| Summary: | A two dimensional hydrodynamic model describing the solar wind interaction with the local interstellar medium, which surrounds the solar system, is used to study the heliosphere both as a steady-state- and dynamic structure. The finite volume method used to solve the associated system of hydrodynamic equations numerically is discussed in detail. Subsequently the steady state heliosphere is studied for both the case where the solar wind and the interstellar medium are assumed to consist of protons only, as well as the case where the neutral hydrogen population in the interstellar medium is taken into account. It is shown that the heliosphere forms as three waves, propagating away from the initial point of contact between the solar wind and interstellar matter, become stationary. Two of these waves become stationary at sonic points, forming the termination shock and bow shock respectively. The third wave becomes stationary as a contact discontinuity, called the heliopause. It is shown that the position and geometry of the termination shock, heliopause and bow shock as well as the plasma flow characteristics of the heliosphere largely depend on the dynamic pressure of either the solar wind or interstellar matter. The heliosphere is modelled as a dynamic structure, including both the effects of the solar cycle and short term variations in the solar wind observed by a range of spacecraft over the past ~ 30 years. The dynamic model allows the calculation of an accurate record of the heliosphere state over the past ~ 30 years. This record is used to predict the time at which the Voyager 2 spacecraft will cross the termination shock. Voyager 1 observations of 10 MeV cosmic ray electrons are then used in conjunction with a cosmic ray modulation model to constrain the record of the heliosphere further. It is shown that the dynamic hydrodynamic model describes the heliosphere accurately within a margin of error of ±0.7 years and ±3 AU. The model predicts that Voyager 2 crossed the termination shock in 2007, corresponding to preliminary results from observations indicating that the crossing occurred in August 2007. === Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.
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