# Calculating the Mathematics of the Alamo Impact

Astronomy and the Bolide Impact

Mathematics can be used to describe the characteristics of the bolide and its trajectory, as well as the diameter and depth of the crater itself. This is important for cases in which the crater is no longer exposed or it has been altered during tectonic events, such as the Alamo Impact Event. Geological and paleontological evidence must be paired with mathematical and geometrical calculations to infer its size and impact depth.

By looking at fossils in the Alamo Breccia, paleontologists found conodonts that come from Late Cambrian Period rocks. In order for these fossils to have been mixed in suggests that the impact punched through at least 1.7 km of seafloor rock.

An estimated minimum Alamo crater size can be calculated using the minimum impact excavation depth. The relationship between the excavation depth (H_{exc}) and transient crater diameter (D_{t}) is represented by the following equation:

H_{exc} = 1/10(D_{t})

Substituting in the minimum excavation depth of 1.7 km, we can calculate the transient crater diameter:

1.7 km = 1/10(D_{t})

D_{t} = 1.7 km ÷ (1/10) = 17 km

The average ratio (D_{A}/D_{t}) between the final apparent crater diameter(D_{A}) and the transient crater diameter (D_{t}) for submarine impacts is about 2.6. We can use this to solve for the minimum final Alamo crater diameter, D_{A}:

D_{A}/D_{t} = 2.6

D_{A}/17 km = 2.6

D_{A} = 2.6 x 17 km = 44 km

The same calculations can be made using the maximum impact excavation depth and transient crater diameter, yielding a final Alamo crater diameter between 44 and 65 km.

The final diameter of an impact is around 20-30 times the diameter of the bolide itself. Using the minimum final Alamo crater diameter of 44 km, the impacting bolide would have had a diameter of around 1.5-2.2 km.