In this paper, we aim to estimate the vertical gradients in the rotational velocity of the Galaxy. This is carried out in the framework of a global thin disc model approximation. The predicted gradient values coincide with the observed vertical fall-off in the rotation curve of the Galaxy. The gradient is estimated based on a statistical analysis of trajectories of test bodies in the gravitational field of the disc and in an analytical way using a quasi-circular orbit approximation. The agreement of the results with the gradient measurements is remarkable in view of other more complicated, non-gravitational mechanisms used for explaining the observed gradient values. Finally, we find that models with a significant spheroidal component give worse vertical gradient estimates than the simple disc model. In view of these results, we can surmise that, apart from the central spherical bulge and Galactic halo, the gross mass distribution in the Galaxy forms a flattened rather than spheroidal figure.

Spiral galaxies are studied using a simple global disc model as a means for approximate determination of mass profiles. Based on rotation curves and the amount of gas (H i+He), we find global surface mass densities consistent with measurements and compare them with B‐band surface brightness profiles. As a result we obtain mass‐to‐light ratio profiles. We give some arguments for why our approach is reliable and sometimes better than those assuming ad hoc the presence of a massive non‐baryonic dark matter halo. Using this model, we study galaxies NGC 7793, 1365, 6946 and UGC 6446. Based on a rotation curve from The H i Nearby Galaxy Survey (THINGS) we also study galaxy NGC 4536 and compare the results with those we published elsewhere for the same galaxy.

We show that Geroch decomposition leads us to Maxwell-like representation of gravity in (3 + 1) metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential V µ and gravitational field tensor F µν that is associated with gravitational interaction. Next we show that gravitational four-current J µ derived for introduced four-potential produce energystress tensor and reproduce main General Relativity formula. Next we introduce valid Lagrangian and equations of motion that explains obtained results. At the end we introduce new approach to quantization of gravity that results in proper quantum values and is open to further generalization.

We estimate the vertical gradient of rotational velocity for several spiral galaxies in the framework of a global thin‐disc model, using the approximation of quasi‐circular orbits. We obtain gradients having a broad range of values, in agreement with measurements, for galaxies with both low and high gradients. To model the gradient, it suffices to know the rotation curve only. We illustrate, using the example of galaxy NGC 4302 with particularly high gradients, that mass models of galactic rotation curves that assume a significant spheroidal mass component reduce the predicted gradient value, which may suggest that the mass distribution is dominated by a flattened disc‐like component. We conclude that the value and behaviour of the vertical gradient in rotational velocity can be used to study the mass distribution in spiral galaxies.

In the last article we have created foundations for gravitational field oriented framework (DaF) that reproduces GR. In this article we show, that using DaF approach, we can reproduce Schwarzschild solution with orbit equations, effective potential and constants of motion. Next we generalize results to other GR solutions and show, how gravitational field affects spacetime curvature and intrinsic spin of the bodies. It also appears, that field oriented approach requests to assign some spin value to the massless particles. Derived DaF framework has therefore significant meaning for searching for field based interpretation of gravity requested by quantum gravity.