  Using ab initio molecular dynamics simulations, we calculate the physical
properties of MgO at conditions extending from the ones encountered in the
Earth mantle up to the ones anticipated in giant planet interiors such as
Jupiter. We pay particular attention to the high pressure melting temperature
throughout this large density range as this is a key ingredient for building
accurate planetary interior models with a realistic description of the inner
core. We compare our simulation results with previous ab initio calculations
that have been so far limited to the pressure range corresponding to the Earth
mantle and the stability of B1-B2 transition around 6 Mbar. We provide our
results for both the EOS and high pressure melting curve in parametric forms
for direct use in planetary models. Finally, we compare our predictions of the
high pressure melting temperature with various interior profiles to deduce the
state of differentiated layer within the core made of MgO in various types of
planets and exoplanets.
