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The Fatal Law of Gravity (repost)

December 5, 2008

This is a repost from Classic ITV, follow the link to see the original posts and comments

I just got out of a marathon meeting with my advisor, and I am still a bit out of it (seems like some of the work I spent a couple of months on is now no longer required). On the one hand I can see this making my Thesis clearer and more concise. On the other, I just wasted a bunch of time I could have better spent graduating. So, I am in the mood to “dump” on those lovable wackaloons who have been giving Eric and Brian grief. I don’t think I will re-cover the same grounds they have. Especially since they have done a far better job than I think I would be capable of. Instead I am going to cover the problems that expanding earth has with GRAVITY. I have seen two sides that expanding earthers like to use to argue about gravity. One camp argues that the mass of the earth is constant, and the earth is just getting less dense. Another camp argues that the mass of the earth is growing, and holds the earth’s density constant. Surely, we can resolve such a fundamental difference by just saying “Hey, the Earth is not expanding, look at all the data”. But that would defeat the purpose of this post and my childish poking fun at the stupid.

First we have the Constant Mass Advocates (CMA). They argue, wrongly, that the earth can grow and those of us living on its surface will feel a constant pull of gravity IF the earth weren’t gaining mass. On the surface of it that seems a reasonable assertion (if you ignore the whole “earth is growing” thing, and the violation of conservation of energy, etc.). After all we learned in our High School Physics class that:

F=ma

Eq.1

Where F = force m = mass of an object a = acceleration (in this case gravity: 9.8 m/s2) This, however, is just a shorthand version of calculating the force on an object due to gravity. You see, this equation needs some tinkering if we are going to calculate the force due to gravity on Mars, or the Moon, or anywhere other than Earth (note: not all places on Earth have the same gravity either, it can vary due to elevation, local rock densities, etc.). This leads us to the Universal Gravity Equation:

F = GMm/D²

Eq.2

Where F = force G = the Gravitational Constant (6.67300 × 10-11 m3 kg-1 s-2) M = Mass of object 1 (usually the larger object, in this case the Earth: 5.9742 × 1024 kg) m = mass of object 2 (usually the smaller object, in this case it is us) D = Distance between the centers of mass (in this case it can be approximated as the radius of the Earth (note: this is why elevation has an effect on gravitational pull) Earth’s radius: 6378.1 km). By setting Eq.1 equal to Eq.2, you can see how scientists can calculate what “a” is equal to:

a = GM/D2

Eq.3

Since we don’t really care about how much force I am exerting on the planet (and it on me) we can just focus on Eq.3 for this discussion. First let’s prove to ourselves that the “a” we learned in High School jives with the Universal Gravity Equation.

a = (6.67300 × 10-11 m3 kg-1 s-2 × 5.9742 × 1024 kg)/(6378.1 km)2 or when I plug it into my calculator and cancel out the appropriate units (remember to convert km to meters in the denominator) a = 9.7998…. m/s2 which can be approximated to 9.8 m/s2

Thanks Mr. Schalhammer! See Physics can work (and prove useful). Now, you may be sitting there asking yourself “Why the hell does this matter to expanding earth? You just showed that the Earth’s gravity is affected by its mass, which is the point of the CMA”. Why yes I did anonymous questioning voice. However, I also showed that the RADIUS of the Earth is far more significant to the gravity we feel on the planet. The Distance to the center of the Earth will affect the gravity we feel on the surface far more rapidly than just keeping mass a constant. The radius of the Earth affects gravity exponentially (mathematically speaking the square) while the mass of the Earth only affects gravity linearly. So take home message to the CMA’s, keeping the earth’s mass constant and increasing the radius will actually DECREASE the gravity we feel on the planet. This is completely antithetical to what we actually observe (you know by practicing science). And furthermore, it defies claims made by other expanding earthers that gravity was less in the past allowing for giant bugs and what not (interestingly enough, an insects size seems to be limited by how efficiently oxygen can cross certain membranes, higher oxygen concentrations mean “bugs” can get bigger. Here is something on that) Through this calculation, we see that the gravity at the surface of the earth would have been GREATER if the earth was smaller. Let’s go to the graph:This is a nice visual way of saying IF the Earth was smaller (assuming constant mass), we would experience a greater pull of gravity. Once again, explaining this away isn’t a problem for Plate Tectonics, because with our firm grip on reality, we don’t expect the Earth to be changing size. Now let’s move on to the more confounding stupid I dub the Gaining Mass Advocates (GMA). They argue that the earth is growing AND it is becoming more and more massive. They use claims like “Gravity was less when the dinosaurs were around, how else did they get so big”. The GMA also argue that the earth is actually gaining mass and therefore gravity is increasing as we move forward in time. But let’s see how that works out with the math. We have already seen that holding the earth’s mass constant doesn’t jive with reality, maybe the trick is to increase the mass of the earth (keep in mind this is still invoking many things that plate tectonics has no need for, meaning this violates parsimony as well). First some disclaimers. This VIOLATES the conservation of matter. We are venturing into a realm of Newtonian Physics that was never meant to be (like the Octoparrot). Second, they stubbornly refuse to mention how much mass is being added, so I am assuming it to be a given volume of mantle (density of mantle: 3.4-5.6 g/cm3, so let’s just call it 4.5 g/cm3). Thirdly, I can’t find where they say HOW MUCH the earth has grown (because, in point of fact, it hasn’t). So I will assume that they only want the earth to increase enough to compensate for the oceans, which comprise ~75% of the Earth surface (361 km2). So back to some equations (ugh…. math). The surface area of a sphere can be expressed as:

A = 4 \pi r^2 \,
Eq.4

A is surface area r is the radius The volume of a sphere can be expressed as:

V = \frac{4}{3}\pi r^3.

Eq.5

V is volume r is the radius and a neat little relationship about Surface Area, Volume, and Diameter emerges. Essentially, when you shrink a sphere to 1/2 it’s original diameter, the new smaller sphere has 1/4 the original surface area and 1/8 the volume of the original sphere. To put this another way. By “shrinking” the earth to the point where it has no oceans (to 1/4 of its surface area), you have reduced its diameter by 1/2 and reduced it’s volume by 7/8.

This would mean the GMA would see a earth with a radius of 3189.05 km. The GMA volume would be 1.35 x 1014 km3. Earth’s GMA mass would be: 1.6948 x 1024 kg. So now let’s plug this in to Eq.3 and see what we get for the gravity (ag) of a GMA earth.

ag = 11.12029 m/s2

Which is still an increase in gravity from what we see today. Meaning even if you add mass to the planet to counteract the effect of moving away from the center of mass, gravity still is far more sensitive to changes in proximity to the center of mass than it is to total mass. The up-shot is that the “dinosaurs were big because there was less gravity” crowd are wrong. For curiosity’s sake the gravity (ac) of a CMA earth of the same size would be

ac =39.19929 m/s2

And just not to let those of us who like reality off the hook, I wonder what those crazy plate tectonic advocates (Scientists) think gravity was like during the Permian (which was when the oceanic crust we have today started to be generated):

a = 9.8 m/s2

As this clearly demonstrates, the RADIUS of the earth is far more important that the MASS of the earth in terms of what things living on the surface of the planet would feel in terms of gravity. As I have said many times throughout this post, this isn’t a problem for the reality based community. Because plate tectonics does NOT invoke the earth changes its size (or ways of adding mass out of nothing, or where the energy is coming from to move particles further away from the pull of gravity, or other magics that expanding earthers like). All the arguments based upon gravity being “lesser” in the past because the “earth was smaller” show not only a misunderstanding of geology, but a FAR greater misunderstanding of gravity. Curse you rational uniformitarianism, you win this round! But they’ll be back, and in greater numbers…

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