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We present a method to calculate gravitational potential gradients withinregions containing few tens of thousands stars with known phase spacecoordinates. The central idea of the method is to calculate orbital arcs foreach star within a given region for a certain parametrised potential(gravitational acceleration) and to assume that position of each star on itsorbital arc is a random variable with a uniform probability density in time.Thereafter, by combining individual probability densities of stars it ispossible to calculate the overall probability density distribution andlikelihood for a given region as a function of gravitational accelerationparameters. The likelihood has a maximum if the calculated probabilitydistribution and the observed distribution of stars in phase space areconsistent. This allows us to constrain gravitational accelerations andpotential gradient values. The method assumes that phases of stars are mixedwithin the regions where stellar orbits are calculated. We tested the methodfor 12 small rectangular regions within simulated disc galaxy from Gaia Wiki.Tests show that even with a rather simple acceleration form the calculatedaccelerations in galactic plane coincide with their true values from simulationabout 5 per cent, misalignment between the calculated and true accelerationvector directions is less than 1 degree (median values). The model can be usedwith the Milky Way Gaia complete solution data.

A method to calculate gravitational accelerations within discrete localised regions in the Milky Way