Constraints on modified Newtonian dynamics theories from radio tracking data of the Cassini spacecraft

The modified Newtonian dynamics (MOND) is an attempt to modify the gravitation theory to solve the dark matter problem. This phenomenology is very successful at the galactic level. The main effect produced by MOND in the Solar System is called the external field effect parametrized by the parameter $Q_2$. We have used nine years of Cassini range and Doppler measurements to constrain $Q_2$. Our estimate of this parameter based on Cassini data is given by $Q_2=(3\pm 3)\times 10^{-27}{\mathrm{s}}^{-2}$, which shows no deviation from General Relativity and excludes a large part of the relativistic MOND theories. This limit can also be interpreted as a limit on an external tidal potential acting on the Solar System coming from the internal mass of our Galaxy (including dark matter) or from a new hypothetical body.

Figure 1

Representation of the effect of the modification of the light propagation due to the $\delta {\mathrm{\Phi }}_N$ term in metric (11) on the Earth-Saturn range.

Figure 2

Representation of range measurement residuals (one per orbit segment).

Figure 3

Plasma contribution to the Earth-Cassini range measurements.

Figure 4

Cassini range measurement residuals (one per tracking pass) when using Doppler data only to fit the spacecraft orbit (the second plot is a zoom of the first one).

Figure 5

Representation of range measurement residuals (one per orbit segment).

Figure 6

Representation of the estimation of the $Q_2$ parameter and its related $1\text{−}\sigma$ uncertainty as function of the subset of data used.

Figure 7

Range residuals previously available.