Secondary Craters: Kinetic Energy & Ejection Velocity

  • Thread starter Kreizhn
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In summary, for part 1, the kinetic energy involved in the impact of an iron meteoroid with a diameter of 300 m and a density of 7000 kg/m3 hitting the Moon at a velocity of 12 km/s is approximately 5.7x10^19 Joules. For part 2, the maximum distance of secondary craters from the main crater can be estimated by using the maximum range expression for a projectile motion, taking into account the Moon's gravitational pull and considering that ejecta with velocities of 500 m/s are actually on suborbital elliptical trajectories. However, there are other factors that can make this calculation more complex, such as some fragments leaving the Moon at higher velocities.
  • #1
Kreizhn
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1

Homework Statement



Consider the impact between an iron meteoroid (density = 7000 kg/m3) with a diameter of 300 m and the Moon.
1)Calculate the kinetic energy involved if the meteoroid hits the Moon at a velocity of 12 km/s.
2) If the rocks are excavated from the crater with typical ejection velocities of 500m/s, calculate how far from the main crater one may find secondary craters.

Homework Equations



The Attempt at a Solution


So part 1) is pretty simple, just using the basic E= [itex] \frac{1}{2} m v^2 [/itex]. I did the work and found the energy is roughly 5.7x10^19 Joules

Now for part 2) I'm wondering if there isn't an obvious way of doing this that I'm somehow missing.

It wouldn't be too hard to say that the maximum distance will occur when ejecta leave the crater at an angle of [itex] \frac{\pi}{2} [/itex] radians, and then use the moon's gravitational pull to find the maximal distance, but I'm wondering if it isn't somehow more obvious than that...
 
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  • #2
I think you mean [itex]\pi / 4[/itex] radians, pi/2 would be straight up ;)

I can't think of any easier way to do this. It's not that hard to do is it? You can see it as a simple projectile motion. With a known velocity and angle you can work out the distance.
 
  • #3
Yes, you are right about [itex] \frac{\pi}{4} [/itex]. Thanks.
 
  • #4
The maximum range expression is probably all they want you to use for the question and that is the simplest way to get an estimate. It will be a bit of an underestimate since the escape velocity of the Moon is 2380 m/sec, so ejecta moving at 500 m/sec are traveling at over 20% of escape velocity, meaning that they are actually on suborbital elliptical trajectories, rather than simple parabolas. (Another way of saying this is that the fragment flies "high enough" that the local acceleration of gravity is no longer essentially constant.) So, properly speaking, we would look for the intersections of elliptical paths with the lunar "sphere".

So there are certainly ways to make finding the answer harder. What you've chosen is what most people would do to get an adequate estimate. (We know that some fragments leave much faster than 500 m/sec. Some few have left the Moon entirely and landed on us! [see, for instance, http://en.wikipedia.org/wiki/Lunar_meteorite ] )
 

What are secondary craters?

Secondary craters are impact craters that are formed when debris from a primary impact event is ejected and strikes the surface of a planetary body.

How are secondary craters formed?

Secondary craters are formed when debris from a primary impact event, such as a meteorite or asteroid, is ejected at high velocities and strikes the surface of a planetary body, creating smaller impact craters.

What is the role of kinetic energy in secondary crater formation?

Kinetic energy plays a critical role in secondary crater formation. The higher the kinetic energy of the ejected debris, the larger and deeper the secondary craters will be.

What is ejection velocity?

Ejection velocity is the speed at which debris is ejected from a primary impact event. This velocity can vary greatly depending on the size and speed of the impactor, and can greatly affect the size and distribution of secondary craters.

Why do secondary craters provide valuable information for scientists?

Secondary craters can provide valuable information about the impact history and surface properties of a planetary body. By studying the size, distribution, and characteristics of secondary craters, scientists can learn more about the past impact events and surface processes that have shaped the planetary body.

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