The NEOTωIST – Impact Calculator is a tool developed and validated to determine the physical crater and ejecta cloud properties created by an hypervelocity impact event on an asteroid.

### Short description

The **NEOTωIST – Impact Calculator** is a tool to calculate an estimate of the most important properties of a hypervelocity impact event on small asteroids with negligible gravity, see the above figure for an overview of the application.

It is assumed that the impactor has a spherical shape, at least the side which touches the target asteroid first.

On the left part of the application the user can make the inputs for the observation, impactor, target and ejecta properties. It can be chosen between Earth or flyby observation, where Earth observation is the default option. Selecting flyby observation will change the field ’Geocentric distance [AU]’ in ’Flyby distance [km]’ for the calculation of the apparent magnitudes of the target and the ejecta as seen from a flyby spacecraft.

Reselecting Earth observation will change the field back to ’Geocentric distance [AU] for the calculation of the apparent magnitudes of the target and the ejecta as seen from the Earth. Possible inputs for the impactor are the size, mass, density, volume and velocity.

This includes the size of the crater, maximum velocity of the ejecta, total ejected mass as well as the observed brightening of the asteroid due to the ejected material.

The **NEOTωIST – Impact Calculator** was implemented during the Master Thesis

“Instrumentation for an asteroid kinetic-impactor demonstration mission” from Steffen Weisenberger. The Master Thesis took place at the Julius-Maximilians-University of Wuerzburg and the Institute of Planetary Research of the German Aerospace Center (DLR). The used formulas and values can be found in the document of the Master Thesis and its referenced articles.

For the use of the NEOTωIST – Impact Calculator your system must support the computer programming language JAVA. Depending on your system configuration, the calculation with a small ‘Step size’ could take some minutes or could lead to a freezing of the application.

### Available resources & downloads for the NEOTωIST – Impact Calculator

- Java application zip-file
- User Manual PDF
- Master Thesis: Steffen Weisenberger – “Instrumentation for an asteroid kinetic-impactor demonstration mission” PDF
- Publication / Extended Abstract “Instrumentation for an asteroid kinetic-impactor demonstration mission” PDF

### Quick reference from the User Manual

IMPACT CALCULATOR DETAILS

In the top menu of the application are two buttons ’**About NEOTωIST**’ and ’**About NEOTωIST – Impact Calculator**’. The buttons can be pressed to show short descriptions about the NEOTωIST mission concept and the NEOTωIST – Impact Calculator.

For the target the inputs are diameter, albedo, density, strength, heliocentric and geocentric distances, G slope parameter and phase angle as well as constants, based on the target properties, needed for the calculation of the crater. The combobox at the target properties includes different target types (’Rock’, ’weakly cemented basalt (WCB)’, ’sand/fly ash (SFA)’, ’perlite/sand mixture (PS)’ and ’Itokawa’).

Selecting one of the types will change the ’Target properties’ and ’Target constants’ to the parameters of the selected target type, based on Housen and Holsapple (Ejecta from impact craters, Icarus 211 (2011)). **The default values are for the target ’Itokawa’, because it is the target of the NEOTωIST mission concept.** The ejecta inputs are ejection angle, albedo, G slope parameter, additive inverse of the size distribution exponent, maximum and minimum ejecta particle size and the step size of the intervals of the particle size distribution.

The results are displayed on the right part, see figure adjacent. **The target absolute and apparent magnitude is calculated.** The calculated crater parameters are the crater radius, depth and volume. The ejecta properties which are calculated are ejecta particle velocity upper limit, total ejected mass, total number of all ejecta particles, total cross–section (assuming all ejecta particles a spheres and form a plane) and the absolute and apparent magnitude of the ejecta cloud.

Also the **combined (target + ejecta) absolute and apparent magnitude are calculated**. The momentum properties include the calculated impactor momentum, normal momentum of the ejecta as well as the combined (impactor + normal momentum of the ejecta) momentum and the resulting momentum multiplication factor β. The bottom menu contains the button ’calculate’ and the checkbox ’write to file’. The button is used to start the calculation.

Every time an input is changed, the button has to be pressed to calculate the new results. If the checkbox is activated, it will create different Excel files (’Size Distribution’, ’Mass Distribution’ and ’Velocity Distribution’), in the directory ’NEOTωIST – Calculations\worksheets’. New calculations will override the existing files. The files can be used to visualize the data for instance as plots.

The **results in the files can be slightly different from the results displayed in the application,** which is because of small rounding uncertainties and a limited accuracy in the smooth particle distribution, depending on the step size of the intervals.

Therefore the cumulative number of particles in the Size Distribution file and the cumulative mass in the Mass Distribution file are not reaching precisely 100%, but with > 99.9% almost all particles and their masses are considered. Also the **total mass in the Mass Distribution file and the Velocity Distribution file are slightly different**, because the calculations in the files are different.

The calculations in the Mass distribution file based on the particle size distribution, whereas **the calculation in the Velocity Distribution file based on the ejected mass** and ejection velocity with respect to the distance to the crater center.

NEOTωIST is an abbreviation for “Near-Earth Object Transfer of angular momentum (w*I) Spin Test”.

The NEOTωIST mission concept is part of the NEOShield-2 project. It is a kinetic-impactor demonstration mission, to transfer an angular momentum to an asteroid to change its spin rate.

EXPRESSIONS USED IN THE PROGRAM

**Top menu bar:**

‘About NEOTωIST’ gives a short description of the NEOwIST mission concept.

‘AboutNEOTωIST – Impact Calculator’ gives a short description about the NEOTωIST – Impact calculator.

**Inputs (left column):**

Observation properties:

This combobox contains two options.

Option ‘Earth observation’ is used for calculation of the apparent magnitudes as seen from Earth.

Option ‘Flyby observation’ is used for calculation of the apparent magnitudes as seen from a flyby spacecraft.

‘Earth observation’ is the default option. Selecting ‘Flyby observation’ will change the field ‘Geocentric distance [AU]’ in ‘Flyby distance [km]’. Reselecting ‘Earth observation’ will change the field back to ‘Geocentric distance [AU].

** Impactor properties includes all fields about the parameters of the impactor.**

Front Area: The area of the impactor, which touches the target asteroid first.

Mass: The total mass of the impactor.

Density: The density of the impactor. It cannot be changed directly, as it depends on the impactor mass and volume. Changing the mass and/or the volume will automatically change the density.

Volume: The total volume of the impactor.

Velocity: The impact velocity of the impactor.

**Target properties:**

The combobox includes different target types (‘Rock’, weakly cemented basalt ‘WCB’, sand/fly ash ‘SFA’, perlite/sand mixture ‘PS’ and ‘Itokawa’).

Selecting one of the types will change the ‘Target properties’ and ‘Target constants’ to the parameters of the selected target type.

The default values are for the target ‘Itokawa’, because it is the target of the NEOTωIST mission concept.

Diameter: The diameter of the target.

Albedo: The albedo of the target.

Density: The density of the target.

Strength: The strength of the target.

Heliocentric distance: The distance between the target and the Sun.

Geocentric distance: The distance between the target and the Earth.

Flyby distance: The distance between the target and the flyby spacecraft.

G slope: The G slope parameter of the target.

Phase angle: The angle between the Sun-target-observer (Earth/Flyby spacecraft).

**Target constants:**

The constants (my, ny, C1, k, H2, n1, n2 and p) are required for the calculation of the impact event, especially the impact crater, ejecta velocity and ejecta mass.

The constants based on the scaling laws of Housen and Holsapple (2011, Ejecta from impact craters. Icarus, 211). The constant ‘depth/diameter’ is used for the calculation of the crater depth.

**Ejecta properties includes all fields about the parameters of the ejecta.**

Ejecta angle: The ejection angle of the ejecta particles.

Albedo: The albedo of the ejecta particles.

G slope: The G slope parameter of the ejecta particles.

Size distribution exponent: The additive inverse exponent of the power law size distribution.

Size max: The upper limit of the ejecta particle size.

Size min: The lower limit of the ejecta particle size.

Step size: The size of the intervals of the particle size distribution. To get close to a continuum size distribution, the step size should be small, at least smaller than the ‘Size min’.

**Results (right column):**

Target properties show the results for the absolute magnitude and the apparent magnitude.

Absolute magnitude: The absolute magnitude is the magnitude that the target would have if it was 1 AU from the Earth and 1 AU from the Sun while having a Solar-phase angle of 0 degrees.

Apparent magnitude: The apparent magnitude describes the apparent brightness of the target seen at a given ‘Heliocentric distance’, ‘Geocentric (or Flyby) distance’, absolute magnitude, ‘G slope’ parameter and the ‘Phase angle’.

**Crater properties:**

Radius: The radius of the impact crater.

Depth: The depth of the impact crater, depending on the ‘depth/diameter’ ratio.

Volume: The Volume of the impact crater.

**Ejecta properties:**

Velocity max: The upper limit of the ejecta particle velocity.

Mass total: The total mass of the ejecta cloud.

Number of particles: The total number of all ejecta particles.

Total cross-section: The total cross-section of all ejecta particles, assuming all ejecta particles are spheres.

Absolute magnitude: The absolute magnitude is the magnitude that the ejecta cloud would have if it was 1 AU from the Earth and 1 AU from the Sun while having a Solar-phase angle of 0 degrees.

Apparent magnitude: The apparent magnitude describes the apparent brightness of the ejecta cloud seen at a given ‘Heliocentric distance’, ‘Geocentric (or Flyby) distance’, absolute magnitude, ‘G slope’ parameter and the ‘Phase angle’.

Target + ejecta properties show the combined absolute and apparent magnitudes of the target and the ejecta cloud.

**Momentum properties:**

Impactor momentum: The momentum resulting of the impactor mass and its velocity, assuming a perpendicular impact on the target surface.

Normal momentum of ejecta: The normal part of the momentum of all ejecta particles, depending on the ‘Ejecta angle’.

Combined momentum: The combined momentum of the ‘Impactor momentum’ and the ‘Normal momentum of ejecta’.

Beta: The multiplication factor describes the momentum gain of the ‘Normal momentum of ejecta’ compared to the ‘Impactor momentum’. A value of 1 means no ejecta will be produced and only the impactor momentum effects the target. A value larger than 1 indicates, that ejecta will be produced.

**Bottom menu bar:**

The bottom menu bar contains the button ‘calculate’ and the checkbox ‘write to file’.

calculate: The button is used to start the calculation. Every time an input is changed, the button has to be pressed to calculate the new results.

write to file: If this checkbox is activated, it will create different Excel files in the directory ‘NEOTωIST – Calculations\worksheets’. New calculations will override the existing files.

DATA AND FILES INSTRUCTIONS

If the ‘write to file’ checkbox is activated, three Excel files will be created in the directory ‘NEOTωIST – Calculations\worksheets’.

**Size Distribution:**

The ‘Size Distribution.xls’ file contains three columns. ‘Interval upper limit size [m]’ ‘Number of particles in this interval’ ‘Cumulative percent of the total number of particles’

In the first column is the upper limit of each interval of the size distribution shown.

In the second column is the number of all particles with sizes between the current and the previous upper limit of the interval.

In the third column is the cumulative amount of particles compared to the total number of particles given in percent.

In the last row the total number of particles is given.

** Mass Distribution:**

The ‘Mass Distribution.xls’ file contains five columns.

‘Interval upper limit size [m]’ ‘Number of particles in this interval’ ‘Mass in this interval [kg]’ ‘Cumulative percent of the total mass’ ‘Mass per particle [kg]’

In the first column is the upper limit of each interval of the size distribution shown.

In the second column is the number of all particles with sizes between the current and the previous upper limit of the interval.

In the third column is the mass of all particles in the interval given.

In the forth column is the cumulative mass compared to the total mass given in percent.

In the fifth column is the mass per particle of the interval given.

In the last row the total number of particles and the total mass of all particles is given.

**Velocity Distribution:**

The ‘Velocity Distribution.xls’ file contains four columns.

‘Distance from crater center [m]’ ‘Ejected mass from this interval [kg]’ ‘Launching velocity [m/s]’ ‘Momentum of this interval [kg m/s]’

In the first column is the upper limit of each interval away from the crater center shown.

In the second column is the mass of all particles ejected from the interval given.

In the third column is the launching velocity of the particles in the interval given.

In the forth column is the normal momentum of all particles of the interval given.

In the last row the total mass of all particles and the normal of the total momentum of all ejecta particles is given.