The centripetal force keeping Kepler-62e in orbit is
semimajor axis = 0.427*1.4960e8 km
orbital period = 122.3874 *24*60*60 s
velocity = 2*pi*0.427*1.4960e8/(122.3874 *24*60*60) = 37.957 kms-1
\({F}_{c62e}\) = 37.957^2/( 0.427*1.4960e8) = 0.0000225 km-2
and for Kepler-62f
semimajor axis = 0.718*1.4960e8 km
orbital period = 267.291 *24*60*60 s
velocity = 2*pi*0.718*1.4960e8/(267.291 *24*60*60) = 29.224 kms-1
\({F}_{c62f}\) = 29.224^2/(0.718*1.4960e8) = 0.00000795 km-2
If we approximate surface gravity with
\({F}_{c} = \frac{{M}_{p}}{{M}_{s}}{g}{s}\) when \({M}_{s}>>{M}_{p}\)
where \({M}_{p}\) is the mass of the planet and \({M}_{s}\) the mass of the sun, then the
ratio of surface gravity Ke62e/Ke62f = 0.0000225/0.00000795*(2.57/3.57) = 2.037
This is not the expected value of 1.087 from the ratio of density of water/ice alone.
However, the ratio of
density*radius Ke62e/Ke62f = \(\frac{density1*radius1}{density2*radius2}\)= \(\frac{mass1}{mass2}(\frac{radius2}{radius1})^2 \)
= (3.57/2.57)*( 1.41/1.61)^2 = 1.065
which is close to the ratio of density between water and ice of 1.087.
May be, the surface gravity is proportional to density and proportional to the planet radius. Planet mass is a derived quantity from observed orbital parameters and radius. The last two numerical value may suggest that gravity is dependent on surface mass density, that between a water and a ice planet, only the relative density of water and ice matters, the underlying mass density does not and the underlying mass does not. The radius of the planet is a measure of how far the planet pushes out into space.
Still, very strained argument, for the case of surface mass density being responsible for surface gravity.
