  For planets other than Earth, interpretation of the composition and structure
depends largely on comparing the mass and radius with the composition expected
given their distance from the parent star. The composition implies a
mass-radius relation which relies heavily on equations of state calculated from
electronic structure theory and measured experimentally on Earth. We lay out a
method for deriving and testing equations of state, and deduce mass-radius and
mass-pressure relations for key materials whose equation of state is reasonably
well established, and for differentiated Fe/rock. We find that variations in
the equation of state, such as may arise when extrapolating from low pressure
data, can have significant effects on predicted mass- radius relations, and on
planetary pressure profiles. The relations are compared with the observed
masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth-
like,' likely with a proportionately larger core than Earth's, nominally 2/3 of
the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an
Fe-based core which is likely to be proportionately smaller than Earth's. GJ
1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy'
composition with a relatively large core or a relatively large proportion of
H2O. CoRoT-2b is less dense than the hydrogen relation, which could be
explained by an anomalously high degree of heating or by higher than assumed
atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation
for hydrogen, suggesting the presence of a significant amount of matter of
higher atomic number. CoRoT-3b lies close to the hydrogen relation. The
pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure
in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa.
