Currently, UAVs are intensively being introduced into topographic-photogrammetric production for topographic digital aerial photography and laser scanning. These technologies have a number of advantages: they don’t require specially prepared platforms and launchers, they are relatively inexpensive unlike large aircrafts, and they are safe. However, there are still many unsolved problems for ultralight UAVs, especially when the aerial photography is made. As you know, the requirements for the implementation of the aerial survey process are quite stringent, first of all, for horizontal flight: the angles of inclination must be within 3–5 degrees, since exceeding these tolerances significantly affects the accuracy for determining the spatial coordinates of objects. Therefore, there was an idea to conduct researches of dependences between the pitch α, roll ω and yaw κ. For this purpose, 100 images obtained from aircraft-type UAV ‘Arrow’ developed and created by specialists from Lviv Polytechnic National University and ‘Abris’ were used. As a result of the study, the multiple correlation coefficient and the parameters of the linear regression equation for the angular elements of the exterior orientation of digital images were calculated. In addition, statistical quality evaluations for the obtained regression model were carried out. Analysis of the received data allows to assert that angular elements of exterior orientation are correlated with each other. Therefore, in the further imaging materials, processing it becomes possible to make compensation of this fact and to improve calculation accuracy of spatial coordinates of points.

This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential. The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional (biorthogonal) polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body. Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.