Mars Center of Gravity not at Center of Shape

[Malenfant]

Be careful, globemaker, you're starting to sound a little pseudoscientific in the vehemence of your defence ("the algorithm has mathematical perfection"?)... Right now I think it's as yet unclear as to whether you have actually found something real or not. If you want to defend your models and convince readers then you have to provide more evidence for your hypothesis - that's how science works.

Let's look at this again.



Personally, I'm a little suspicious of your speculations here because I'm wondering if we're seeing effects caused by way the topography is exaggerated. If you're exaggerating by 250 times, then isn't the distance that the Centre of Gravity (COG) displaced from the Centre of Figure (COF, the green dot) going to be exaggerated by 250 times too? I'd want to see a 1x exaggerated globe and see if your lines would be anywhere near as displaced - I suspect that on a 1x globe the COG and the COF would be much closer together. And if they really are a couple of kilometres apart then that's nothing really special.

Plus, you draw lines through the volcanoes that look like they go through the a common point that is not the COF - but we're only seeing a 2d projection that shows that. I'd want to see several views of this global model (and the same lines) from a variety of different viewing angles to show that the lines do actually go through a small area in the interior of the planet that you could explain as being the COG.

Also, it's hard to get ones bearings on this model. Where is the northern-southern hemisphere boundary, between the smoother, lower northern plains and the higher, cratered southern highlands? Where is Valles Marineris, I can't see it from this angle (surely such a huge trench would be visible here if that's the Tharsis Bulge at top left). Again, more views from different angles are necessary to convince.

It also seems to me that one can draw a flat plane over the bit on the right of the image, above and to the right of the green lines you've drawn. But this may be a result of perspective of viewing angle here, in which case couldn't the flat area shown by the green lines be a perspective effect too?

Finally, if you really are convinced that you've found something, have you considered actually writing a paper about it and submitting it to a journal (eg Icarus, JGR-Planets, Geophysical Research Letters) to see if it'd get published?

(that said, getting papers published takes forever, and more often than not actually costs you a lot of money!).

[cpotting]

Personally, I'm a little suspicious of your speculations here because I'm wondering if we're seeing effects caused by way the topography is exaggerated. If you're exaggerating by 250 times, then isn't the distance that the Centre of Gravity (COG) displaced from the Centre of Figure (COF, the green dot) going to be exaggerated by 250 times too? I'd want to see a 1x exaggerated globe and see if your lines would be anywhere near as displaced - I suspect that on a 1x globe the COG and the COF would be much closer together. And if they really are a couple of kilometres apart then that's nothing really special.

Actually, it's the opposite. I was about to agree with globemaster when it occured to me that what he is actually doing is bisecting the angle at the apex of an irregular triangle. However, as you increase the height of the triangle without increasing the base (exagerating the height), the angle of the bisecting line moves closer and closer to 90 deg to the base - imagine, an infinetly tall triangle: the bisecting line would as close to perpendicular as you could get.

Therefore, the lines through his 250x volcanoes are actually closer to vertical than the same lines drawn through 1x volcanoes. This leads me to beleive that if they happen to meet at 250x, it is coincidental, since the angles would be even greater at 1x and so would not converge.

However, it does beg the questions "why do all these martian volcanoes point all over the place?" and "is the same true of Earth?".

Plus, you draw lines through the volcanoes that look like they go through the a common point that is not the COF - but we're only seeing a 2d projection that shows that. I'd want to see several views of this global model (and the same lines) from a variety of different viewing angles to show that the lines do actually go through a small area in the interior of the planet that you could explain as being the COG.

Yes. At this point, I would agree. Does the same convergence hold true when the model is seen at various angles? Lines that may seem to cross when seen (or drawn) from one vantage point may have absolutely no points in common (even remotely in common - e.g. the side of a building seems to cross the line of the horizon, but there is no convergence - the two are separated by many kilometres. similarly the contrails of several jets may converge on a single point or area, but in reality the jets are actually separated by hundreds and even thousands of metres (at least I hope they are)).

Globemaker, would it be possible to view the same lines through the same volcanoes from a different angle?

[GlobeMaker]

I have every intention of granting all of your wishes. Just to get started, I have posted several new pictures on my website at http://www.reliefglobe.com/mars_gravity.html

Those have exaggerations of 7x, 97x, 150x and 250x.

Here is an example with 250x:
The North Polar Ice Cap is at the top. The South Pole is at the bottom.
In the discovery image on this forum, Valles Marineris is on the left horizon, not visible.

The image viewer I use (Solidview) may have a perspective option turned on or off. I will check that tomorrow. But perspective has little effect on the image with lines on it, since the volcanoes are perpendicular to the view. Also, I will make a 500x version tomorrow.

Malenfant asks : "If you're exaggerating by 250 times, then isn't the distance that the Centre of Gravity (COG) displaced from the Centre of Figure (COF, the green dot) going to be exaggerated by 250 times too?"

This is not clear to me. My working theory is that the displacement is independent of the exaggeration, but I am not sure. I have posted a 7x picture, but I cannot draw lines with confidence. I will prepare 3 images at the same angle : 125x, 250x, 500x and see if the COG shifts. Tomorrow...

Tharsis bulge (Alba Patera ) is in front of Olympus Mons in the picture with lines. The North Pole is under the place where the lines converge.
I have motion picture of Mars rotating at 150x exag. (.avi format). I cab publish a paper if my speculations hold up to this informal scutiny. Thank you for you comments! More will be posted in 12 hours.

[Malenfant]

Thanks. At 7x it's actually starting to look recognisable...

It never fails to impress me how much detail in Mars' terrain you can see with just topography alone (but that's because MOLA was so good at getting the data).

Just as a request I wouldn't mind seeing what Venus looked like at 7x exaggeration too.

Though it occurs to me - yes, an asteroid obviously did hit Mars to create Hellas, but it couldn't possibly have continued inside Mars because Impactors are vaporised on impact. (I just found a rather intriguing paper about the size of the Hellas impactor (and the ones that formed other basins) here - turns out an object about 250-300 km in radius could have made Hellas!) . But even impactors that big wouldn't penetrate far into the crust.

The impactor that smashed into the early earth and formed the moon is a different case, because it was comparable in size to the protoearth (well, about half the size anyway) so its core could merge and settle into ours. But then it also obliterated everything on the surface of the planet too and blasted a good chunk of it into orbit. The Hellas impactor couldn't possibly do that.

[wcomer]

Wcomer said : "volcanos do not point to the center of mass...Volcanos point to the surface normal".

Where did you get that idea? It is not credible.

GlobeMaker,

By surface normal, I am of course referring to the normal to the spheroid or more specifically to the local surface of the geoid. I'm not referring to topographic normals, my appologies if this wasn't clear.

Now gravity is not the only force acting on the planet. Because Mars is spinnning there is a significant centrifugal force at play as well. It is precisely this force which causes Mars to take a spheroidal shape. And this same force necessarily acts on the volcanos. In addition mass is not distributed homogenously, therefore there are additional distortions to the local gravitation equipotential surface and this leads to the geoid corrections to the spheroid. Generally the centrifugal effect is larger than the mass distribution effect (though this isn't strictly true for all points on the surface.)

Now that we have established that Mars is a spheroid and volcanos ought to point to the normals of this spheroid, it should be obvious that we do not expect the volcanos to point to the center of mass.

I remain convinced, based on the images that I've seen, that there are additional artifacts causing the large distplacement. I doubt that the artifact is physical (past or present.)

cheers,
Walton

[Malenfant]

Now gravity is not the only force acting on the planet. Because Mars is spinnning there is a significant centrifugal force at play as well. It is precisely this force which causes Mars to take a spheroidal shape. And this same force necessarily acts on the volcanos. In addition mass is not distributed homogenously, therefore there are additional distortions to the local gravitation equipotential surface and this leads to the geoid corrections to the spheroid. Generally the centrifugal effect is larger than the mass distribution effect (though this isn't strictly true for all points on the surface.)

This abstract (of the paper I linked to earlier) shows the Bouguer anomaly map of Mars - it shows the effects of mass concentrations and basins on the local gravity field. These effects are fairly significant (1 milligal = 1 cm/s^2).

Centrifugal acceleration isn't included in that, but I'd guess it'd be largest at the equator and smallest at the poles? I've never heard of it affecting any geological processes though - atmospheres and oceans are certainly affected because they're fluid, but the shape of volcanoes isn't.

Now that we have established that Mars is a spheroid and volcanos ought to point to the normals of this spheroid, it should be obvious that we do not expect the volcanos to point to the center of mass.

I don't think it's obvious at all. Volcanoes - especially large ones, plus the Tharsis bulge - themselves affect the shape of the geoid and the gravitational field of Mars. That much is evident from the anomaly map. But generally the spheroid is broadly symmetrical, and the deviations from that symmetry caused by mascons and basins are relatively small, so why shouldn't they point roughly to the centre of mass? (admittedly Mars has a large shape asymmetry that may cause this deviation though)

[wcomer]

Actually the distortion to the normal vector would be greatest at the mid lattitudes and have no distortion at the equator or the poles. The charts you showed are purely gravitatonal. The strong variations in the gravitational field will naturally lead to significant corrections in the geoid.

I've never heard of [centrifugal forces] affecting any geological processes though - atmospheres and oceans are certainly affected because they're fluid, but the shape of volcanoes isn't.

Whether you've heard of this or not doesn't matter. It is basic Newtonian physics. Rotation of the planet affects the local plumb line. It affects the shape of volcanos. It affects the direction buildings stand. It affects the way you stand. It affects ships in the sea. It affects everything. There is no magical off switch to stop its affects, nor is there any size limit. This shouldn't be in dispute. Thus we don't expect the volcanos to point to the center of the planet.

[Malenfant]

Actually the distortion to the normal vector would be greatest at the mid lattitudes and have no distortion at the equator or the poles. The charts you showed are purely gravitatonal. The strong variations in the gravitational field will naturally lead to significant corrections in the geoid.

OK. In geological gravity surveys, there is a correction term for latitude, that you have to subtract from the measured gravity field (the Bouguer map already has this latitude correction subtracted from it). On Earth, the difference in g-field between pole and equator due to the combined effect of flattening and rotation is about 5180 milligals (about 0.05 m/s^2). On Mars, presumably that'd be a bit less because the difference in radius between pole and equator is 12 km instead of about 22 km. It should be noted however that there is no longitudinal term here - there is not correction for a specific direction (e.g. in the direction of rotation) involved here. It's hardly enough to make any kind of difference to the shape of volcanoes anyway.

You may be right in that the centrifugal effect is larger than the effect of mass distribution - the latitude subtraction is usually greater than the variation on the final bouguer anomaly map (this also has terrain corrections and tidal effects subtracted too), which is why it's removed from it since it'd totally mask the gravitational field caused by the mass distribution. But the fact that the gravitational vector is skewed a little by the rotation seems to make no practical difference to anything in geological terms - if it did, geologists would account for it when they're collecting data.

(also I think there's some terminology confusion here. A "surface normal" is a perpendicular line projecting from a given surface. I don't think that's what you actually are referring to here, I think you're talking about an extra sideways vector component to gravity caused by rotation that prevents it from pointing directly to the centre of gravity)

Whether you've heard of this or not doesn't matter. It is basic Newtonian physics. Rotation of the planet affects the local plumb line. It affects the shape of volcanos. It affects the direction buildings stand. It affects the way you stand. It affects ships in the sea. It affects everything. There is no magical off switch to stop its affects, nor is there any size limit. This shouldn't be in dispute. Thus we don't expect the volcanos to point to the center of the planet.

The fact that centrifugal force (or at least, the appearance of it caused by rotation) exists isn't in dispute. What I'm disputing is that centrifugal force has a demonstrable effect on the shape of volcanoes - at least more so than erosional forces, what side the lava lands on that builds the volcano, random landslides etc. AFAIK a significant effect on the shape of volcanoes caused by the earth's rotation has never been recorded or catalogued. If there is one, it's insignificant compared to the other forces affecting the shape of geological features.

If you want to claim that the shape of volcanoes are significantly affected by centrifugal force caused by planetary rotation then by all means please provide the evidence and observational data to support that claim. Saying "it's basic newtonian physics" isn't good enough - yes, that affects everything, but the question is whether it affects geological processes like volcano- or mountain-building enough to make any kind of difference. And I'm not convinced that it does.

[GlobeMaker]

Several new globes were designed today : Mars with no exaggeration (1x), Mars 125x, Mars 500x, and Venus 7x. Here is the website with the new pictures of Mars :
http://www.reliefglobe.com/mars_gravity.html

Here is the Venus page with 7x exaggeration pictures and 6 data points per degree of latitude and longitude :

http://www.reliefglobe.com/venus_7x_6deg.html

The Mars pictures do not support my speculation. The shift in Mars' center seems to be due to the lowlands near Ellysium Mons getting closer to the center of the planet when exaggerated. Here is a Mars 500x image withthe same orientation as the image posted with lines drawn on it :

[Malenfant]

Thanks for doing the 7x Venus globe, I hadn't seen it that way before

As for Mars - oh well, at least we can say we've investigated this somewhat .