a mm accuracy.