Tuesday, May 13, 2014

What else is there? Speculating about Water and Ice

In the expression for centripetal force,

\({F}_{planet}\)=\(\frac{{M}_{planet}}{{M}_{planet}+{M}_{sun}}{g}_{s}\)

surface gravity \({g}_{s}\) can be estimated from a close moon of the planet or other satellite in low orbit, the mass of the planet can then be estimated, because the actual value of \({F}_{planet}\) is calculated from orbit speed and orbital radius about its sun.

\({F}_{planet}\) = \(\frac{V^2_o}{O_{planet}}\)

Both orbital parameters can be observed more readily that planet masses.  But still planet masses are more likely to be expressed as relative values than absolute, even if the home planet mass can be evaluated more accurately.

Orbital speed calculated from the drop in GPE is the minimum velocity the moon goes into orbit with, added to this value is the initial velocity of the moon when it is captured.

\(V_o\) = \(\sqrt{3{g}_{s}{R}_{planet}}\)    -----------------  (*)

Orbital distortion provide two values for orbital velocities, the difference of which is the perpendicular component of the initial velocity at capture (perpendicular here is 90 degrees to the orbital path).  The parallel component is the difference between the average of the two orbital velocities (which is the velocity when the orbit is not distorted) and the orbital velocity calculated from GPE drop from (*).  The perpendicular component and the average orbital velocity are the two rotating velocities that give the orbit its oblong shape.  The satellite is at its least distorted orbital path position when it is captured.

Being able to estimate surface gravity is important.  From the published surface gravity values for Jupiter, Saturn and Neptune, it seem that planet surface gravity is independent of planet radius.  It may just be that some planet rotating core are contributing a magnetic pull towards the Sun;  that gravity is not the singular factor of planetary motion.  If gravity is solely due to compressed space around a planet then surface gravity will be dependent on surface mass density of the planet alone.  And large oceans on the planet will distort gravity, considering salinity and possible suspended particles in the water.  Ice on a planet will distort gravity too and will be predictable if the relationship between surface gravity and water is found.

All very much speculative.