[1] We derive the high-frequency, compressible, dissipative dispersion and polarization relations for linear acoustic-gravity waves (GWs) and acoustic waves (AWs) in a single-species thermosphere. The wave amplitudes depend explicitly on time, consistent with a wave packet approach. We investigate the phase shifts and amplitude ratios between the GW components, which include the horizontal (u H ′ ) and vertical (w′) velocity, density (r′), pressure (p′), and temperature (T ′) perturbations. We show how GWs with large vertical wavelengths l z have dramatically different phase and amplitude relations than those with small l z . For zero viscosity, as jl z j increases, the phase between u H ′ and w′ decreases from 0 to $À90 , the phase between u H ′ and T′ decreases from $90 to 0 , and the phase between T ′ and r′ decreases from $180 to 0 for l H ≫ jl z j, where l H is the horizontal wavelength. This effect lessens substantially with increasing altitudes, primarily because the density scale height H increases. We show how in-situ satellite measurements of either (1) the 3D neutral wind or (2) r′, T′, w′, and the cross-track wind, can be used to infer a GW's l H , l z , propagation direction, and intrinsic frequency w Ir . We apply this theory to a GW observed by the DE2 satellite. We find a significant region of overlap in parameter space for 5 independent constraints (i.e., T′ 0 /r′ 0 , the phase shift between T ′ and w′, and the distance between wave crests), which provides a good test and validation of this theory. In a companion paper, we apply this theory to ground-based observations of a GW over Alaska.Citation: Vadas, S. L., and M. J. Nicolls (2012), The phases and amplitudes of gravity waves propagating and dissipating in the thermosphere: Theory,