The problem with my understanding came from using a circle's radius (one dimensional line of distance) and comparing its length when trying to understand scientist's description of a three dimensional volume (Volume = V, V=4/3╥r3).
I was incorrectly cross referencing the flat surface area of a circle with the depth of a spherical three dimensional object. I may still need to learn more about these concepts but I'm starting to get a handle on it and thought it would be worth clarifying my mis or missed information on the subject. A single line of length or radius is a measure of distance or length (one dimension). Two lines of direction, length times height is used to calculate the two dimensional area of a flat surface like a square but when the area is a circle we square the radius accounting for the entire circular area in two dimensions. Three lines of direction, length times height times width is used to calculate a three dimensional box or the volume of a 3D space like a sphere in which case we cube the radius to account for a three dimensional spherical space. |
The density of a planet or moon is obtained by dividing its mass by its volume. Water's density is considered 1 g/cm3 while silicate rock varies but is typically averaged to be anywhere from 3 to 3.5.
Above, Nimmo assumes an ice density of 0.95 g/cm3, McKinnon assumes it to be 0.9. Other sources like Wiki indicate ice on Earth at 1 atmosphere is 0.917 so I will use this known figure for ice although compressed ice II is more dense and ice I at lower gravity is less dense. Silicate rock comes in many different densities from 1.99 to 7.50 g/cm3 but the most common range for rock is between 3 and 3.5. I created this table using various percentages of rock to ice. I assumed an ice density of 0.917 and used a range of rock densities of 3 and 3.5 so that I could plot this range in a chart. |
Fifty percent of Pluto's radius is 1188/2 = 595 km (pink).
Ten percent of Pluto's core volume takes up close to half its radius at 552 km. The orange zone is how much of a radius the rock consumes at 40% its volume assuming a fully differentiated core. The volume rings from 20, 40, 60, 80 & 100% show how they get smaller and smaller as they grow outward from the core. |
If Jupiter's moon Callisto had a fully differentiated core at 34.6% of its volume it would consume 70% of its radius yet wiki indicates the largest Callisto's core can be is 600 km (yellow) or 25% its radius.
Even though I understand better why 10 percent of the volume of a planet is nearly 50% its radius, the concept of Pluto having a fully differentiated core that's 71-74% the circumference of its radius while Callisto's core can't be anymore than 25% its radius still doesn't make sense to me. Wiki quote The density and moment of inertia are compatible with the existence of a small silicate core in the center of Callisto. The radius of any such core cannot exceed 600 km, and the density may lie between 3.1 and 3.6 g/cm3 Either something is completely wrong here or as before, there's something I'm not understanding. |
While reading this paper I obtained some information about Pluto's small moon Hydra.
These values were calculated pre-flyby and were based on their albedos ranging from 35% to 4% Nix is actually 56% and Hydra is a whopping 83% so there are obvious discrepancies in the estimations but they're the only ones I've found. |
shape_mean_radius_gravity_field_and_interior_structure_of_callisto.pdf | |
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The MOI of Saturn's moon Titan is 0.3414 which based on the above paper indicates it should only be partially differentiated like Callisto but instead scientists interpret these figures to mean it is fully differentiated.
Hydrous silicate core means clay. An Interesting article about Titan |
One point I'd like to note, in all these silicate core models of Pluto/Charon, iron is totally missing from the core concept. Yet when we consider the core of moons like the Galilean moons we assume an iron core. If iron were tossed into these rock mass ratio's the radius of Pluto's rocky core of radiogenic material would shrink further. |
This Space.com poster was created after our arrival at Pluto but before Bill McKinnon's press conference at LPSC 2016. The image of a rocky core being 71-74% the radius of Pluto is now being embedded in the minds of people everywhere and serves to make Bill's subsurface ocean concept more feasible. |
>>>>>>>>>>> Prior to the flyby NASA displayed Pluto's core like this image which seems to reflect the 71-74% rock radius. <<<<<<<<<<<< But this image on the left is also how NASA depicted Pluto prior to the flyby. |
![]() Possible interior models for Pluto are shown above: (left) ice-shell, ocean, core, (middle) thick ice-shell, core, (right) uniform density (undifferentiated).
Conclusions. Pluto will need to have an interior > 200 K. It is likely that due to tidal heating (when orbital and rotational energy are dissipated as heat in the crust, which would be happening for Pluto despinning after formation), Pluto would melt and differentiate. The most self-consistent models include an ocean.
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These are the three model scenarios presented in July of 2013. https://blogs.nasa.gov/mission-ames/tag/pluto/ A uniform core was still on the table two years prior to arriving at Pluto. Pi = ice density Pr = rock density Pw = water density P bar = uniform density |
The thing for me is this, scientists knew how to calculate Pluto's rock mass, density and volume when they created images similar to the above which leaves me asking a question.
Why did they depict such a tinny core similar to Callisto's or uniform densities or no internal ocean as viable options (they knew Pluto's rotation rate, mass, density and radius) but after LPSC 2016 they only consider Pluto's core to be fully differentiated taking up 71% of its radius with an ocean? Why such a massive discrepancy from 2013 to 2016? |
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If anyone sees the error in my math, I'd love to hear from you.
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Its showing how, over time, our interpretation of data has changed regarding our understanding of the thickness of Mercury's crust. In 2001 or 2002 Nimmo indicated Mercury's crust was 200 km but subsequent years and data have demonstrated how the trend in our perception of its thickness continues to reduce to the point we now think it is only 26 km thick.
My point is, anyone can make mistakes and just because Nimmo is a smart scientists doesn't mean his interpretations of information is always correct.
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Without realizing it, Keane has drawn an image which does a great job of showing my concept about the polygonal cells and how they are NOT convection cells created by convection currents.
I have said the polygonal cells are large ice sheets and the edges where more aggressive sublimation pits exist are evidence that the warmest part of the cell is along its edges not at the center. This Keane image depicts my concept perfectly. Nitrogen softens and breaks bed rock or bed-ice off the crust. The bed-ice floats into SP and ends up becoming large polygonal cells the thickest part of which is at the center. |
This article shows how multiple studies demonstrate how at least half of evolutionary biologist and ecologist fudge their results.
Fraser and colleagues targeted three questionable practices. The first of these was p-hacking, the use of data mining to uncover apparent (or real) correlations that were not included in the original hypothesis. A consequence of p-hacking, wrote researchers from the Australian National University in 2015, is that “nonsignificant results become significant”. The team also asked about cherry-picking – selecting results that are statistically significant while ignoring others – and a practice known as HARKing, which involves formulating a hypothesis after, instead of before, results are in. |
The results, posted on preprint site Open Science Framework (OSF), are disturbing. Across both ecologists and evolutionary biologists, a whopping 64% confessed to cherry-picking. Some 42% indulged in p-hacking, mainly by collecting more data after the results were in. And 51% admitted to reporting unexpected results in ways that made it appear they had predicted them from the start.
The scientists surveyed, Fraser and colleagues relate, offered a raft of reasons to justify their transgressions, including publication bias, pressure, and the need to present a neat, coherent narrative. |
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