Weekend Rebel Science Excursion - 40

"TGIF" as they say, so let's talk some science.

I want to fuse the subject matter of several series into recent scientific developments.

A paper in Nature has been talked about in the science press.

That paper presents evidence and argument that there is a hot ocean underneath the surface of a moon of Saturn, under the surface of Enceladus (Researchers Think There's A Warm Ocean On Enceladus).

I want to tie this in with the EPH (Exploded Planet Hypothesis, Weekend Rebel Science Excursion, Weekend Rebel Science Excursion - 11) and the nature of our civilization (Civilization Is Now On Suicide Watch), compared with the (Tenets of Ecocosmology).


Let's begin by considering a scale that describes hypothetical evolution of civilization, in terms of that civilization's use of energy (Kardashev Scale).

Now let's add to that, the hypothesis of civilizations using a Dyson Grid or Sphere to harness solar energy in a way not commonly considered (Wikipedia: Dyson Sphere).

One Dredd Blog extension or addition to the EPH (The Challenge of the Exploded Planet Hypothesis, Cambridge Journals Online, International Journal of Astrobiology / Volume 6 / Issue 03 / July 2007, pp 185-197) is that there are remains of the structure of the Dyson Grid or Sphere still visible in the solar system (Saturn - Home of the Hexagon Mystery, Saturn Hexagon Mystifies Scientists).

Cosmologists and astronomers use the word "bombardment" to describe what put craters and destruction throughout our solar system  (e.g. early and late bombardment).

Note that "bombardment" and "exploded" go together.


Civilizations on Earth have not been free from lethal mistakes, and in fact lethal mistakes are the rule rather than the exception according to a noted historian:

"In other words, a society does not ever die 'from natural causes', but always dies from suicide or murder --- and nearly always from the former, as this chapter has shown."

(A Study of History,  by Arnold J. Toynbee). So, let's consider a hypothetical mistake of an earlier civilization on a planet that exploded not too far from here, as a result of that mistake.

A planet between Mars and Jupiter, where only a debris field remains now.

A debris field being studied even as we blog (Dawn Mission Nears Ceres Orbit Maneuvers).

So, to answer the question the title of this section asks, one thing that could go wrong is that a Dyson Grid or Sphere could malfunction.

Such a vast structure handles so much energy that a malfunction could be catastrophic.

Let's go figure.


One of the expectations or assertions of the EPH is that Enceladus is a chunk of the planet that exploded.

Enceladus contains, among other things, remnants of that planet's ocean.

Outer layers of that water are now frozen over, except that, as mentioned above in the new paper (Nature: Ongoing hydrothermal activities within Enceladus), under the thick ice is liquid ocean water, and some of it is hot.

How do we test that in terms of the EPH?

We can go back to the hypothesis that the planets and their moons are parts of the dust cloud that eventually condensed into planets and the Sun (On the Origin of the Genes of Viruses - 8) "around 4.5 billion years ago".

We can use what we know about Enceladus to calculate the water there, and how long it would take to lose / eject that water.


Let's begin with a statement from the paper published in Nature and linked to in section IV above:

"Gravitational field measurements suggest a regional south polar subsurface ocean of about 10 kilometres thickness located beneath an ice crust 30 to 40 kilometres thick."

(ibid, paper in journal Nature). It is interesting to note that the "regional south polar subsurface ocean" water is not uniform, it is mostly at the south pole, which indicates an abnormality that would be expected in the helter skelter debris of a planetary explosion.

Let's try to calculate the amount of water there, the amount that has been ejected, and how far backwards and forwards that holds out.

Fig. 1 (ocean water & ice cap @ South Pole)

The first thing we need to do is to calculate the volume of water in that south polar ocean, and in the ice cap.

Then we will calculate how long it would take for that water to be ejected into space to make Saturn’s E ring, to finally exhaust all water, and ultimatelly, how that comports with the theory of the formation of Enceladus was  some 4.5 billion years ago (or to the contrary when the planet exploded to eject its pieces into space).

Fig. 2 (concept of ice & water on Enceladus)

We will begin by calculating the volume of the ice layer.

This we do by calculating the whole volume of Enceladus, then calculating a sphere 40 km smaller (assume the ice layer is 40 km thick).

When subtracting the difference between the two, we derive the volume of the ice layer.

Hence: V = 4/3 π r³ [sphere volume]
V = 4/3 * 3.14 * 252³
V = 4/3 * 3.14 * 16003008
V = 1.33 * 50249445.12
V = 66,831,762 cu. km.
(now for the smaller sphere)

Fig. 3 (hot ocean water venting into space)

V = 4/3 π r³ [sphere volume]
V = 4/3 * 3.14 * 212³
V = 4/3 * 3.14 * 9528128
V = 1.33 * 29918321.92
V = 39,791,368 cu. km.

Now we can subtract the smaller sphere's volume from the larger sphere's volume to derive Enceladus' ice layer volume to be 27,040,394 cu. km. (66,831,762 cu. km. - 39,791,368 cu. km.).

To calculate the volume of water in the subsurface southern polar ocean, we use the following formula applied to the smaller sphere, to derive:
V = (π/3)H²(3R - H)  [cap of a sphere, Fig. 1]
V = (3.14/3)10²(3*212 - 10)
V = (1.05)*100*(3*202)
V = (105)*(606)
V =  63,630 cu. km.

Now we calculate the ejection of water into space to, among other things, form Saturn’s E ring.

We can do this roughly by using a formula we have already used to calculate water hypothetically venting from the asteroid Vesta in the debris field:

The violent ejections marked those strata with the "holes that were left as the water escaped" which after all these billions of years, still "stretch as much as 0.6 miles (1 kilometer) across and go down as deep as 700 feet (200 meters)."

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For illustration only, the amount of water to fill just one of those cone shaped surface vents would be:

vent diameter = 1 kilometer (3280.8 ft)
radius (r) = 3280.8 / 2
r = ~1640 ft

height (h) = 700 feet

cone volume formula: v = 1/3 * 3.14 * r² * h

v = .33 * 3.14 * 2,689,600 * 700

v = 1,950,874,464 ft³

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assume there are 7.48 gallons of water per ft³

water in cone = 1,950,874,464 ft³ / 7.48 ft³

gallons of water = ~260,812,094 gal (for 1 vent)

I don't think meteorites would have the volume of water to cause such focused, and violent ejections to make cone-shaped vents a kilometer across and 700 feet deep, because among other things, the meteorite types with the most water are carbonaceous chondrite types, having 3% - 22% water by weight.

(Weekend Rebel Science Excursion - 11).  The use of the venting calculations helped to see that at least one venting hypothesis was unlikely in the case of Vesta.


Figure 3 is an illustration of the venting taking place on Enceladus.

Six or seven vents are shown ejecting water from the subsurface southern ocean into the space around Enceladus (which makes Saturn's E ring).

The 63,630 cu. km. in the subsurface ocean is 35,313,378,458 cu. ft. of water (63,630 * 3280.8³ * 7.48), or 264,144,070,866 gallons.

If the water began to vent a billion years ago, that equates to a loss of only 264 gallons a year, or only 132 gallons a year at 2 billion years ago (before the ocean is completely emptied into space).

And this solar system, and supposedly this moon formed 4.5 billion years ago.

If the planet exploded only 5 million years ago, that would mean a venting of  52,829 gallons a year, or 2.5 million years ago, then 105,658 gallons a year.

All those numbers seem unlikely (way too small), so the ice layer must be melting into the ocean because of the heat, and replenishing the water (so as to allow venting of much, much more water).

In other words, the ice and water on Enceladus is evidently melting away, and will do so at least until the core heat goes away, or ultimately all the ice and water is gone.


An exploded planet about 1-3 million years ago (maybe 65 mya @ KT-boundary Fifth Mass Extinction), or some other explanation, would seem to be more likely origins of Enceladus than any hypothetical origin 4.5 billion years ago.

One can only wonder how long it will take for Enceladus to look like Vesta.

Any suggestions or corrections?

Have a good weekend.