Astronomy 1 Lab Manual
Craters
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Crater Formation
Introduction
Craters are found on the surface of all terrestrial planets and moons. Originally, they were thought
to be mainly volcanic in origin. That began to change around 1960, but it wasnt until the manned
exploration of the Moon that it was finally confirmed that the vast majority of planetary craters
were formed by the violent impacts of projectiles from space. It is now recognized that impact
cratering from projectiles is an important process in the geology of planets and their moons.
This lab involves making craters in a box of sand using ball bearings to confirm that collisions at
oblique angles create circular craters and to study the relation between the energy of the impact to
the size (diameter) of the resulting crater.
Crater Formation Theory
When it was first proposed that craters on the Moon were caused by impacts from space rocks, a
major objection was that the vast majority of craters on the Moon are circular, but only rocks that
hit straight down (at right angles to the surface) would create circular craters. It was thought that
oblique angle impacts would create non-circular craters. However, space rocks hit at very high
velocities, and penetrate the surface before they explode when the kinetic energy is converted into
thermal energy. This release of energy is the same in all directions, yielding circular craters.
The size of a crater is naturally going to be related to the energy of the impacting object (like an
asteroid). As the energy of the asteroid increases, it releases more energy on impact, making a
bigger crater. However, it turns out that the relationship is not linear (twice as much impact energy
will not make a crater twice as big in diameter), but is rather some form of a power law:
D = k ∗ En
(1)
where E is the energy of the asteroid (kinetic and potential), D is the diameter of the crater, k is
an unknown constant, and n is some unknown factor that describes how the diameter of the crater
scales with the energy of the asteroid. In this lab, you will determine values of n and k by looking
at our scaled version of asteroids and craters.
Energy comes in a variety of forms; energy associated with motion is called kinetic energy and
can be calculated from the equation KE = mv2 /2, where m is the mass of the object and v is the
velocity of the object. The unit of energy is a Joule when one uses kilograms for mass, meters
for distance, and seconds for time.
Energy can also be associated with the gravitational force, and is called gravitational potential
energy. When an object is near the surface of the Earth, the gravitational acceleration g is constant
(9.8m/s2 ), and the potential energy of an object is given by the equation PE = mgh where m is the
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mass of the ball bearing (in kg), and h is the height of the ball. The zero of gravitational potential
energy can be chosen at any point (like the choice of the zero of a coordinate system).
The total energy in a system is conserved (energy is a constant) and when you drop a ball (or
an astroid falls onto a planet), gravitational potential energy is converted to kinetic energy and
the velocity of the ball will increase. When you drop a ball bearing into the box of sand, the
kinetic energy of the ball bearing on impact is equal to its potential energy before it is released,
1/2mv2 = mgh.
If we drop the ball bearings from different heights, or use ball bearings with different masses, we
get different values of energy of the impact and hence different resulting crater diameters.
References
Review sections 6.2 in your textbook (‘Investigating Astronomy’) before coming to the lab.
Apparatus
The equipment used in this laboratory consists of a several ball bearings of different masses, an
electromagnet, sand in a tupperware container, a long hollow plastic tube, a tape measure, a meter
stick, a ruler, a protractor, a balance scale and a light.
Figure 1: The equipment setup for the crater lab.
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Procedure
Oblique Impacts
1. Hold the long plastic tube at a fairly steep angle to the horizontal (> 45◦ ) with one end
resting on the edge of the tupperware container. Hold the smallest ball bearing at the end
of the tube, and release it (do not throw, or push the ball bearing), so that the ball bearing
rolls down the tube and hits the sand. The ball bearings are traveling much slower than
impactors that create craters in the solar system, and at shallow angles, the ball bearing will
skip across the sand, and create an oval impact crater. Vary the angle of the tube with respect
to the horizontal and determine the minimum angle required to create a circular crater, using
your eye to estimate weather the crater is oval or circular.
Question 1: Where is the ball bearing located after it has created a circular crater? If you
come across an impact crater on the Earth, what does this imply for where you should look
to find the meteorite?
2. Measure the critical angle (from the horizontal) for the creation of circular craters using
the protractor. When using the protractor, make sure you hold it horizontally, and that
the cross-hairs on the protractor are centered on the end of the tube near the edge of the
tupperware container. Estimate the uncertainty in your angular measurement and explain
how you determined the uncertainty.
3. Using the tape measure, measure the distance that the ball bearing rolled before hitting the
sand. Estimate the uncertainty in your measurement and explain how you determined the
uncertainty.
Question 2: Assuming that energy is conserved (i.e.: kinetic energy at impact is equal to the
gravitational potential energy when you released the ball) use this distance and the angle you
measured previously to determine the minimum velocity of the ball at impact that creates a
circular crater. Make sure you show all the details of your calculation. Note – you will have
to remember your high school trigonometry – how the lengths of the sides of a right angled
triangle are related to each other.
Energy-Crater Diameter Relationship
4. Measure the masses (m) of the ball bearings on the balance scale.
Question 3: What is the uncertainty in your mass measurement? Explain how you determined the uncertainty in your measurement.
5. Make sure the sand is not compacted and is level by gently shaking the plastic bowl back
and forth.
6. Turn on the electromagnet by pressing the button. Attach one of the smaller ball bearings
to the magnet and wait for it to stop moving. Measure the height (h) from the center of the
ball to the top of the sand. Release the button to drop the ball. Measure the resulting crater
diameters (D) for each. The diameter is defined as being the very top of the circular lip; use
the light to illuminate the sand from the side so that you can clearly see the lip of the crater.
Record your data using the table at the end of this lab manual. Keep the impact site near the
center of the bowl so that the crater does not get interrupted by the edges of the bowl.
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7. Gently shake the sand container back and forth to level out the sand.
8. Repeat your experiment a few times for a given height. The range in diameters you measure
is an indication of the uncertainty in your diameter measurement.
9. Drop the ball from two or three different heights. Try to get as large a range in height as you
can, but don’t take measurements from very low heights (less than 2cm).
Question 4: What is your uncertainty in your height measurement? Explain how you determined the uncertainty in the height measurement.
10. Using the other ball bearings, drop each of them from two or three different heights, measuring the crater diameters each time. Note: you don’t need to repeat you experiment for
every height for a given ball bearing; just repeat a few of your measurements so that you can
estimate the uncertainty in your diameter measurement.
Analaysis
Graphing crater diameter as a function of energy allows you to determine the values of n in equation (1). However, since this is a power law relationship (n is an exponent), a simple graph of
diameter as a function of energy would be a curved line, and it would be very difficult to determine the value of n. Instead, if we plot the log of the diameter as a function of the log of the energy
then the data points will lie along a nice straight line. The slope of this line is n, our power law
exponent. If you don’t remember how logs work, or don’t understand why plotting log(D) as a
function of log(E) will make a straight line, ask your TA for an explanation.
Calculate the energy E, log(E) and log(D) for each for your measurements.
Question 5: How do the uncertainties in your measurements in height and mass translate into an
uncertainty in the impact energy?
Plot your data either using either a computer graphing program, or by hand on normal graph paper
(included at the end of this lab manual). When you plot your data, indicate the uncertainty in your
measurements by including an error bar on each of your points, using your repeat measurements
to estimate the uncertainty in your diameter measurements, and your answer to question 3 above
to estimate the size of your energy errors bars. On the graph, the size of your error bars should
correspond to the size of your uncertainties.
Draw a “best-fit” line through the data points on the graph. A best-fit line is a straight line that
comes close to, but probably not through all the points, just near to as many points as possible. If
you are using a graphing program that can fit lines to data, you may use the program to do the fit,
but must explain in your lab writeup how the program determines the best-fit line.
Find the slope of this best fit line and estimate the uncertainty in your measurements the slope.
Explain how you determined the uncertainty in the slope. If you drew your graph by hand, mark
the two places on your line that you used to find the slope. This slope is equal to n in the equation
above. Recall that the slop of a line is just the change in the y-coordinate divided by the change in
the x-coordinate; i.e.: slope = (δy)/(δx) = (δ log D)/(δ log E) .
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We also need to know the constant k in the equation relating crater diameter and impact energy. To
find k, you can use just one of your data points. Pick a data point that is close to your best-fit line
(that is, one that you think is a good value), and plug D, E, and your value for n into equation (1):
D = kE n . You can then solve that equation for the value of k.
Application of Your Results
The Chicxulub crater in the Yucatan peninsula in Mexico is 65 million years old, and the impact
associated with this crater may have lead to the extinction of the dinosaurs. The Chicxulub crater
is 180 km in diameter. Use the results of your experiment to answer the following questions:
Question 6: How much kinetic energy did that asteroid have when it hit the Earth?
Question 7: A good guess for the velocity of this asteroid when it hit the Earth would be about 20
km/s. Assuming that is true, what was the mass of the asteroid?
Question 8: Assuming a density of about 3 gm/cm3 = 3000 kg/m3 (an average density for asteroids) and a roughly spherical shape, what was the radius of the asteroid that killed off the
dinosaurs?
Writing up the Lab
Make sure your names are on your data sheet, and have the TA sign your data sheet before you
leave the lab. If you and your lab partner are handing in separate lab reports, then one of you will
hand in the original data sheet, while the other student can hand in a photocopy.
Lab reports are due one week after you complete the lab.
Follow all of the guidelines for lab reports which are posted onto Canvas. Aside from your data
sheets, you must use complete sentences throughout your report.
Lab reports are to be put into the A1 lab report box which are located to the left of the main stairs
when you enter Wilder Lab.
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Pre-Lab Questions
You must answer the following questions individually before you come to lab. Hand in your
answers to the TA at the start of your lab section.
The answer to all these questions can be found in your textbook and the lab itself. The pre-lab
questions will account for 15% of your lab grade. By reading the lab and thinking about it in
advance of performing the lab, you will find that the lab makes much more sense when you start
collecting data.
1. Why are impact craters always circular, even when an asteroid hits a planet at an angle?
2. Suppose you dropped a 0.030 kg ball bearing from a height of 0.50 m. What would be
the impact energy of the ball bearing when it hits the sand? What is the log of the impact
energy?
3. I drop the same ball bearing from the same height three times in a row and measure crater
diameters of 0.150, 0.152 and 0.148 meters. What is the uncertainty in my diameter measurement? Explain.
4. If you wish to maximize the range in impact energies you study, should you drop the least
massive ball bearing from large or small heights? Should you drop your most massive ball
bearing from large or small heights? Explain your reasoning.
Astronomy 1 Lab Manual
Craters
Height
Mass
Impact Energy Crater Diameter
(meters) (kilograms)
(Joules)
(meters)
Log (Enegy) Log (Diameter)
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