Abstract. In addition to the pericentre ω, the mean anomaly and, thus, the mean longitude λ, also the orbital period P_b and the mean motion n of a test particle, are modified by the Dvali–Gabadadze–Porrati gravity. While the correction to P_b depends on the mass of the central body and on the geometrical features of the orbital motion around it, the correction to n is independent of them, up to terms of second order in the eccentricity e. The latter amounts to about 2 × 10⁻³ arcsec per century. The present-day accuracy in determining the mean motions of the inner planets of the solar system from radar ranging and differential very long baseline interferometry (ΔVLBI) is 10⁻²–5 × 10⁻³ arcsec per century, but it should be improved in the near future when the data from the spacecraft to Mercury and Venus will be available.

Key words: extra dimensions; gravity

Received 11 October 2005, accepted for publication 19 December 2005
Published 10 January 2006