Estimating the Size of the Meteorite and Energy Applied to the Crust

John Michael Fischer, 2006, 2019
www.newgeology.us

Summary
A 44 mile diameter chondritic meteorite travelling at 20 km/sec impacting at a 30 degree angle above the surface is sufficient to produce kinetic energy equal to that of all the landmasses that moved, sliding away from the impact with near zero friction as explained by the Shock Dynamics geology theory.  Even though the surrounding continental crust was expelled, enough indicators remain to project a crater size of 1000 km (621 mi) see "Ground Zero".  To form a crater that big, a 78 mile diameter chondrite is estimated to be needed, and that is likely to approximate the size and type of the Shock Dynamics meteorite.

Introduction
On June 30, 1908, a meteor exploded in the air over Siberia.  More than 300,000 acres of pine forest were leveled in an instant.  The Tunguska event is thought to have been caused by a 50 to 60 meter diameter object exploding 8 kilometers above the ground. Whether it was the fragment of an icy comet or a rocky meteor, the energy of the blast is estimated to have been between 10 and 20 megatons of TNT; equivalent to a hydrogen bomb.^J  Larger and denser objects reach the Earth's surface and penetrate, often to a depth equal to their diameter.  The densest meteorites, iron-nickel type, weigh 7.8 grams per cubic centimeter^K (g/cm³), compared to upper continental crust density of 2.67^L g/cm³. The typical speed of an impacting meteorite is in the vicinity of 20,000^K meters per second (m/s), or 44,740 miles per hour.  For comparison, the velocity of artillery shells is generally between 300 and 1000 m/s^N.

Psyche is an iron/nickel asteroid over 200 km (120 mi) in diameter,
orbiting between Mars and Jupiter

If you have reviewed the presentation at the www.newgeology.us website, you have seen that the arrangement of continents, mountain ranges, and trenches is completely explained as the consequence of a single explosion in the proto-continent north of present day Madagascar.  This is not at all what one would expect given our current understanding of physics.  Blast effects and pressure waves should dissipate rapidly away from the impact site, and continents should not budge.  Yet the event was on a scale vastly larger than humans have ever experimented with.  As mentioned in the website, experience with comparatively smaller events (though still large for humans) such as earthquakes, complex craters, and long-runout landslides suggests that a change occurs in the rheological properties of the crust at large scales of energy and mass.  Continents slide smoothly as if on ice, while pressure and shear waves propagate unattenuated for thousands of miles.  The apparent sudden freezing in place of these elements at the end of the event indicates a distinct threshold energy for such effects. As unpalatable as this seems, the flawless fit of crustal features with the shock dynamics scenario leaves us with no other choice.

Energy estimates
The apparent "superfluid" nature of large-scale crustal physics makes calculating the forces involved in setting the continents in motion simply a matter of transmitting the kinetic energy of the meteorite to the crust to set the pieces in motion.  Based on the shock dynamics scenario, the meteorite struck at an angle (from the ground) of 30 degrees, azimuth 93 degrees.  It had a density of 7.8 g/cm³ if iron/nickel, or 3.35 g/cm³ if chondritic, and a velocity of 20 km/s. The diameter will be calculated below.  The greatest part of the explosion struck the smaller, "East block" of continental crust.  All of the East block collided with Asia, and while Australia and a number of islands rolled off farther to the east, they lost momentum in the collision. The computer animation shows that parts of the East block (New Zealand, Philippines, Australia) interacted with the crustal wave.  This indicates that these pieces of continental crust, and therefore the whole East block before it shattered, slid at surface wave velocity, about 150 m/s^M.  This is considerably slower than P (pressure) body waves, which pass through the interior of the Earth at 8000 to 14000 m/s.  However, Rayleigh surface waves, like ocean waves, travel at near shear wave velocities that are dependent on wavelength and the medium they travel through.  Shear wave velocities in sediments are quite low, such as 20 m/s in high porosity clay or 50 m/s in sandy sediment.^O  An ideal tsunami ocean wave, in waters 7000 m deep, wavelength 282 km, travels at 943 km/hr or 262 m/s.  Because the energy in the shock wave was far above that needed to fluidize the crust, it passed through the crust as a fluid medium, similar to a tsunami wave in waters 2000 m deep, wavelength 151 km, and velocity 504 km/h or 140 m/s.  Also, body wave energy falls off at a rate of 1/r² since it is an expanding sphere, whereas surface wave energy falls off much more slowly, at a rate of 1/r since it is an expanding circle.  A study of three powerful tsunamis in the Pacific^Q concluded that "shorter-period waves attenuate much faster than longer-period waves".  The wavelength resulting from the giant impact would have been extremely long.  Thus the crustal Rayleigh wave travelled far from the impact site before the shock energy fell below the fluidizing level, and the wave froze in place.  The potential distance travelled by all pieces of the East block are assumed to have been the same as the unimpeded portion of the crustal wave that ended as the Tonga-Kermadec Trench. Measurement of distance was made from the east edge of the crater to the trench.  Crustal thickness is 35 km, and overall crustal density is 1/3 of upper crust density (2.67 g/cm³) and 2/3 of lower crust density (2.9 g/cm³)^L, making it 2.82 g/cm³.

Total: 17,336,953 km²
Potential East block travel distance (crater edge to Tonga Trench): 12,900 km

Kinetic energy (KE) of East block:
17,336,953 km² x 35 km = 6.0679 x 10⁸ km³ = 6.0679 x 10²³ cm³
6.0679 x 10²³ cm³ x 2.82 g/cm³ = 1.7111 x 10²⁴ g = 1.7111 x 10²¹ kg
Rayleigh wave moving through the crust at 150 m/s^M,
KE = 1/2 mass x velocity²  so .5 x (1.7111 x 10²¹ kg) x (150 m/s)²
= 1.925 x 10²⁵ Joules

KE of West block
The West block was much more massive than the East block.  When a large ball is hit with the same force as a small ball, the large ball moves more slowly.  So the West block would have moved slower, but how much?  All other things being equal, a comparison of distances travelled versus velocity is a reasonable measure.  The East block would have travelled 12,900 km (measured from the crater to the Tonga-Kermadec Trench), with a velocity of 150 m/s.  The distances travelled by components of the West block are shown below.  Because of the significant rotation of South America, the northern and southern halves are listed separately.

and applying the equation KE = 1/2 mass x velocity² to each part gives us

*Mass = km² x 35 km x 2.82 g/cm³ x 10¹²

The total mass for the West block is 5.877 x 10²¹, and the KE is 1.213 x 10²⁵ Joules

Diameter of the meteorite
As an imperfect elastic collision, the efficiency of the transfer of momentum from meteorite to target is generally quoted as 90%^K, but 25% is used here (Ef) as a conservative estimate of that part of the overall energy directed laterally.  Meteorite velocity is 20 km/s.  Meteorite density is 7.8 g/cm³ iron/nickel or 3.35 g/cm³ chondritic.  Vol = meteorite volume in km³.  Vertical high velocity impacts form a shock wave in the target that is equal in all directions.  An impact at 30 degrees from the ground, as postulated for the Shock Dynamics event, distributes the energy unevenly, with most in the downrange (forward) direction, and the least to the sides and uprange (back).  The left image is a side-view cross section; on the right is the view from above, with arrow thickness indicating strength.

The combined KE required to move the two blocks is (1.925 x 10²⁵) + (1.213 x 10²⁵) = 3.138 x 10²⁵ J.  Using 1/2 m x v², KE of the meteorite is 1/2 its mass x (20 km/s)².  The efficiency of the imperfect elastic collision is conservatively estimated at .25 transfer of KE to the crust.  The first calculation is for a chondritic meteorite, the second for an iron/nickel meteorite:

1) 3.138 x 10²⁸ g(m/s) = 1/2 meteorite mass x (20 x 10³⁾² m/s x .25 Ef.
There are 1 x 10¹⁵ cm³ in a km³, so a density of 3.35 g/cm³ gives us
3.138 x 10²⁸ g(m/s) = 1/2(Vol km³ x 3.35 x 10¹⁵ g/cm³) x 4.0 x 10⁸ m/s x .25,
yielding 1.873 x 10⁵ = Vol km³.
Assuming for simplicity a spherical bolide, volume of a sphere is 4/3 pi r³,
4/3 pi r³ = Vol km³, so 1.873 x 10⁵ km³ = 4/3 pi r³
r³ = 4.472 x 10⁴ km³
r = 35.5 km, so if it was a chondritic meteorite, the diameter was  2r, or 71 km (44 miles) and total impact energy is 1.255 x 10²⁶ Joules = 3 x 10¹⁰ megatons of TNT.

2) 3.138 x 10²⁸ g(m/s) = 1/2 meteorite mass x (20 x 10³)² m/s x .25 Ef.
There are 1 x 10¹⁵ cm³ in a km³, so a density of 7.8 g/cm³ gives us
3.138 x 10²⁸ g(m/s) = 1/2(Vol km³ x 7.8 x 10¹⁵ g/cm³) x 4.0 x 10⁸ m/s x .25,
yielding 8.046 x 10⁴ = Vol km³.
Assuming for simplicity a spherical bolide, volume of a sphere is 4/3 pi r³,
4/3 pi r³ = Vol km³, so 8.046 x 10⁴ km³ = 4/3 pi r³
r³ = 1.921 x 10⁴ km³
r = 26.78 km, so if it was an iron/nickel meteorite, the diameter was 2r, or 53.6 km (33.3 miles) and total impact energy is 1.255 x 10²⁶ Joules = 3 x 10¹⁰ megatons of TNT.

For comparison, estimated parameters of the Chicxulub impact are:
bolide diameter 10.6 to 80.9 km, mass 1.0 x 10¹⁵ to 4.6 x 10¹⁷ kg, yielding kinetic energy at  1.3 x 10²⁴ Joules to 5.8 x 10²⁵ Joules^R, which is one to two orders of magnitude less.

While these estimates are only approximations, they do show how a moderately large meteorite with a typical velocity would have had the necessary kinetic energy to accomplish the actions described in the Shock Dynamics scenario.  Also, while the mass of the West block is over 3 times larger than the East block, its components travelled much shorter distances, in accordance with an oblique impact that directed its energy (61%) to the east.  It flung Australia all the way to the Pacific and plunged India/Southeast Asia into Asia, raising the largest mountains in the world. Clearly a central force divided the protocontinent, not random drift as claimed by Plate Tectonics.

Underground nuclear weapons test formula - crater size and blast energy

Source:  U.S. Congress, Office of Technology Assessment, The Containment of Underground Nuclear Explosions, OTA-ISC-414 (Washington, DC: U.S. Government Printing Office, October 1989), 80 pages.

"The radius r (in feet) of the cavity is proportional to the cube root of the yield y (in kilotons):

For example, an 8-kiloton explosion would be expected to produce an underground cavity with approximately a 110-foot radius." (page 37)

"At first, the explosion creates a pressurized cavity filled with gas that is mostly steam. As the cavity pushes outward, the surrounding rock is compressed. Because there is essentially a fixed quantity of gas within the cavity, the pressure decreases as the cavity expands. Eventually the pressure drops below the level required to deform the surrounding material. Meanwhile, the shock wave has imparted outward motion to the material around the cavity." (page 34)

Applying the formula to the Shock Dynamics crater: 311 miles x 5280 feet = 1642080 feet,
1642080 divided by 55 = 29856, 29856³ = 2.6613063 x 10¹³ kilotons or 2.6613063 x 10¹⁰ megatons of TNT.

We see that the estimated force needed to impel the landmasses without friction in the Shock Dynamics scenario matches the explosive force needed to form the Shock Dynamics crater:  3 x 10¹⁰  versus  2.66 x 10¹⁰ megatons of TNT.

Estimating meteorite diameter from crater size
It is interesting to see the results from an interactive website sponsored by Imperial College of London and Purdue University.  The Earth Impact Effects Program, by Robert Marcus, H. Jay Melosh, and Gareth Collins, allows us to input parameters and view the calculated estimate.

The observed diameter of the Shock Dynamics crater is about 1000 km (622 miles) see "Ground Zero".

For a chondritic meteorite with 71 km diameter, 3500 kg/m³ density, 20 km/sec velocity, 30 degree impact angle, and 2750 kg/m³ target density, the final crater is 602 km (374 mi) across and 2.03 km (1.26 mi) deep.  To make a 1000 km-wide crater the chondritic meteorite would need a diameter of 126 km (78 mi).

For an iron/nickel meteorite with 53.6 km diameter, 7800 kg/m³ density, 20 km/sec velocity, 30 degree impact angle, and 2750 kg/m³ target density, the final crater is 636 km (395 mi) across and 2.07 km (1.28 mi) deep.  To make a 1000 km-wide crater the iron/nickel meteorite would need a diameter of 90 km (56 mi).

Let's see how the program deals with the much smaller "Meteor Crater" (Barringer Meteorite Crater) in Arizona.  Plugging in a meteorite with 40 m diameter, 7800 kg/m³ density, 12.8 km/sec velocity, 45 degree impact angle, and 2500 kg/m³ target density, the final calculated crater is 1.11 km (0.689 mi) across and 236 m (775 feet) deep.  The actual crater is 1.2 km (0.739 mi) across and 170 m (560 feet) deep.

Largest piece of the iron/nickel meteorite that formed Meteor Crater, Arizona

Shiva crater

*  *  *  *  *  *  *  *
References

^J Vitaly V. Adushkin and Ivan V. Nemchinov, "Consequences of Impacts of Cosmic Bodies on the Surface of the Earth", Hazards Due to Comets and Asteroids, ed. Tom Gehrels (Tucson: The University of Arizona Press, 1994), p. 722.

^K H. J. Melosh, Impact Cratering - A Geologic Process. Oxford University Press, New York, 1989.

^L The Great Geographical Atlas. Rand McNally & Co., 1982.

^M Ralph B. Baldwin, "On the tsunami theory of the origin of multi-ring basins", Multi-ring Basins, Proceedings of the Lunar and Planetary Science Conference (1981), 12A, pp. 275-288.

^M Ralph B. Baldwin, "The Tsunami Model of the Origin of Ring Structures Concentric with Large Lunar Craters", Physics of the Earth and Planetary Interiors, Vol. 6, 1972, pp. 327-339.

^M W. G. Van Dorn, "Tsunamis on the moon?", Nature, Vol. 220, 1968, pp. 1102-1107.

^M Freeman Gilbert, "Gravitationally perturbed elastic waves", Bulletin of the Seismological Society of America, Vol. 57, No. 4, 1967, pp. 783-794.

^N Ian V. Hogg, The Illustrated Encyclopedia of Artillery. Chartwell Books Inc., 1988.

^O Michael D. Richardson, Enrico Muzi, Luigi Troiano, "Shear wave velocity in surfictal marine sediments: A comparison of in situ and laboratory measurements", The Journal of the Acoustical Society of America, Vol. 83, Issue S1, May 1988, p. S78.

^P Matthias A. Meschede, Connor L. Myhrvold, Jeroen Tromp. 2011. Antipodal focusing of seismic waves due to large meteorite impacts on Earth. Geophysical Journal International, Vol. 187, pp. 529-537.

^Q Rabinovich, Alexander B., Rogerio N. Candella, Richard E. Thomson. 2013. The open ocean energy decay of three recent trans-Pacific tsunamis. Geophysical Research Letters, Vol. 40, pp. 1-6, doi: 10.1002/grl.50625.

^R Durand-Manterola, Hector Javier, Guadalupe Cordero-Tercero. 2014. Assessments of the energy, mass and size of the Chicxulub Impactor. arXiv:1403.6391