The document describes an experiment simulating asteroid impacts on Earth. It varied the size, angle, and velocity of simulated impactors and measured the resulting crater size. Bigger impactors, those traveling faster, and those hitting at closer to perpendicular angles produced larger craters, as predicted. The relationships between some variables and crater size were nonlinear. More data and considering additional variables could improve the model. A maximally destructive impactor would be very massive, fast, and hit at a perpendicular angle.

1. Methodology be.
In this experiment I set all initial values for the simulator at
the middle of their range
Impactor size: 7500m
Impactor Angle: 45
Impactor Velocity: 30 Km/s
I also set the material of the impactor to be porous rock and
the target to be sedimentary rock. The Distance from crash
site was set at 0km. I did not modify the distance from crash
site variable as it gave subjective descriptions which were not
relevant to establishing relationships between impactor
variables.
I then changed each parameter in isolation, to attempt to see
the difference on crater size each variable had.
I plotted each variable against the kinetic energy of the
impact the fireball radius, the crater depth and the crater
width. I chose these values for a number of reasons. The
crater depth and width values allow us me to answer the
question as they give me the size of the crater.
A diagram illustrating deflection relative to a perpendicular
The kinetic energy of the impact and fireball size give us an cosine, indicated by the dashed line.
idea of the power of the impactor itself, and we can study the
raw power it delivers, regardless of the effects of the impact, Results:
which would be variable depending on the target surface. In this section I chart and analyze my impact data. Scientific
explanations are discussed later in the hypotheses section.
I plotted 10 values of this variable in attempt to notice if the
relationship between the values was linear or exponential, as The first variable I changed [all others remaining equal] was
with a higher number of values my results would be more Impactor Size [set 1]:
accurate.
My results are contained in an attached excel spreadsheet.
Predictions:
Now I will discuss my predictions for the data I will collect.
Kinetic Energy = 0.5 m v^2
Therefore KE is affected by both increasing the mass and/or
the velocity, however it is more sensitive to velocity.
Therefore results should reflect this.
KINETIC ENERGY DELIVERED: The greater the kinetic
energy delivered by the impactor, the larger the crater will
be. This is because larger amounts of kinetic energy displace
more material, creating a larger excavated area. From this I conclude that my prediction was correct
MASS: An impactor of higher mass, all other factors being The second variable I changed [all others remaining equal]
equal, has more inherent kinetic energy contained in its was Impactor Angle [set 2]:
mass. Therefore, the larger the impactor, the more energy
released and the larger the crater.
VELOCITY: the velocity of the impactor also affects the
crater size, the greater the velocity, the greater the amount of
energy applied to the excavation. this is because greater
velocities impart more potential kinetic energy to the
impactor, all other factors remaining equal.
ANGLE: Angle affects efficiency of excavation due to force
deflection. Angles closer to perpendicular lose less force to
deflection, as the force penetrates and is not deflected.
Defined by trigonometry, If the angle is defined as that from
From this I conclude my prediction was correct. I also
the line perpendicular to the surface, the penetrative force is
observe that the relationship is a nonlinear [negative
the dependant on the cosine of the angle. the smaller the
exponential] one. It suggests that angles closer to
angle, the closer it’s cosine is to 1. The closer it is to 1, the
perpendicular deliver energy more efficiently, but there are
more efficient the force penetration. In this instance, the
diminishing returns
closer the angle will be to 90, the greater the crater width will

2. absorptive qualities of the target surface, and local
The third variable I changed [all others remaining equal] was atmospheric conditions, an angle closer to 90 [all other
Impactor Velocity [set 3]: factors remaining equal] would cause ejecta to reimpact
closer to their site of origin. Material excavated at a lower
angle may cause ejecta to impact at a greater distance from
the crash site [as in the Boltysh example].
Trajectories of ballistic ejecta from the Chicxulub Crater
have been located as far as Belize, 500km from ground zero,
suggesting an impact of substantial force (Ocampo et al.
2003)
From this I conclude that that we have another negative
exponential relationship of diminishing returns, however it is
not as steep in declination as the curve given for angle,
demonstrating that velocity has a greater effect on the impact
energy.
I then plotted the changes against each other on a 4th graph to
try and establish a comparison between these 3 variables.
Starting positions on the X axis are irrelevant, I
hypothesize that shapes with a steeper gradient have a
greater effect on the impactor’s energy.
Complex craters are caused by the collapse of simple
craters, on scales greater than 100m, and dominated by the
slumping of the steep cavity walls under the action of gravity.
Simply put, they are caused by the creation of a crater too
deep to support a simple shape. (COLLINS & MELOSH
2002)
The work of Shoemaker was important to the development of
our understanding of complex cratering. By comparing the
composition of nuclear detonation sites with craters, he
deduced that both events created similar immense pressures
upon their impact sites, creating shocked quartz and other
material artifacts and deformations that could not be created
in a seismic event [as pressures where not high enough]. This
proved that that these craters were not geological formations.
Overall conclusions: a cursory glance at graph 4 shows us
that all other factors remaining equal, the mass of the Complex cratering offers some problems with volume
impactor has the greatest effect on the impact energy estimation due to the non uniform shape. One of the main
delivered and therefore, the crater size. The second most problems comes from the compression phase dynamics
important variable is the impactor velocity. involved in an impact event. The shockwave released by the
impactor changes it’s velocity depending on the absorptive
Variables Not Factored Into Experiment properties of the material it strikes. In a target region with a
Ejecta, Reimpactors, Target Material and Complex disparate composition, this can result in cratering with a lot
Cratering: Impactors delivering massive force can cause of variables to consider. After the impact, lingering effects of
material [ejecta] to be violently thrown out with enough force the modification stage may go on for many years after, as the
that upon it’s return to earth it can cause secondary damage unstable crater reforms under the effects of gravity and
[for example, excavating more material]. Ejecta can also be terrestrial geological processes. (King n.d.).
used later on as a deductive tool to learn about the event that
released it. For example, ejecta fragments found in Ukraine Although modeling these craters can be complex, scientists at
were used to estimate the size and date of the Boltysh crater Imperial College are developing a computer simulator to
impact event. (Bobina & Gurov 2000) account for the additional environmental variables that
complex cratering introduces (COLLINS et al. 2005).
The angle also effects the odds of secondary impacts upon
the crater. Notwithstanding factors such as the deflective and Conclusion, Commentary and Areas for Improvement:

3. Each result table has only 10 results per variable. Ideally
more data would have allowed me to create a more accurate
set of results. I would also like to have used different material
variables for the impactor and the target. This would have
given me more data and the ability to make comparisons
between material variances. I add the caveat that I believe it
would be very rare for an impacted area to consist completely
of one form of rock, and therefore in using one kind of
material for the impactor or the target, we are making a
simplification.
In future I would also like to try and chart a relationship
⇦
between impact energy quantity, and angle of ejecta released.
I believe if I had better understanding of the debris mechanics
of ejecta it would help me recreate impact events with greater
accuracy.
I also attempted to calculate the volume of the crater using These man made airfoils are aerodynamically efficient.
depth x width x pi squared, however this was a problem as it Impactors resembling this teardrop shape [and approaching
would have given me a spherical value. This is obviously at the correct angle – in the direction of the arrow] would be
wrong, as these craters are not equal in their volumes due to more likely to survive atmospheric entry intact.
various factors, such as variances in the density of the target
material and the angle at which an impact occurs. Observing Final Conclusion/How to Destroy Planet Earth:
crater mechanics suggests that impact energy may be I am somewhat confused by my data. The KE equation
distributed more in a conical shape, as the asteroid often suggests that velocity is the most important variable in the
burrows some way into the earth’s surface before losing it’s equation should be mass, however, looking at my
remaining kinetic energy. This is also notwithstanding the comparative graph, it seems that the value with the highest
previously mentioned complications of a complex crater. influence on crater size, all other factors remaining equal is
Therefore, I abandoned this idea, feeling my spherical mass. This is because the other two factors are negative
mathematics to be a gross oversimplification. exponential, which implies that the greater they become, the
less effective they become on the overall result. I believe that
From this I gather we can more accurately predict the energy I have not considered the relationship between variables
delivered by an impactor to the planet, much more accurately enough. I imagine that plotting results changing two variables
than the type of crater it would produce. per set may help alleviate this.
Another piece of data which would be helpful in better This suggests my mathematical skills fall short and I am
understanding the efficiency of the excavation would be to failing to grasp the big picture.
the shape of the impactor. To use the analogy of a knife,
applying the same force over a smaller volume results in A ‘perfect’ impactor – [one that caused maximum damage] –
greater surface penetration as more joules are applied per would be very massive, extremely fast moving, and hit the
square inch. I would speculate that objects of a smaller earth at a perpendicular angle. Asides from being an
surface area [other factors remaining equal] would result in a ‘efficient excavator’ it would also be an ‘efficient killer’ –
deeper crater. and if delivering enough force would not only sterilize the
planet, but could significantly structurally alter the earth.
There is another consideration resulting the shape of Although the theory is not airtight, it has been suggested that
impactor. Differences in asteroid shape would cause the earth’s moon was formed by collision with a Mars sized
distinctly different responses to atmospheric shock, with object [dubbed ‘Thea’] around 4.6 billion years ago (Britt
more aerodynamic shapes likely to hold up under the kinetic 2001). Needless to say, an impact of this magnitude today
stresses of atmospheric entry. This suggests that certain would be disastrous for life. One can also speculate that
aerodynamic impactors would be more likely to impact the impactors of even greater kinetic energy could be capable of
target in one piece. New scientific models created by destroying the planet.
researchers at Imperial College and the Russian Academy of
Sciences, on the protective effects of the earth’s atmosphere “Scientists have already identified more than 700 of the
suggest that for asteroids to reach the earth’s surface and not estimated 1,100 "Earth killers" [capable of causing
airburst in the higher atmosphere, they need be comprised of widespread destruction to life]—asteroids bigger than one
either extremely dense iron, or be aerodynamically efficient kilometer (about a thousand yards) across—out there. They
in shape (Perkins 2003). concluded that none are on a collision course with the Earth
during the next century.”- National Geographic News
(Lovgren 2004)
REFERENCES
Bobina, N. & Gurov, E., 2000. FORMATION OF THE BOLTYSH IMPACT STRUCTURE:
CATASTROPHE OF REGIONAL SCALE.
Britt, R.R., 2001. SPACE.com -- 24 Hours of Chaos: The Day The Moon Was Made. Space.com. Available
at: http://www.space.com/scienceastronomy/solarsystem/moon_making_010815-1.html
[Accessed March 2, 2010].
COLLINS, G.S., MARCUS, R.A. & MELOSH, J.H., 2005. Earth Impact Effects Program: A Web-based
computer program for calculating the regional environmental consequences of a
meteoroid impact on Earth. Meteoritics & Planetary Science, 40, 817 - 840.
COLLINS, G.S. & MELOSH, J.H., 2002. Hydrocode Simulations of Chicxulub Crater Collapse and Peak-
Ring Formation. Icarus, 24-33.

4. King, D.T., Impact Crater. Science.Jrank.com. Available at: http://science.jrank.org/pages/3531/Impact- Ocampo, A. et al., 2003. New Location of Chicxulub's Impact Ejecta in Central Belize.
Crater.html [Accessed March 2, 2010].
Perkins, S., 2003. Atmosphere blocks many small stony asteroids. (Protective Blanket). - Free Online
Lovgren, S., 2004. Undetectable Asteroids Could Destroy Cities, Experts Say. National Geographic News. Library. The Free Library / Science News. Available at:
Available at: http://www.thefreelibrary.com/Atmosphere+blocks+many+small+stony+asteroids.+
http://news.nationalgeographic.com/news/2004/04/0414_040414_earthkillers.html (Protective+Blanket)-a0106098178 [Accessed March 2, 2010].
[Accessed March 2, 2010].