  Radio occultations are commonly used to assess remotely the thermodynamic
properties of planets or satellites' atmospheres within the solar system. The
data processing usually involves the so-called Abel inversion method or the
numerical ray-tracing technique. Both these approaches are now well
established, however, they do not allow to easily determine the uncertainty
profiles in the atmospheric properties, and this makes the results difficult to
interpret statistically. Recently, a purely analytical approach based on the
time transfer functions formalism was proposed for modeling radio occultation
data. Using this formulation, we derive uncertainty relationships between the
frequency shift and the thermodynamic properties of the neutral atmosphere such
as the temperature, pressure, and neutral number density. These expressions are
important for interpreting previous results from past radio occultation
experiments. They are especially relevant for deriving the system requirements
for future missions in a rigorous manner and consistently with the scientific
requirements about the atmospheric properties retrieval.
