This is the first in a series of papers examining large-scale gravity waves in the thermosphere and their ability to transfer energy from high to low latitudes during magnetic disturbances. The gravity wave source is assumed to be either the Lorentz force of auroral electrojet currents or else a heat input due to energetic particle precipitation or to Joule heating. It is pointed out that the characteristic vertical width of the gravity wave source should usually lie between 2 and 4 pressure scale heights, placing constraints on the vertical wavelengths and horizontal velocities of the generated waves. A simplified analytic model of small-amplitude wave generation by a current source shows how wave energy production depends on the temporal and spatial dimensions of the source, on the electric field strength, and on the electron density enhancement. The steep thermospheric temperature gradient in the vicinity of the source altitude strongly influences the properties of upward and downward propagating waves compared with waves generated in an isothermal atmosphere. Waves produced by the Lorentz force of Hall currents, by the Lorentz force of Pedersen currents, and by Joule heating are influenced quite differently by this temperature gradient. Because upgoing waves above the source are combinations of waves originally launched upward and waves originally launched downward but reflected around 110 km altitude, the mean effective source altitude is about 110 km for the far field response in the thermosphere. Large-scale traveling ionospheric disturbances observable at middle latitudes are most likely produced primarily by Pedersen, rather than Hall, currents. The temperature structure of the thermosphere generally causes gravity wave packets to refract upward; waves traveling with a horizontal component of velocity faster than 250 m/s and with an initial downward component of group velocity will always be reflected upward in the lower thermosphere. The effects of viscosity, heat conduction, and Joule dissipation tend to filter out shorter-period and slower moving waves from observation points at some distance from the source, so that only long-period fast moving waves can reach low latitudes from an auroral source. For example, a wave with a 94-min period moving horizontally at 605 m/s is largely dissipated by the time it has traveled 4000 km from a typical auroral source. A numerical simulation using a fairly realistic thermospheric model illustrates many of the points described from analytic considerations.