The Sun's corona has interested researchers for multiple reasons, including the search for solution for the famous coronal heating problem and a purely practical consideration of predicting geomagnetic storms on Earth. There exist numerous different theories regarding the solar corona; therefore, it is important to be able to perform comparative analysis and validation of those theories. One way that could help us move towards the answers to those problems is the search for observational methods that could obtain information about the physical properties of the solar corona and provide means for comparing different solar corona models.In this work we present evidence that VLBI observations are, in certain conditions, sensitive to the electron density of the solar corona and are able to distinguish between different electron density models, which makes the technique of VLBI valuable for solar corona investigations. Recent works on the subject used a symmetric power-law model of the electron density in solar plasma; in this work, an improvement is proposed based on a 3D numerical model.

One of the problems arising in modern celestial mechanics is the need of precise numerical integration of dynamical equations of motion of the Moon. The action of tidal forces is modeled with a time delay and the motion of the Moon is therefore described by a functional differential equation (FDE) called delay differential equation (DDE).Numerical integration of the orbit is normally being performed in both directions (forwards and backwards in time) starting from some epoch (moment in time). While the theory of normal forwards-in-time numerical integration of DDEs is developed and well-known, integrating a DDE backwards in time is equivalent to solving a different kind of FDE called advanced differential equation, where the derivative of the function depends on not yet known future states of the function.We examine a modification of Adams-Bashforth-Moulton method allowing to perform integration of the Moon's DDE forwards and backwards in time and the results of such integration.

We present an updated public version of EPM (Ephemerides of Planets and the Moon). Since the last public version, EPM2017, many improvements were made in both the observational database and the mathematical model. Latest lunar laser ranging observations have been added, as well as radio ranges of Juno spacecraft and more recent ranges of Odyssey and Mars Reconnaissance Orbiter. EPM2021 uses a new improved way to calculate radio signal delays in solar plasma and has a major update in the method of determination of asteroid masses. Also, a delay-capable multistep numerical integrator was implemented for EPM in order to properly account for tide delay in the equations of the motion of the Moon. The improved processing accuracy has allowed to refine existing estimates of the mass of the Sun and its change rate, parameters of the Earth–Moon system, masses of the Main asteroid belt and the Kuiper belt; and also to raise important questions about existing numerical models of solar wind.

Solar wind plasma as a cause of radio signal delay plays an important role in solar and planetary science. Early experiments studying the distribution of electrons near the Sun from spacecraft ranging measurements were designed so that the radio signal was passing close to the Sun. At present, processing of spacecraft tracking observations serves a different goal: precise (at metre level) determination of orbits of planets, most importantly Mars. The solar wind adds a time-varying delay to those observations, which is, in this case, unwanted and must be subtracted prior to putting the data into the planetary solution. Present planetary ephemerides calculate the delay assuming a symmetric stationary power-law model for the solar wind density. The present work, based on a custom variant of the EPM lunar–planetary ephemeris, questions the accuracy and correctness of that assumption and examines alternative models based on in situ solar wind density data provided by OMNI and on the ENLIL numerical model of the solar wind.