### IIIA. CRATER SIZE

Note: This activity is written for two levels.
Level one is appropriate for pre-algebra students, and
level two involves more sophisticated algebra skills including the manipulation of an equation with two variables.

[see "Just how big is big?" in Craters!]

• Graphing data
• Interpreting graphs
• Proportionality
• Making generalizations from data
• Drawing conclusions

Crater Size (Level One)

Crater size is related to the mass and velocity of the impacting body. Mass and velocity can be combined to find the kinetic energy of an impactor. Increasing either the mass or the velocity of the impactor increases the kinetic energy of the impact. Review the results of your crater experiments in section IIA. The size of the crater increased with the mass of the bolide, and also with the height from which it was dropped (which is proportional to the speed of impact). This fundamental physical relationship allows an estimate of impactor mass to be made from crater diameter.

Activity:

• Reexamine your results from activity IIA.

Graph the mass of the bolide against the diameter of the resulting crater (for bodies dropped from the same height).

What relationship do you get?

• As the mass of the bolide increases, the diameter of the crater increases.

• What are you assuming is constant, by graphing mass vs. crater diameter for bodies dropped from the same height?

• Height or velocity is being held approximately constant.

• Graph the height from which the bolide is dropped vs. the crater diameter for objects of the same mass.

What can you observe from your graph?

• As the impact velocity increases, the crater diameter increases.

• What conclusion can you draw from this?

• Crater size is proportional to the mass of the impactor, and the velocity of impact. Given that the kinetic energy of the impact is related to mass and velocity, we can see that the experimental results support the theory that crater diameter is related to the kinetic energy of the impact.

• Look at some images of planetary surfaces. (Example images 1, 2)

Which craters do you think resulted from larger bolides?

What assumptions are you making?

• Larger craters result from larger bolide masses, assuming a constant impact velocity.

Concepts (Level Two):

• Algebra
• Manipulation of multi-variable equations
• Proportionality
• Solving equations
• Scaling relations
• Graphing
• Drawing conclusions from graphed data

Crater Size (Level Two)

Crater size is related to the size and velocity of the impacting body. These two quantities can be combined to find the kinetic energy of an impactor, defined as

K = 1/2 m v2

where K is the kinetic energy, m is the mass of the impacting body, and v is the velocity of the impactor. Review the results of your crater experiments in section IIA. The size of the crater increased with the mass of the bolide, and also with the height from which it was dropped (which is proportional to the speed of impact). This fundamental physical relationship allows an estimate of bolide mass to be made from crater diameter.

Activity:

• Reexamine your results from activity IIA.

Graph the mass of the bolide, m, against the cube of the diameter, D3, of the resulting crater (for bodies dropped from the same height).

Describe and explain the relationship.

• The results should follow an approximately straight line, due to the relationship below.

• The total amount of energy, K, required to form a crater is proportional to the volume, V, of material excavated in the impact.

• Since a crater is basically a hemisphere (half a sphere), its volume, V, is proportional to the diameter, D, of the crater. (V = 2/3 [pi] (D/2)3 )

• So the energy, K, needed is proportional to the diamete cubed, D3.

• The energy of an impact is the kinetic energy, as defined above:

K = 1/2 m v2.

• Since the energy K, is proportional to D3, we can predict

D3 is proportional to 1/2 m v2

Measuring the diameters of craters allows us to estimate the size of the impacting bolide. The diameter is proportional to both the mass of the bolide and its impact velocity. We can measure the estimate the size of the impacting bolide. The diameter is proportional to both the mass of the bolide and its impact velocity. We can measure the diameter of the crater, but unless we know either the mass or the velocity of the bolide, we can't solve for the other. By assuming a constant impact velocity, however, we can predict relative bolide masses for different crater diameters.

• Assuming a constant impact velocity, we know that the mass of an impactor is proportional to the diameter of the crater cubed. (m is proportional to D3 )

• In order to produce a crater twice as large as another, how much larger must a bolide's mass be? What about a crater 10 times larger? 100 times larger?

A: 8 times; 1000 times; 1000000 times.

• Look at some images of planetary surfaces. (Example images 1, 2) Measure the crater diameters and estimate how much more massive the bolide which formed the largest crater in the picture was than the bolides which formed the smaller craters.

• What other factors affect crater diameter?

A: Answers include impact velocity, bolide composition, planetary surface composition, and others.

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This module was written by Cynthia Phillips, Dept. of Planetary Sciences, University of Arizona, Tucson AZ, and funded in part by the NASA Spacegrant program.

Galileo Solid State Imaging Team Leader: Dr. Michael J. S. Belton

The SSI Education and Public Outreach webpages were originally created and managed by Matthew Fishburn and Elizabeth Alvarez with significant assistance from Kelly Bender, Ross Beyer, Detrick Branston, Stephanie Lyons, Eileen Ryan, and Nalin Samarasinha.

Last updated: September 17, 1999, by Matthew Fishburn