G456/556
 

Equipment needed: calculator, internet connection and web browser; and graphing program (e.g. Excel). (See the end of this lab for possibly useful constants and conversions.)

Objective: Explore the consequences of hurling various objects at solar system objects. We will be using a solar system collider program.

Return to G456/556 homepage.

Solar System Collider:   http://janus.astro.umd.edu/astro/impact/   or    http://janus.astro.umd.edu/astro/impact.html

The collisional velocities in Table 1 are calculated from the expression:

Vcoll² = Vesc² + Vapp²

where Vcoll = collisional velocity, Vesc = escape velocity, and Vapp = approach velocity of an impactor in orbit around the sun. Vesc depends on the mass and size of the target planet:

Vesc = (2GM/R)^0.5

where G = gravitational constant, M = mass of planet, and R = radius of planet.

For an object in orbit around the sun, Vapp is constrained by the expression:

v² = GM(2/r - 1/a)

where v = orbital velocity, M = mass of the sun, a = semi-major axis, and r = distance between the object and the sun. The approach velocity is not necessarily the same as the orbit velocity as it depends on the difference in orbital velocities for the impactor and target.  (Velocity includes both a direction as well as a magnitude.)

Q2. In general, what are the characteristics of an impactor orbit which will result in the highest collisional velocities for a given target planet?  HINT: Consider the possibility of impactor orbits that may be either prograde (asteroids, comets) or retrograde (many comets) [a sketch might be helpful?] and consider the difference that semi-major axis (symbol: a) makes in the equations above.
 
 
 
 
 
 
 
 
 

Q3. Calculate the collisional velocity on Earth for projectiles that have an approach velocity of 20 km/s. Show your work.
 
 
 
 
 
 
 
 
 

Q4. Hurl rocky projectiles of varying sizes at Earth's land surface for the collisional velocity you calculated in Q3. In Table 2, record the results and calculate the impactor flux, defined here as the number of projectiles hitting the target in 1 billion years (Ga). Round the flux value to 3 significant digits. For more on significant digits, click here.

Q5. Now hurl the same projectiles at the Earth's moon and complete Table 3. Round the flux to 3 significant digits.  For more on significant digits, click here.

Q6. Looking at your results in Tables 2 and 3,what is the approximate ratio of crater diameter to projectile diameter for these collisional speeds on the Earth and Moon? Why aren't the projectile and crater diameters the same?
 
 
 
 
 
 
 
 

Q7. For a given projectile size and approach velocity, what is the approximate ratio of crater diameter on the Moon to crater diameter on the Earth? How do you explain this difference between the Earth and Moon?
 
 
 
 
 
 
 

Q8. For a given projectile and approach velocity, what is the approximate ratio of impactor flux on the Moon to impactor flux on the Earth? What is the explanation for the difference in flux for the Earth and Moon?
 
 
 
 
 
 
 

Q9. Numerous ~0.5-km-diameter fragments from comet Shoemaker-Levy 9 impacted Jupiter in 1994. This comet was in orbit around Jupiter before it collided with the planet. Use the Collider to (a) describe the predicted effects of the collision and to (b) estimate when the next similar event on Jupiter will occur.
 
 
 
 
 
 
 

Q10. The 1.2-km-diameter Meteor (or Barringer) crater in northern Arizona was created almost 50,000 years ago by an iron meteoroid projectile. This impact event probably had a significant effect on the ecology of northern Arizona when it occurred-- it might have been exciting to be a resident of Winslow or Flagstaff. Use the Collider to constrain (a) the projectile diameter for this event, and (b) the frequency of this type of event.  HINT: use the maximum and minimum limits for collisional velocity in Table 1 to bracket the minimum and maximum projectile sizes, respectively.
 
 
 
 
 
 
 

Q11. The now-buried 170-km-diameter Chixulub crater in the Yucatan is believed to have resulted in the extinction of the dinosaurs and many other species (K-T extinction) and changed the course of evolution 66 million years (Ma) ago. Mammals became ascendant.  The impactor could have been either a comet or asteroid; assume it was an icy comet. Using the Collider, estimate (a) the projectile diameter for this event and (b) when Earth is next due for a planetary-scale extinction Chixulub-type event. HINT: use the maximum and minimum limits for collisional velocity in Table 1 to bracket the minimum and maximum projectile sizes, respectively.
 
 
 
 
 
 
 
 
 
 

Q12. Using the data for the Moon in Table 3, create two types of size-frequency diagrams showing (a) projectile diameter (x-axis) vs. impactor flux (y-axis) and (b) crater diameter (x-axis) vs. the impactor flux (y-axis). Use a graphing program to create log-log plots, and label the axes, including the appropriate units (e.g., "log impact flux (objects/Ga)" and "log crater diameter (km)"). What does this type of diagram indicate about the number of impacting objects and the numbers of craters of different sizes we should expect to see on planetary surfaces, in the absence of atmospheres or geologic processes that can obliterate craters?
 
 
 
 
 
 
 
 
 

Gravitational constant: G = 6.67 x 10^-11 N m²/kg²

Mass of Sun: M sun = 2 x 10³⁰ kg

Mass of Earth: M earth = 6.0 x 10²⁴ kg

Mass of Moon: M moon = 7.4 x 10²² kg

Mass of Jupiter: M jupiter = 1.9 x 10²⁷ kg

Radius of Earth: R earth = 6.4 x 10⁶ m

Radius of Moon: R moon = 1.7 x 10⁶ m

Radius of Jupiter: R jupiter = 7.1 x 10⁷ m

Force: 1 N = 1 kg m/s²

Distance: 1 km = 10⁵ cm = 10³ m

Time: 1 Ga = 1 billion years = 3.15 x 10¹⁶ sec = 5.25 x 10¹⁴ min = 8.75 x 10¹² hrs = 3.65 x 10¹¹ days = 1.20 x 10¹⁰ months = 1 x 10³ Ma (millions of years)