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We introduced an empirical equation D = CE 1/5 for the relationship between the kinetic energy (E) of an impacting object (e.
We introduced an empirical equation D = C×E1/5 for the relationship between the kinetic energy (E) of an impacting object (e.g., meteoroid or asteroid) and the diameter (D) of impacting crater on the surface of a planet/satellite, where C is a parameter determined by a few variables (e.g., densities of the impacting object and the planet/satellite, surface gravity of the planet/satellite, the size of the impacting object, and impacting angle to the surface of the planet/satellite). Let us assume that an asteroid with mass ~ 5 × 108 kilograms and diameter ~ 60 meters impacts a planet with a velocity of 2000 meters per second. Assuming the parameter C in the empirical equation has a value ~ 0.6. Let us use the empirical equation D = C×E1/5 to estimate the diameter of crater (D) on the surface of the planet and answer the following question.
Note: The empirical equation D = C×E1/5 is used with units of meter, kilogram, and second (MKS). All variables/parameters in this question are given in MKS units, so you do not need consider unit conversion in the empirical equation when estimating the diameter of the crater on the planet (i.e., only use numbers in the question).
What is the ratio between the diameter of the asteroid (~ 60 meters) and the diameter of crater (D) on the surface of the planet?
(A) ~ 1:3 (B) ~ 1:6 (C) ~ 1:10 (D) ~ 1:15
thx(:
