Cratering asymmetries and the orbital histories of outer solar system satellites

Abstract

On a tidally locked satellite, the leading hemisphere should display higher impact crater densities than the trailing hemisphere. Ganymede displays a weaker-than-expected cratering asymmetry, whereas Triton displays a stronger-than-expected cratering asymmetry. These deviations from the theoretically predicted cratering asymmetry have been attributed to true polar wander, recent nonsynchronous rotation, or crater saturation. Here we use new observations of impact crater distributions on icy satellites in conjunction with a Bayesian statistical model to infer the orbital properties of impactor populations and to test the plausibility of true polar wander and geologically recent nonsynchronous rotation.

1. Introduction

Impact crater populations provide a record of the past rotation, geologic history, and surface evolution of icy satellites. Shoemaker and Wolfe (1982) and Horedt and Neukum (1984) first noted that a "windshield effect" should cause an apex-antapex cratering asymmetry on synchronously locked satellites.

Zahnle et al. (1998, 2001)



In [1]:

    
import pymc
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline



In [2]:

    
# Define key parameters

Vp = 13070 # Orbital velocity of Jupiter, m/s



In [3]:

    
# Calculate distribution of encounter velocities

x1 = pymc.Uniform('x1', lower=0.0, upper=1.0) # Uniformly distributed random number
num_obs = 1000
v_inf = np.empty(num_obs)
for obs in np.arange(num_obs):
    v_inf[obs] = Vp*(1-0.45* np.log10(1/(x1.random()+0.2)-0.832))



In [4]:

    
# Plot distribution of encounter velocities

plt.hist(v_inf)
#plt.show()









    Out[4]:





(array([ 183.,  243.,  210.,  152.,  113.,   56.,   19.,   14.,    6.,    4.]),
 array([  9427.19250892,  11422.18930121,  13417.18609351,  15412.1828858 ,
         17407.1796781 ,  19402.17647039,  21397.17326269,  23392.17005499,
         25387.16684728,  27382.16363958,  29377.16043187]),
 <a list of 10 Patch objects>)



In [5]:

    
np.log10(100)









    Out[5]:





2.0



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In [7]:

(( block bibliography )) \bibliographystyle{unsrt} \bibliography{ipython} (( endblock bibliography ))



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