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!]

Concepts (Level One):

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

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.

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

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

  
  

• 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.

Next Page

• Introduction

• I. Location of features on the surface of a planet: latitude and longitude

• II. Crater formation, modification, and removal
  • A. How are craters made?

  • B. Where have all the craters gone?

  • C. Focus on the Galilean satellites

• III. Crater Image Interpretation
  • A. Crater size

  • B. Crater depth

  • C. Crater size distribution and surface ages

• Conclusion