Rings...Who's Calling? Saturn Who? Saturn Lee...

What if  \(g_T\)  and  \(g\) crosses not just once but multiple times!  This is possible because  \(g_T\)  depends on  the distribution of  \(T(x)\).  With reference to a high \(T_o=T_{max}\),  \(g_T\)  increases with lower  \(T(x)\).  We would expect  \(T\)  to bunch around the point  \(g_t-g=0\) because of  the conditions for SHM.   We would also expect  \(T\)  to thin out at the farthest along its SHM path.  As such   \(g_T\) varies with local conditions and its curve is not fixed by just the boundary conditions.

If  \(g_t\)  and \(g\)  crosses multiple times,  \(T\)  will then perform SHM about the multiple zeros.   And so bunches around the same zeros.  If we can see such heat as plasma than we will see them as rings around suns.

In general, if a planet radiates heat into outer space, at distances far beyond where  \(g\)  is low and  \(g_T\)  is non zero we might see \(g_T\)  and  \(g\) crosses multiple times and results in gravity bands.  After all, both  \(g_T\)  and  \(g\)  are gravity terms.  Such gravity belts are illustrated below

This gravity profile looks like air pressure profile in a longitudinal sound wave.  Mass may be capture around the centers of the gravity bands and form rings around the heat radiating planet.  Where gravity points away in both directions, we will see the gaps that separate one ring from another.  Bear in mind that in outer space where no other forces are acting, small strength gravity bands do have a visible effect.

So, we might see suns and heat radiating planets with such gravity bands around it, from considering thermal gravity and mass gravity.

Suddenly, I'm in motion,  Oh ohoh oh oh...And there are rings... around Ju...pit...er...