A global, three-dimensional, time-dependent numerical model of the thermosphere has been created to simulate the dynamical behavior of the earth's thermosphere under a wide variety of geophysical conditions. Comparison of the model's predictions with the available data from ground-based, rocket and satellite techniques has shown that thermospheric dynamics can be realistically simulated by considering only three processes which deposit energy, or energy and momentum, in the thermosphere. Comparisons between the simulations and available data allow assessment of the magnitudes of the various processes as functions, particularly, of solar and geomagnetic activity. The model is fully self-consistent in solving the neutral gas equations of momentum, energy and continuity, including all the Coriolis, inertial, viscosity and nonlinear terms, but assumes that the thermosphere contains a single species whose mean molecular weight varies only with the pressure. At times when the mean meridional wind is large (>20 m s−1), such as at the solstices and during strong and long geomagnetic storms, this assumption will cause the meridional temperature gradient, in particular, to be underestimated. The ion continuity equation is not handled in a self-consistent manner and, although the dynamo (V ∧ B) electric field term is universally computed, the present simulations do not include the “external” component of the electric field, either as a result of an empirical model or by computation of the polarization field. With the above provisos, the dynamics of the thermosphere can be simulated under a wide variety of solar and geomagnetic conditions, using one major and ubiquitous energy source, due to solar UV and EUV radiation, and an additional geomagnetic source of both energy and momentum (Joule heating and ion drag) due to a polar electric field. Both the mean temperature and the mean meridional winds need further fine tuning, which may be realistically related to an additional high-latitude energy source for which relatively low-energy particle precipitation (suprathermal to a few hundred eV) is the most obvious candidate, rather than auroral (keV) electrons. Recent values of the solar EUV flux are adequate to explain observed thermospheric temperatures at very low geomagnetic activity if a small residual polar source remains (geomagnetic) and if the heating efficiency is significantly increased, from about 0.3–0.35 to about 0.45. Polar electric fields, following the empirical models of Heppner (1977), as given analytically by Volland (1978), are adequate to explain wind structures at middle, auroral and polar latitudes under quiet geomagnetic conditions (Kp 0–1 = Volland model 1) and “average” geomagnetic conditions (Kp 3–4 = Volland model 2) at the equinox, and at summer and winter solstices, for low solar activity (F10.7 ∼ 75 × 10−22 W cm−2 s−1) and for moderately high solar activity (F10.7 ∼ 165 × 10−22 W cm−2 s−1), when a small amount of additional high-altitude high-latitude energy is included—values range between 109 and 1010 W per hemisphere depending on season, and solar and geomagnetic activity. The results presented in this paper relate exclusively to the steady-state behavior of the thermosphere, and a series of further papers are in preparation describing some of the interesting results of the various time-dependent simulations we have performed, in particular to study the consequences of geomagnetic substorms of different magnitudes and at different seasons and different levels of solar activity. In later papers we will also consider the constraints arising from the major energy and momentum sources of the thermosphere in a quantitative way.