March 6, 2018
I recently quoted Neil deGrasse Tyson, it goes something like this.
If you want to speak to someone from Spain, learn to speak Spanish.
If you want to speak to someone from China, learn to speak Chinese.
If you want to speak to the Universe, learn to speak math.
It's been a while since I was in school learning math and have, consequently, forgotten the majority of what I learned. I have not earned my living in a field where algebra, geometry and calculus are required, consequently, I remember very little of it. Neil's words, however, struck a cord with me. While trying to understand Pluto, I have, on more than one occasion, encountered math scenarios which left me scratching my head.
A case in point;
Ever since I sent this email to Francis Nimmo in July of 2017, I've wanted to understand these apparent differences in the values. I knew then as now there was something wrong with my understanding of the math.
The email I sent to Nimmo.
I'm trying to understand what appears to be a discrepancy in one of your papers but I'm assuming it's just that I don't understand something. I have a blog site and would like to accurately represent your information so I was hoping you could help me comprehend, what to me is, a point of confusion.
In this paper
Thermal evolution of Pluto and implications for surface tectonics and a sub-surface ocean. By Guillaume Robuchon, Francis Nimmo
Page 3
Thus, it is reasonable to assume the same range of rheological proprieties and compositions for Pluto (McKinnon et al., 2008). Pluto’s ice/rock+ice ratio is supposed to be about 0.65 (McKinnon et al., 1997) and for a differentiated Pluto the silicate core would be roughly 40% of the volume.
Page 5
As in previous studies (McKinnon et al., 1997; Hussmann et al., 2006; Schubert et al., 2010), we suppose that the interior is differentiated into a silicate core and icy mantle. Assuming an ice density of 950 kg m−3, we obtain a core radius, Rc, of 849.6 km and a silicate density, ρ sil, of 3361 kg m−3.
Nimmo did not reply and for some time now, I've periodically asked myself what am I missing?
Why does he get a core radius of 850 km when 40% of 1188 km is 475 km. This question has nagged me since I wrote page 73 seven months ago but I set it aside at the time and moved forward as though my figure of 475 km was correct even though it wasn't. I've gone back and corrected this error on that page but now need to weed through every subsequent page to fix any related errant statements.
If you want to speak to someone from Spain, learn to speak Spanish.
If you want to speak to someone from China, learn to speak Chinese.
If you want to speak to the Universe, learn to speak math.
It's been a while since I was in school learning math and have, consequently, forgotten the majority of what I learned. I have not earned my living in a field where algebra, geometry and calculus are required, consequently, I remember very little of it. Neil's words, however, struck a cord with me. While trying to understand Pluto, I have, on more than one occasion, encountered math scenarios which left me scratching my head.
A case in point;
Ever since I sent this email to Francis Nimmo in July of 2017, I've wanted to understand these apparent differences in the values. I knew then as now there was something wrong with my understanding of the math.
The email I sent to Nimmo.
I'm trying to understand what appears to be a discrepancy in one of your papers but I'm assuming it's just that I don't understand something. I have a blog site and would like to accurately represent your information so I was hoping you could help me comprehend, what to me is, a point of confusion.
In this paper
Thermal evolution of Pluto and implications for surface tectonics and a sub-surface ocean. By Guillaume Robuchon, Francis Nimmo
Page 3
Thus, it is reasonable to assume the same range of rheological proprieties and compositions for Pluto (McKinnon et al., 2008). Pluto’s ice/rock+ice ratio is supposed to be about 0.65 (McKinnon et al., 1997) and for a differentiated Pluto the silicate core would be roughly 40% of the volume.
Page 5
As in previous studies (McKinnon et al., 1997; Hussmann et al., 2006; Schubert et al., 2010), we suppose that the interior is differentiated into a silicate core and icy mantle. Assuming an ice density of 950 kg m−3, we obtain a core radius, Rc, of 849.6 km and a silicate density, ρ sil, of 3361 kg m−3.
Nimmo did not reply and for some time now, I've periodically asked myself what am I missing?
Why does he get a core radius of 850 km when 40% of 1188 km is 475 km. This question has nagged me since I wrote page 73 seven months ago but I set it aside at the time and moved forward as though my figure of 475 km was correct even though it wasn't. I've gone back and corrected this error on that page but now need to weed through every subsequent page to fix any related errant statements.
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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. |
Various rock densities
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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. |
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Using the formula, Density = (% rock) x (rock density) + (% ice) x (ice density) divided by 100, I developed a chart showing how much rock is found in icy solar system moons as a percentage of the total mass when the density is known.
I plotted these points on a graph to get a visual idea of how the density of a moon would translate into its percent of rock. The percent of rock values can be calculated mathematically but they come out to be pretty much the same as can be seen in the graph. While calculations are more precisely accurate, I like the graph as it gives a visual idea of the same data.
I plotted these points on a graph to get a visual idea of how the density of a moon would translate into its percent of rock. The percent of rock values can be calculated mathematically but they come out to be pretty much the same as can be seen in the graph. While calculations are more precisely accurate, I like the graph as it gives a visual idea of the same data.
With Pluto's density at 1.854 g/cm3 and plotting for a rock density of 3 and 3.5 the range of the percent of rock to ice is roughly between 36 and 44 percent. Bill McKinnon assumed the rock density to be 3.3 g/cm3 (nearly half way between 3 and 3.5) correlating to a 40% rock/ice ratio which is right in the middle of my chart's range. Charon's rock to ice density is roughly 32 to 39 percent making its middle point roughly 36% rock to ice.
One thing I knew instinctively but didn't understand the math thus lacking the language to explain it properly was how a small percent of mass takes up a large quantity of space in the inner portion of a sphere. The Volume formula solved that problem for me now my only problem is I don't have the software to draw the spherical image which I have in my mind from the math but I do have some paper, a pencil, highlighters, a compass and a camera.
First lets do a little math and calculate the volume of Pluto's 40% rock to ice ratio then translate that back relative to its radius.
Volume = 4/3╥r3 ---- Stated four thirds pi r cubed.
we already know the radius of Pluto is 1,188.3 g/cm3.
Four thirds = 1.3333, Pi = 3.14.
Four thirds times pi equals 4.18666
Pluto's radius of 1,188.3 cubed = 1677947202.387 km x 4.18666 = 7024994434.346
Multiplying this volume value by 0.40 gives us forty percent Pluto's volume which is its rock content based on its density.
To put this three dimensional volume back into a linear single line radius dimension we need to divide by 4.18666 and find the cube root of that value to have the 40% volume value expressed in kilometers of the total radius.
7024994434.346 x 0.40 = 2809997774/4.18666 = 671178881
The cube root of 671178881 = 875 km.
I did this same formula for various percentage values to show how the rings of radii get smaller and smaller the larger the sphere.
The Pluto v Charon drawings are to scale as are the inner radii rings relative to the outer diameter ring.
One thing I knew instinctively but didn't understand the math thus lacking the language to explain it properly was how a small percent of mass takes up a large quantity of space in the inner portion of a sphere. The Volume formula solved that problem for me now my only problem is I don't have the software to draw the spherical image which I have in my mind from the math but I do have some paper, a pencil, highlighters, a compass and a camera.
First lets do a little math and calculate the volume of Pluto's 40% rock to ice ratio then translate that back relative to its radius.
Volume = 4/3╥r3 ---- Stated four thirds pi r cubed.
we already know the radius of Pluto is 1,188.3 g/cm3.
Four thirds = 1.3333, Pi = 3.14.
Four thirds times pi equals 4.18666
Pluto's radius of 1,188.3 cubed = 1677947202.387 km x 4.18666 = 7024994434.346
Multiplying this volume value by 0.40 gives us forty percent Pluto's volume which is its rock content based on its density.
To put this three dimensional volume back into a linear single line radius dimension we need to divide by 4.18666 and find the cube root of that value to have the 40% volume value expressed in kilometers of the total radius.
7024994434.346 x 0.40 = 2809997774/4.18666 = 671178881
The cube root of 671178881 = 875 km.
I did this same formula for various percentage values to show how the rings of radii get smaller and smaller the larger the sphere.
The Pluto v Charon drawings are to scale as are the inner radii rings relative to the outer diameter ring.
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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. 
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.0The larger the sphere the less radius required to produce an identical percent of volume. Forty percent of Pluto's volume is rock while 60% is ice. The 40% rock by volume takes up 71-74% of Pluto's radius 875/1188 = 73.65% (Nimmo 849.6/1188.3 = 71.49%). The 40% rock retains 66.6% of its mass according to McKinnon while the ice makes up 33.3% by mass. Nimmo's radius of 849.6 equates to a rock percent rate of 36.5% which sits right at the rock density value of 3 g/cm3 even though his paper indicates he uses a value roughly 0.40% in line with McKinnon. I suppose one could say 36.5% is roughly 0.40%. For most of my calculations I've used 0.40% but perhaps 36% would have been a better choice.
Since drawing the above images, I did some calculations using McKinnon's rock density value of 3.36 g/cm3, the rock mass would then calculate to 73% by mass. Using a rock density range of 3 and 3.5 the rock mass calculates to be anywhere from 65% to 75%. I have chosen to use 3.25 g/cm3 which puts Pluto's rock to ice mass ratio at 70%. This seems high to me and McKinnon's actual figure of 73% is really too high so I am confused as to how he gets a rock mass ratio of 67% when his density value calculates out to 73%. Charon's rock to ice mass ratio is 69% using a rock density of 3.25 g/cm3.
Callisto's rock ice mass ratio calculates out to 61% and this makes since as it has evaporated away fewer of its volatile ices relative to the remaining rock compared to an active Pluto.
Once I can visualize a thing, I understand it. I think I finally understand how all these things relate to each other.
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If 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. |
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I'm looking into their collective moment of inertia's to see if the answer may be found in their rotation rates but currently I still don't understand how Callisto at twice Pluto's size is considered uniform while Pluto is considered differentiated.
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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. |
Hydra was estimated to have a maximum density of 0.88 or less dense than water ice (6 months prior to flyby) when an albedo of 35% was considered to be the maximum rate of reflection. Comet 67P has a density of 0.533 and is about the size of Styx (smaller) so it seems plausible that Hydra is also less dense than water. Comet 67P also becomes more porous (even less dense) towards its core indicating the rocky/gravel/dusty/silicate material is not able to sink through the outer shell of ice at its small size.
Below are Callitsto (Jupiter moon), Enceladus (Saturn moon), Triton (Neptune moon), Pluto and its moon Charon drawn to scale with their respective core rock radius' based on density assuming those core's were fully differentiated which is not the case for Callisto.
Below are Callitsto (Jupiter moon), Enceladus (Saturn moon), Triton (Neptune moon), Pluto and its moon Charon drawn to scale with their respective core rock radius' based on density assuming those core's were fully differentiated which is not the case for Callisto.
High moment of inertia (MOI) values suggest less dense cores. Low MOI's indicate solid dense cores. Rotational angular velocity for low MOI planets or moons should generally spin faster than high MOI cored bodies. But axial spin is also influenced by the gravity of a parent body and tidal bulge. Take for example Mercury, it has a solid massive iron core and low MOI and should spin fast on its axis but it's axial rotation is actually slower than it's orbit around the Sun. In other words it's day is longer than its year.
Callisto is reasoned to have a maximum sized core of 600 km because of its moment of inertia (MOI).
According to a Bill McKinnon paper of 1989, Pluto's MOI is assumed to be 0.282 and Charon is assumed to be 0.4. These values were assumed prior to flyby and multiple flyby or orbits are required to develop formula's that can suggest the MOI of a body.
In 1997 Callisto's MOI was figured to be 0.406 by this paper called "Mystery of Callisto: Is It Undifferentiated?" which also stated the following. the moment-of-inertia for a totally undifferentiated Callisto is 0.38 (not 0.40). In 2001 according to this paper "Shape, Mean Radius, Gravity Field, and Interior Structure of Callisto, Callisto's MOI is more accurately calculated to be 0.3549 (because of multiple orbits or flybys) meaning Callisto is undifferentiated with a partial tiny core no more than 25% its radius. A MOI of at least 0.38 is needed for a uniform interior, only partial differentiation is implied below but near 0.38.
Callisto is reasoned to have a maximum sized core of 600 km because of its moment of inertia (MOI).
According to a Bill McKinnon paper of 1989, Pluto's MOI is assumed to be 0.282 and Charon is assumed to be 0.4. These values were assumed prior to flyby and multiple flyby or orbits are required to develop formula's that can suggest the MOI of a body.
In 1997 Callisto's MOI was figured to be 0.406 by this paper called "Mystery of Callisto: Is It Undifferentiated?" which also stated the following. the moment-of-inertia for a totally undifferentiated Callisto is 0.38 (not 0.40). In 2001 according to this paper "Shape, Mean Radius, Gravity Field, and Interior Structure of Callisto, Callisto's MOI is more accurately calculated to be 0.3549 (because of multiple orbits or flybys) meaning Callisto is undifferentiated with a partial tiny core no more than 25% its radius. A MOI of at least 0.38 is needed for a uniform interior, only partial differentiation is implied below but near 0.38.
| 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 |
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Wiki quote about Titan
Surface features were observed by the Cassini spacecraft to systematically shift by up to 30 kilometers (19 mi) between October 2005 and May 2007, which suggests that the crust is decoupled from the interior, and provides additional evidence for an interior liquid layer.
In a year and a half Titan's surface shifted 30 km (19 miles). It's incredible how far a planet's decoupled crust can shift on such short time scales. Titan does experience tidal flex energy. If Pluto's crust is decoupled then its skin slip forming the banding stripes could easily be created within its 2.8 myr Milankovitch cycle time scale. (page 78 Wobble, page 81 Slip). Titan has a radius of 2576 km, Callisto is 2410 km, Pluto is 1188 km and Charon is 606 km.
The question becomes how can Charon be assumed to be uniform while Pluto is assumed to be fully differentiated yet Callisto is mostly uniform with partial differentiation while Titan is considered fully differentiated? By these figures, size has nothing to do with rock ice separation. In other words internal gravitational collapsing forces don't drive separation, external forces do this. But lets look at the situation more for what it is than just making assumptions about numeric values. Charon displays obvious visual evidence it expelled an internal liquid ocean onto its surface. That means rock fell out of the liquid ocean, sunk towards its core and separated. This means Charon is differentiated. Pluto is also likely differentiated as the eccentric orbital dance between the two which differentiated Charon did the same to Pluto. Callisto which is much larger than Pluto and Charon combined, on the other hand, is partially differentiated and dormant. Tidal Flex is the only reasonable thing that can answer these questions.
My next goal is to figure out how Bill came up with a MOI of 0.282 for Pluto and 0.4 for Charon and whether or not these are reasonable assumptions. What I do know is that these values are assumptions. Enceladus is little more than a third the size of Charon and does not have enough material for radiogenic heat to make it active but it is active. Charon at nearly two thirds the size of Enceladus is considered uniform while Enceladus is differentiated. Enceladus is almost 10 times smaller than Callisto (Enceladus is active Callisto is not), if the quantity of radiogenic material is considered to be the source of energy driving core formation and geologic activity Callisto should be active and Enceladus should not but instead we observe the opposite. The only force that could be responsible for Enceladus' energy is tidal flex as it orbits Saturn.
Charon's southern hemisphere is visual evidence a subsurface ocean spilled onto and smoothed the surface during a catastrophic event. If there was an ocean below Charon's surface, there was rock/ice separation and tidal flex is the only reasonable explanation to create the energy required for the rock/ice separation and subsurface ocean formation. My conclusion, Charon is differentiated because of its previous eccentric orbital dance with Pluto/Triton and that core is not responsible for its gelology. If the quantity of radiogenic material is responsible for Pluto's geologic activity and its theoretic ocean then surely Callisto at twice the size and twice the quantity of radiogenic material would also have an ocean and be geologically active.
Triton does not have a known MOI because we only flew-by once (just like Pluto) but based on active plumes ejecting dark minerals onto the surface the MOI is likely low indicating a large interior rock core oriented near the southern pole where all the plumes exist. Triton's axial tilt is zero degrees relative to Neptune further supporting the idea its differentiated core is uniformly spherically shaped and closer to the south pole than the north.
These facts lead me to ask how does Callisto have the oldest surface in the solar system with a tinny dead core partially differentiated while Charon shows signs that it once had a subsurface ocean that spilled onto the southern hemisphere's surface? Charon is a quarter the size of Callisto, Charon at 606 km is the size of Callisto's partial tinny core of 600 km. Callisto is dead, with the oldest surface in the solar system. Callisto's 34.6% rock has not fully separated from the hard ice in 4 byr. What separates these two worlds? In my opinion Callisto formed in-situ (in-place around Jupiter) while Charon was captured into an eccentric dance with Pluto and this is the difference (energy transfer via tidal flex or tidal bulge). This is why Charon at a quarter Callisto's size has a young southern hemisphere and Callisto has the oldest dead surface in the solar system.
McKinnon tried to explain it by a massive impact between two equally sized differentiated planets in which both planets are destroyed and Charon forms in-situ around Pluto, Robin Canup's model forces that collision to be gentle and slow enough that too little heat is generated to separate rock from ice in Charon and both planets, pre-collision, had to have been uniform in order to conform to angular momentum rules, Bill accepts the strength of this model over his previous assumption of two similar sized differentiated planets colliding and yet Charon was uniform and not heated in Canup's model.
On the previous page, I explain how a recent Israeli paper tries to explain Charon's geologic activity by instantaneous in-situ capture (what they call circularization) with no tidal flex energy released developing a circular orbit in which they reference a paper written by Cheng where both planets are destroyed and Charon forms in-situ in a circular orbit around Pluto. Cheng's paper references Canup's impact model which again does not destroy or even heat Charon. Following this broken trail, the Israeli paper concludes Charon could form in a captured circular orbit in its current location with a radius larger than its current radius then a contraction expansion process takes place based on radiogenic material contained in the silicate rock.
I explain Charon's subsurface ocean and geology by an eccentric orbital capture dance on my Triton page. The Israeli paper acknowledges this as a possible and feasible scenario while at the same time excluding in-situ, collision and capture. Seems odd that the one scenario that could reasonably explain Pluto/Charon's geologic activity is the only one ignored (capture with eccentric tidal flex energy).
Surface features were observed by the Cassini spacecraft to systematically shift by up to 30 kilometers (19 mi) between October 2005 and May 2007, which suggests that the crust is decoupled from the interior, and provides additional evidence for an interior liquid layer.
In a year and a half Titan's surface shifted 30 km (19 miles). It's incredible how far a planet's decoupled crust can shift on such short time scales. Titan does experience tidal flex energy. If Pluto's crust is decoupled then its skin slip forming the banding stripes could easily be created within its 2.8 myr Milankovitch cycle time scale. (page 78 Wobble, page 81 Slip). Titan has a radius of 2576 km, Callisto is 2410 km, Pluto is 1188 km and Charon is 606 km.
The question becomes how can Charon be assumed to be uniform while Pluto is assumed to be fully differentiated yet Callisto is mostly uniform with partial differentiation while Titan is considered fully differentiated? By these figures, size has nothing to do with rock ice separation. In other words internal gravitational collapsing forces don't drive separation, external forces do this. But lets look at the situation more for what it is than just making assumptions about numeric values. Charon displays obvious visual evidence it expelled an internal liquid ocean onto its surface. That means rock fell out of the liquid ocean, sunk towards its core and separated. This means Charon is differentiated. Pluto is also likely differentiated as the eccentric orbital dance between the two which differentiated Charon did the same to Pluto. Callisto which is much larger than Pluto and Charon combined, on the other hand, is partially differentiated and dormant. Tidal Flex is the only reasonable thing that can answer these questions.
My next goal is to figure out how Bill came up with a MOI of 0.282 for Pluto and 0.4 for Charon and whether or not these are reasonable assumptions. What I do know is that these values are assumptions. Enceladus is little more than a third the size of Charon and does not have enough material for radiogenic heat to make it active but it is active. Charon at nearly two thirds the size of Enceladus is considered uniform while Enceladus is differentiated. Enceladus is almost 10 times smaller than Callisto (Enceladus is active Callisto is not), if the quantity of radiogenic material is considered to be the source of energy driving core formation and geologic activity Callisto should be active and Enceladus should not but instead we observe the opposite. The only force that could be responsible for Enceladus' energy is tidal flex as it orbits Saturn.
Charon's southern hemisphere is visual evidence a subsurface ocean spilled onto and smoothed the surface during a catastrophic event. If there was an ocean below Charon's surface, there was rock/ice separation and tidal flex is the only reasonable explanation to create the energy required for the rock/ice separation and subsurface ocean formation. My conclusion, Charon is differentiated because of its previous eccentric orbital dance with Pluto/Triton and that core is not responsible for its gelology. If the quantity of radiogenic material is responsible for Pluto's geologic activity and its theoretic ocean then surely Callisto at twice the size and twice the quantity of radiogenic material would also have an ocean and be geologically active.
Triton does not have a known MOI because we only flew-by once (just like Pluto) but based on active plumes ejecting dark minerals onto the surface the MOI is likely low indicating a large interior rock core oriented near the southern pole where all the plumes exist. Triton's axial tilt is zero degrees relative to Neptune further supporting the idea its differentiated core is uniformly spherically shaped and closer to the south pole than the north.
These facts lead me to ask how does Callisto have the oldest surface in the solar system with a tinny dead core partially differentiated while Charon shows signs that it once had a subsurface ocean that spilled onto the southern hemisphere's surface? Charon is a quarter the size of Callisto, Charon at 606 km is the size of Callisto's partial tinny core of 600 km. Callisto is dead, with the oldest surface in the solar system. Callisto's 34.6% rock has not fully separated from the hard ice in 4 byr. What separates these two worlds? In my opinion Callisto formed in-situ (in-place around Jupiter) while Charon was captured into an eccentric dance with Pluto and this is the difference (energy transfer via tidal flex or tidal bulge). This is why Charon at a quarter Callisto's size has a young southern hemisphere and Callisto has the oldest dead surface in the solar system.
McKinnon tried to explain it by a massive impact between two equally sized differentiated planets in which both planets are destroyed and Charon forms in-situ around Pluto, Robin Canup's model forces that collision to be gentle and slow enough that too little heat is generated to separate rock from ice in Charon and both planets, pre-collision, had to have been uniform in order to conform to angular momentum rules, Bill accepts the strength of this model over his previous assumption of two similar sized differentiated planets colliding and yet Charon was uniform and not heated in Canup's model.
On the previous page, I explain how a recent Israeli paper tries to explain Charon's geologic activity by instantaneous in-situ capture (what they call circularization) with no tidal flex energy released developing a circular orbit in which they reference a paper written by Cheng where both planets are destroyed and Charon forms in-situ in a circular orbit around Pluto. Cheng's paper references Canup's impact model which again does not destroy or even heat Charon. Following this broken trail, the Israeli paper concludes Charon could form in a captured circular orbit in its current location with a radius larger than its current radius then a contraction expansion process takes place based on radiogenic material contained in the silicate rock.
I explain Charon's subsurface ocean and geology by an eccentric orbital capture dance on my Triton page. The Israeli paper acknowledges this as a possible and feasible scenario while at the same time excluding in-situ, collision and capture. Seems odd that the one scenario that could reasonably explain Pluto/Charon's geologic activity is the only one ignored (capture with eccentric tidal flex energy).
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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 core would shrink further. |
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A surprising representation of Pluto's core from space.com
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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. |
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>>>>>>>>>>> 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. |
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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 |
In the above the radius of Pluto is considered 1147 km while the rock radius based on mass is 928 km making the rock to ice radius ratio 81%. Even with that large ratio a uniform core along with no subsurface ocean were considered viable options for Pluto's core, however, today Pluto's radius is considered 1188.3 km and its rock core radius 849.6 km (by Nimmo) making the rock to ice radius ratio 71.5% or 10% smaller than shown in this image and yet with a ten percent smaller rocky core a uniform and non ocean interior are no longer considered viable options for Pluto.
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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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The flyby did not change the actual numbers significantly enough to draw these conclusions. In 2011 (four years before the flyby) Nimmo calculated the rock radius to be 850 km based on the rock to ice mass ratio and that number still stands today. Was it the surface of Sputnik Planitia the Uplands and the area around Wright Mons where viscous relaxation is so prevalent that no impacts are seen. Perhaps this visual evidence indicates more rapid geology hence more inferred heat. I really don't know why such a massive swing in reasoning took place.
Wikipedia describes Callisto like this.
The average density of Callisto, 1.83 g/cm3, suggests a composition of approximately equal parts of rocky material and water ice,
Ganymede is composed of approximately equal amounts of silicate rock and water ice.
Callisto's rock/rock+ice mass ratio is considered 45% and Ganymede with a density of 1.936 g/cm3 is about 50% rock but Pluto's with its 1.854 g/cm3 density is supposed to be 67% rock by mass. Obviously, I still need to continue to explore this question.
What I've learned about Moment of Inertia is, that for planets, calculating its value is complicated and multiple orbits are needed to obtain the most reliable results.
I decided to run some numbers to figure out the rock mass ratio to ice for Pluto and several moons.
Wikipedia describes Callisto like this.
The average density of Callisto, 1.83 g/cm3, suggests a composition of approximately equal parts of rocky material and water ice,
Ganymede is composed of approximately equal amounts of silicate rock and water ice.
Callisto's rock/rock+ice mass ratio is considered 45% and Ganymede with a density of 1.936 g/cm3 is about 50% rock but Pluto's with its 1.854 g/cm3 density is supposed to be 67% rock by mass. Obviously, I still need to continue to explore this question.
What I've learned about Moment of Inertia is, that for planets, calculating its value is complicated and multiple orbits are needed to obtain the most reliable results.
I decided to run some numbers to figure out the rock mass ratio to ice for Pluto and several moons.
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There is a slight discrepancy between the calculated values in the attached .doc compared to the .xls file. Excel apparently doesn't calculate values beyond 0.000000 but my computer's calculator does. I intend to run these numbers through a couple calculators to make sure my calculations at least in the doc file are correct.
There are a couple interesting things to glean from these numbers.
Europa is very rock rich and this is why we see mineral deposits in the cracks on its surface. The rock is close enough to the ice crust surface and the tidal flex energy is strong enough to have evaporated away most of the volatile water and other ices to make Europa mostly a rock ball with a thin ice layer. Enceladus on the other hand while puny has little rock content by comparison and as active as it is, is likely very young geologically else it would have depleted its water leaving its rock ratio much higher. Europa may experience stronger tidal flex energy but its is massive by comparison and Enceladus is actively spewing out water ice crystals forming Saturn's E ring. Europa is not creating a ring around Jupiter so Enceladus must be significantly younger than Europa.
Another interesting fact is that assumptions have to be made as to what values to use for rock densities and depending on what you choose a planets rock mass can be calculated to be larger than its actual size. Bill McKinnon chose to use 3.36 g/cm3 to calculate his rock mass for Pluto. Had he used this same value to calculate the rock mass ratio for Europa the rock would have been 2 percent larger than the physical planet. Assumptions have to be made to draw any conclusions but conclusion can be massaged to fit a pre-desired outcome. I chose to use different ice densities and rock densities than Nimmo and McKinnon so my values differ slightly from theirs.
Who's right, who's wrong?
Nobody really knows.
I placed a range for rock densities of 3 and 3.5 just to show how far of a range there is in rock mass when one assumes differing densities. Pluto's rock mass ratio could be anywhere from 64.72% to 75.51% or it could be less, however, its very unlikely it is more. Bill says the rock density can't be any more than 66.6%. When I use his density number of 3.36 g/cm3, I get 72.92% rock by mass. Not sure why there's a discrepancy unless its the excel spread sheet calculator which gave me slightly different values than my computer's calculator. To Bill's credit his 67% rock mass value is hugging the low end of the spectrum and this value indicates there,s a large rock to ice mass ratio in Pluto.
Triton (75.69%) and Europa (98.16%) have the highest rock to ice mass ratio and they both show signs of surface mineral deposits. Enceladus, however, actively spews plumes of water ice into space and with a low rock mass ratio only expels water ice not minerals. Pluto is active but does not show signs of plumes or mineral deposits on its surface with a rock mass ratio between 65% and 75%. Triton could be as high as 82% but is likely closer to 75% if Pluto's rock mass were at the high end of its range we would likely see minerals deposited on its surface like we do on Triton and Europa this suggests Pluto's rock mass is closer to its low end.
Elliot crater is a cryovolcano and has erupted recently as can be seen by the presence of the same nitrogen which covers the surface of Sputnik Planitia spilling out Elliot's volcano mouth page 71. Even though Elliot erupted recently, minerals were not deposited down the sides of the volcano only fluid nitrogen.
Bill indicates Charon has a rock mass of 60% my numbers indicate the range is between 63.45% and 74.03%. I'm going to have to recheck my math. This is why I do this, one answer leads to 5 questions and one question leads to ten more. My Callisto numbers are also high as Wiki indicates the rock mass ratio is between 45% and 51% my range indicates it is between 56.59% and 66%. I need to figure this out.
Europa is very rock rich and this is why we see mineral deposits in the cracks on its surface. The rock is close enough to the ice crust surface and the tidal flex energy is strong enough to have evaporated away most of the volatile water and other ices to make Europa mostly a rock ball with a thin ice layer. Enceladus on the other hand while puny has little rock content by comparison and as active as it is, is likely very young geologically else it would have depleted its water leaving its rock ratio much higher. Europa may experience stronger tidal flex energy but its is massive by comparison and Enceladus is actively spewing out water ice crystals forming Saturn's E ring. Europa is not creating a ring around Jupiter so Enceladus must be significantly younger than Europa.
Another interesting fact is that assumptions have to be made as to what values to use for rock densities and depending on what you choose a planets rock mass can be calculated to be larger than its actual size. Bill McKinnon chose to use 3.36 g/cm3 to calculate his rock mass for Pluto. Had he used this same value to calculate the rock mass ratio for Europa the rock would have been 2 percent larger than the physical planet. Assumptions have to be made to draw any conclusions but conclusion can be massaged to fit a pre-desired outcome. I chose to use different ice densities and rock densities than Nimmo and McKinnon so my values differ slightly from theirs.
Who's right, who's wrong?
Nobody really knows.
I placed a range for rock densities of 3 and 3.5 just to show how far of a range there is in rock mass when one assumes differing densities. Pluto's rock mass ratio could be anywhere from 64.72% to 75.51% or it could be less, however, its very unlikely it is more. Bill says the rock density can't be any more than 66.6%. When I use his density number of 3.36 g/cm3, I get 72.92% rock by mass. Not sure why there's a discrepancy unless its the excel spread sheet calculator which gave me slightly different values than my computer's calculator. To Bill's credit his 67% rock mass value is hugging the low end of the spectrum and this value indicates there,s a large rock to ice mass ratio in Pluto.
Triton (75.69%) and Europa (98.16%) have the highest rock to ice mass ratio and they both show signs of surface mineral deposits. Enceladus, however, actively spews plumes of water ice into space and with a low rock mass ratio only expels water ice not minerals. Pluto is active but does not show signs of plumes or mineral deposits on its surface with a rock mass ratio between 65% and 75%. Triton could be as high as 82% but is likely closer to 75% if Pluto's rock mass were at the high end of its range we would likely see minerals deposited on its surface like we do on Triton and Europa this suggests Pluto's rock mass is closer to its low end.
Elliot crater is a cryovolcano and has erupted recently as can be seen by the presence of the same nitrogen which covers the surface of Sputnik Planitia spilling out Elliot's volcano mouth page 71. Even though Elliot erupted recently, minerals were not deposited down the sides of the volcano only fluid nitrogen.
Bill indicates Charon has a rock mass of 60% my numbers indicate the range is between 63.45% and 74.03%. I'm going to have to recheck my math. This is why I do this, one answer leads to 5 questions and one question leads to ten more. My Callisto numbers are also high as Wiki indicates the rock mass ratio is between 45% and 51% my range indicates it is between 56.59% and 66%. I need to figure this out.
However, figuring out the volume of a sphere using the formula Volume = 4/3╥r3 is pretty straight forward and yet the numbers I calculate seem to differ from the numbers obtained by other scientists. I find this confusing and frustrating, how can my math differ from others when we are theoretically using the same formula? When I calculate Nimmo's rock radius of 849.6 km it calculates to a rock volume ratio of 36.5% which one could say is roughly 40% but that's pretty rough indeed.
I suppose the thing I've learned most from this exercise is that sometimes 2+2 = 5. All these formulas are conceptual math models, there is a degree of value in them but also a degree of interpretive flexibility. Time for me to pick on Nimmo a bit, sorry but I need to demonstrate how anyone can be wrong (including me). James Keane is drawing images of notes taken at the recent LPSC 2018 conference and produced this drawing.
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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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Credit James Keane
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Just because he and McKinnon agree with each other and others align with them in saying Pluto is fully differentiated and that its core is radioactively hot and there is a subsurface ocean and Sputnik Planitia is a positive gravity anomaly, doesn't mean they are right. Just because everyone wants to agree with each other and produce mathematical models to support their hypotheses doesn't mean its correct.
While I am starting to accept the idea, there is likely a partial core, I certainly am not convinced its hot or that there is an ocean of ammonia infused water and I definitely don't believe Sputnik Planitia is a positive gravity anomaly. Sunken deep planes are far more often negative gravity features as can be seen on Earth and Mars. Also, similar to our moon with its tidally locked densest side facing Earth, rotating worlds stop rotating with the densest side facing the parent planet just like a rolling ball with unevenly distributed mass settles with its dense side facing the center of the Earth.
While I'm on the subject of LPSC 2018, I'll make a couple more points.
While I am starting to accept the idea, there is likely a partial core, I certainly am not convinced its hot or that there is an ocean of ammonia infused water and I definitely don't believe Sputnik Planitia is a positive gravity anomaly. Sunken deep planes are far more often negative gravity features as can be seen on Earth and Mars. Also, similar to our moon with its tidally locked densest side facing Earth, rotating worlds stop rotating with the densest side facing the parent planet just like a rolling ball with unevenly distributed mass settles with its dense side facing the center of the Earth.
While I'm on the subject of LPSC 2018, I'll make a couple more points.
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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. |
Credit James Keane
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Many scientists still believe impacts created the mare (large dark zones) on the moon. But its now known that these are dense lava deposits. Keane also drew these notes on the moon where it is shown that the mare have fault wrinkles lining the mare. This along with gravity maps demonstrate how these are geological lava features not impacts. Yet scientists continue to call these mare impacts. From a logic standpoint it makes no sense that the largest impacts on the moon would occur on the side protected by the Earth. But years ago it was hypothesized that these were impacts and to this day most people still reference them as such.
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Study hard what interests you the most in the most undisciplined, irreverent and original manner possible. Richard Feynman
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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. |
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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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The above results come from surveys conducted to draw some conclusion based on theoretically science based studies. This is not an apples to apples comparison with science papers. So its not accurate to compare the survey style results with science papers but the thing I'm trying to highlight is this, reasons to justify their transgressions, including publication bias, pressure, and the need to present a neat, coherent narrative. There are outside as well as internally created pressures to produce results and those pressures can and do influence some conclusions. Scientists are human just like the rest of us.
