# Calculate Projectile Size from Crater Diameter

This program estimates the size of a projectile that made a gravity-dominated crater of the given size. Three different estimates are presented, but the Pi-scaling method is currently considered the best.

### Crater Descriptor

Enter the crater diameter in km

This diameter is: Transient Final  (See definitions below)

### Projectile Descriptor

Enter the projectile density in kg/m3
 or 917 kg/m³ for ice 1500 kg/m³ for porous rock 3000 kg/m³ for dense rock 8000 kg/m³ for iron

### Impact Conditions

Enter the impact velocity in km/sec
 or 17 km/sec for Earth and Moon asteroidal impacts 50 km/sec for Earth and Moon cometary impacts 72 km/sec for retrograde impactors at Earth (Leonids)  7 km/sec for Martian asteroidal impacts 45 km/sec for Martian cometary impacts  5 km/sec typical asteroid belt impact

Enter the impact angle in degrees

The impact angle is measured between the approach trajectory and a plane tangent to the surface. This angle is 90 degrees for a vertical impact.

### Target Descriptors

Enter the target density in kg/m3
 or 917 kg/m³ for ice 1500 kg/m³ for porous rock 3000 kg/m³ for dense rock 8000 kg/m³ for iron

Enter the acceleration of gravity in m/sec2
 or 3.7 m/sec² for Mercury 8.9 m/sec² for Venus 9.8 m/sec² for Earth 1.6 m/sec² for the Moon 3.7 m/sec² for Mars 1.8 m/sec² for Io 1.3 m/sec² for Europa 1.4 m/sec² for Ganymede 1.2 m/sec² for Callisto 1.4 m/sec² for Titan
Target Type
liquid water
loose sand
competent rock or saturated soil

## Results

The three scaling laws yield the following projectile diameters: (note that diameters assume a spherical projectile)

 Yield Scaling meters Pi Scaling (Preferred method!) meters Gault Scaling meters Crater Formation Time seconds

Using the Pi Scaling method this impactor would have struck the target with an energy of
Joules (  MegaTons).

These results come with ABSOLUTELY NO WARRANTY.

## Definitions

Transient Crater: The cavity formed immediately after the end of crater excavation, before it undergoes collapse and modification. Its outer extent is defined by the boundary between excavated and non-excavated (but possibly displaced) target material, and its depth is the maximum achieved by material that will eventually form the floor of the true crater after cratering motions cease. Although it is by nature temporary, laboratory-derived scaling relations apply only to the diameter of the transient crater, not the final collapsed crater form. Collapse of a transient crater produces both simple and complex impact craters.

Final Crater: The distance from rim to rim of the cavity once collapse has completed.

## The Carolina Bays

The Carolina Bays are shallow elliptical basins in the Atlantic Coastal Plain. The program to calculate projectile size from crater diameter assumes that the crater is circular. By equating the area of a circle to the area of an ellipse, we obtain the equivalent radius of the ellipse as the square root of the product of the semimajor(a) and semiminor(b) axes. The diameter of the ellipse (2r) can then be used to calculate the projectile size.

$$A = \pi r^2 = \pi ab$$
$$r = \sqrt{ab}$$

The width-to-length ratio of a Carolina Bay corresponds to the sine of the impact angle. $$sin(\theta) = W / L$$
Thus, the impact angle can be calculated as $$\theta = arcsin(b/a)$$.

The program is based on a FORTRAN 77 program originally written by Prof. H. Jay Melosh and converted to Perl by Ross A. Beyer. More information about the equations can be found in the book by Melosh: Impact Cratering: A Geologic Process, Oxford University Press, 1989, or in the related publication, below.

This program was originally hosted at the Lunar & Planetary Laboratory of the University of Arizona. The files were removed when Prof. Melosh transferred to Purdue University. The HTML file was archived on 3:28:10 Jan 11, 2016 and retrieved from the Internet archive on 22:27:34 Feb 4, 2016. The program is free software under the terms of the GNU General Public License.
UPDATE Jun 1, 2019:
As of this date, the program was back in operation at URL:
https://pirlwww.lpl.arizona.edu/~rbeyer/crater_p.html

Related Publication:
Gareth S. Collins, H. Jay Melosh and Robert A. Marcus, Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth, Meteoritics & Planetary Science 40, Nr 6, 817–840 (2005). PDF