| Nuclear planetology is a new research field, tightly constrained by a coupled
187Re-232Th-238U systematics, which by means of nuclear astrophysics aims also
at understanding the thermal evolution of Earth-like planets after Mercury-like
contraction and Fermi-pressure controlled gravitational collapse events towards
the end of their cooling period [1]. In nuclear planetology, Earth-like planets are
regarded as old (redshift z >15), down-cooled and differentiated black dwarfs (Fe-C
BLD’s), so-called interlopers from the Galactic bulge [1], which are subjected to
endoergic 56Fe(γ,α)52Cr (etc.) reactions (photodisintegration), (γ,n) or (γ,p) and fusion
reactions like 12C(α,γ)16O. It has recently been pointed out [1] that beside its surface
temperature Teff of its outer core surface, the Earth shows also striking similarity
in volume V (radius rEarth ≈6.370 km) with an old white dwarf star (WD;
rWD ≈6.300 km) like WD0346+246. This major boundary condition for nuclear
planetology can be described in terms of V Earth = V WD = V const=4•π•r3/3
(rWD ≈ rEarth). However, in addition to the fact that Earth is habitable, the most
obvious difference between a WD and the Earth is their density ρ (ρ=m/V; m mass, V
volume): while a WD may contain 1MO(MO= solar mass) per V const, the mass of the
Earth is only a tiny fraction of this, ≈3•10−6 MO per V const. Therefore, it is
crucial to understand ∂ρ, or why mEarth«mWD for V const. Here I argue that the
application of principles constrained by the theory of relativity [2] may offer a
possible answer to this question: it is generally accepted that mass is directly related to
energy, E=m•c2 (E energy; m mass; c velocity of light) or m=E/c2. From m∼E
we derive that any mass change can be described in terms of energy change [3].
Instead of ρ=m/V we may thus write ρ=E/c2•V, and because of the special scenario
V Earth = V WD = V const discussed here, the denominator of this equation becomes a
constant term C=c2•Vconst =9.73•1037m5s−2. From this it follows, that ρ=E/C, or ρ•C=E.
Therefore, we arrive at ρ ∼E for the WD/FeC-BLD case or, considering the evolution of the
system over time t: ∂ρ/∂t∼∂E∕∂t.Hence, concerning time integrated planetary evolution it
may be concluded that any density change ∂ρ of an old stellar remnant towards a
≈3•10−6 MO habitable Earth-like planet is a measure for the system’s energy change
∂E.
[1] Roller (2016), Geophys. Res. Abstr. 18, EGU2016-291-3. [2] Einstein (1905),
Annalen d. Physik, 18, 639-641. |