TEST OF ESABASE/DEBRIS - Space Environmentspace-env.esa.int/Reports/Final_Report_149_98_BIELER.pdf3) The Zenithal Hourly Rate (ZHR) Output is a PostScript file and/or a screen-plot,

MODELLING OF IMPACTS FROM METEOROID STREAMS TEST OF ESABASE/DEBRIS

FINAL REPORT Work performed under

Consultancy No. 149/98/BIELER

Torsten Bieler Welkenrather Str. 65

52074 Aachen Germany

Tel: +49-241-83088 Mail: [email protected]

Table of Contents 1. General Information .............................................................................................2 2. Overview of Activities ...........................................................................................2 3. Application.............................................................................................................3

3.1 General Description of STREAM.PRO...................................................................... 3 3.2 General Description of AKC.PRO.............................................................................. 6 3.3 Application.................................................................................................................. 7

3.3.1 Stream Parameter................................................................................................. 7 3.3.2 Zenithal Hourly Rate (ZHR).............................................................................. 10 3.3.3 Mass Dependent Stream Flux............................................................................ 12 3.3.4 Penetration Stream Flux .................................................................................... 19

4. First Test of ESABASE/DEBRIS Tool ..............................................................28

4.1 Deficiencies in the ESABASE/DEBRIS Tool .......................................................... 28 4.2 Deficiencies in the ESABASE/DEBRIS Tool-Documentation ................................ 28

5. Suggestions for future enhancements and applications...................................29 REFERENCES...........................................................................................................29 ANNEX A-1 Modelling the Meteoroid Environment A-2 Thin Plate Damage Equation explanation within the ESABASE/DEBRIS Technical

Description A-3 Grün Model explanation within the ESABASE/DEBRIS Final Report (Release 2) A-4 STREAM.PRO file A-5 AKC.PRO file A-6 stream_default.dat file A-7 stream_change.dat file A-8 Useful reference data

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1. General Information The consultancy, with the number 149/98/BIELER, was carried out within the period from 26.10.1998 – 30.04.1999. Several visits to ESA/ESTEC, TOS-EMA were undertaken during that period. The contact point was Mr. G. Drolshagen (TOS-EMA)

2. Overview of Activities Several aspects of the new ESABASE/DEBRIS tool (received by ESTEC in 1998) were tested. Some deficiencies were discovered and reported to Mr. G. Drolshagen TOS-EMA. After an initial assessment of the ESABASE/DEBRIS tool, it was agreed with Mr. Drolshagen that reference values for validation of the tool would be required. Another tool, to produce such reference values for meteoroid streams would be developed and be the main task of the consultancy. For this purpose two, PV-WAVE based, programmes (STREAM.PRO and AKC.PRO) were developed. These programmes are described below. Some reference calculations for normal stream flux activities and an assumed Leonid-Meteoroid-Storm were performed.

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3. Application

3.1 General Description of STREAM.PRO The STREAM.PRO- program calculates, 1) The Penetration Stream Flux, for a single plate with given thickness

With the input parameters, target thickness and impact angle. 2) The cumulative Meteoroid Stream Flux, depending on the minimum mass

With the input parameter, meteoroid mass. 3) The Zenithal Hourly Rate (ZHR) Output is a PostScript file and/or a screen-plot, where the plot range can be defined. The stream model parameters, which are needed as input, are contained in a data file. You can use either the ‘stream_default.dat’ or, eg. for storm simulations, the ‘stream_change.dat’, with user specified changes. To change stream parameters in ‘stream_change.dat’, the ‘AKC.PRO’-program yields the required parameters α, k and b, which can then be used in the ‘stream_change.dat’ file. These values are calculated as described in [4, which is reproduced in Annex 1]. The ‘AKC.PRO’ program description can be found in chapter 3.2 below. An example is presented at the end of this description. Input Parameters for STREAM.PRO: STREAM.PRO runs under “PV-WAVE”. The following files are needed in one directory-folder:

STREAM.PRO STREAM_DEFAULT.DAT STREAM_CHANGE.DAT

Note: To avoid printout irritations, first be sure, that all PV-WAVE graphic windows are closed. To close a graphic window under PV-WAVE, you can use the command “wdelete”. After this you can start the program, by typing: “.run stream.pro” [A] First select output option: “0” for screen only, “1”for screen and PostScript file. For option “1”, a PostScript file, will be stored on the disc under “WAVE.PS”. [B] Next choose which calculation should be performed. Input “1” for penetration stream flux, “2” for stream flux depending on a given mass or “3” for the Zenithal Hourly Rate. [C] Then choose which data file should be used. “0” for stream_default.dat or “1” for stream_change.dat [D] Next you are asked if you want to define the solar-longitude-plot-range. “1” to define it or “0” and a whole year will be displayed

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[E] After you have chosen to define the plot range, input the lower (min. 0) and the upper bound (max. 360). Either as single values or divided by a comma. [F] The next required input is how many calculation steps per solar-longitude-degree should be made. Because of the currently used values for the solar-longitudes of each stream, a maximum of 10 steps is sufficient. A higher number of steps only increase the computing time. From now on the input depends on what you have decided to calculate. I) Penetration Stream Flux

Input parameters are the target thickness in cm and the impact angle in degrees, where 0 means perpendicular. Output is the flux in [penetrations/m2/s] versus the solar longitude in [degrees]. The ‘ESABASE Thin Plate’ single wall ballistic limit equation (as described in Annex 2) is used. It yields the minimum diameter and the critical mass causing a penetration. For the target a 2.719g/cm3 and for the particles a 1.0g/cm3 density is assumed. If the user wants to change these parameters, he has to edit the source file STREAM.PRO. Then the yearly stream flux is computed. It is assumed that particles from all streams impact with the same, user defined, angle. II) Mass-Dependent Stream Flux

Input parameter is the minimum meteoroid mass in kg. Output is the flux in [particles/m2/s] versus the solar longitude in [degrees]. The stream flux, for mass equal and larger then the given one is computed. For I) as well as for II) as reference the cumulative flux of particles with the given mass or larger as obtained by the Grün Model ([3] and Annex 3) is given. III) Zenithal Hourly Rate (ZHR) The ZHR is calculated as explained in Annex 1.

Output is the ZHR versus the solar longitude in [degrees]. Plot: Depending on whether you have chosen only a screen plot or not, the PostScript file and/or the screen plot is generated. Note: Problems possibly occur on the screen plot while creating the PS-file. The screen plot differs also a little from the PostScript file.

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Example: An example of an annual penetration stream flux plot, for a single plate with 0.2cm thickness, an particle impact angle of 30 degrees, normal meteoroid stream flux activity and 10 calculation steps per solar longitude degree is given in the following. After you started PV-Wave on your computer, type in “.run stream.pro”. [A] Because a PostScript file and a screen plot is wanted, the input is “1” [B] To calculate the penetration stream flux, input “1” [C] Input “0” for normal meteoroid stream flux activity (stream_default.dat) [D] Input “0” for a whole 360 degrees solar cycle plot [E] A solar longitude range input is not required here [F] Input “10” to fix the number of 10 calculation steps per degree Then you are asked for the target thickness in cm, therefore the input is “0.2”. At last you have to type in the particle impact angle in degrees, while 0 means a perpendicular impact. Input “30”. A screen plot will appear on your screen and the PostScript file ‘WAVE.PS’, which is shown below is generated.

Figure 1: The 'WAVE.PS' Meteoroid Stream Flux plot for the example

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3.2 General Description of AKC.PRO Program AKC.PRO derives meteoroid stream parameters for user defined visual meteor stream intensities and duration. It computes the following meteoroid stream values, which are necessary to calculate quantitative fluxes for meteor showers or storms. 1) α the cumulative mass distribution index 2) k the constant in the cumulative flux equation 3) b the profile description index These values are derived as described in Annex 1 to the description of the program STREAM.PRO and can then be incorporated in the ‘stream_change.dat’ file for further usage within the STREAM.PRO’ program. An example for ‘AKC.PRO’ is presented at the end of this description. Input Parameter: The input parameters are the meteoroid stream velocity v in km/s, the meteor distribution index (see Table 1) χ, the maximum Zenithal Hourly Rate ZHRmax, the meteor magnitude used for fitting (see Annex 1) m and the stream duration, given as the full width at half maximum in days AKC.PRO runs under “PV-WAVE”. Input “.run akc.pro” to start the program. [A] At first you are asked for the individual meteoroid stream velocity in km/s. [B] Then you have to type in the meteor distribution index χ (typical range 2.4 – 3.5). [C] Further input the maximum Zenithal Hourly Rate (ZHR). [D] Next it is asked for the meteor visual magnitude m, to be used for model calibration, which usually can be assumed as 0.5. [E] The last input is the full width at half maximum (FWHM), which reflects the stream or storm duration, in days. Standard values of these stream parameters can be found in Table 1. α, k and b are calculated as described in Annex 1. Also the description of these parameters is given in Annex 1. Results: At the end α, k and b are displayed on the screen. These values can now be used in the ‘stream_change.dat’ file to calculate the fluxes for the user defined meteor shower or storm with the ‘STREAM.PRO’ program.

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Example: In this example, new values for a Leonid meteor storm with a new ZHRmax of 1000 are calculated. The meteor visual magnitude m is assumed as 0.5. The velocity 71 km/s and the meteor distribution index χ=3.4 as found in table 1 is used. The duration (FWHM) should be 0.125 day (3 hours). Therefore the program yields: α=1.22240 k=1.442700e-18 b=4.88338 Comment: α and k are only influenced by v, χ and ZHRmax, while b also depends on FWHM.

3.3 Application In this chapter tool applications are presented. Results for normal stream flux activities as well as enhanced activities including a Leonid meteoroid storm model are given. A meteor storm is just an intense meteor outburst with Zenithal Hourly Rates above 1000. Presented are examples of the different meteoroid stream flux values that can be calculated by the new tool. These values are: • Zenithal Hourly Rate • Mass Dependent Stream flux • Penetration Stream Flux

3.3.1 Stream Parameter The Zenithal Hourly Rate (ZHR) is the hourly rate of meteors seen by a standard observer under optimum conditions for each stream, as described in [2]. It is given in Annex 1, that the major streams are well represented by a set of exponential curves: ZHR=ZHRmax∗10-b*|λ −λ max| (1) • λ is the solar longitude (shown in Figure 2) • λ max is when the shower or storm maximum occurs • ZHRmax and b are given in Table 1 These values were found by observations specified in [2]. Further the cumulative particle flux in [particles/m2/s] with mass greater or equal m in [kg] can be described by F(m)=k∗m-α (2)

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• m is the minimum meteoroid mass in [kg] • k is a constant • α is the mass distribution index (For F(m)max k and α are presented in Table 1) The cumulative flux for any solar longitude is given as F(m)= F(m)max∗10-b*|λ −λ max| (3) For an assumed Leonid meteoroid storm the parameters α, k and b have to be recalculated. This can be done with the new AKC.PRO tool. Needed are the stream velocity, the ZHRmax , the meteor distribution index χ, the meteor visual magnitude (which can usually be assumed as 0.5) and the full width at half maximum (FWHM), defining the storm duration. The formulas used in Annex 1 are given below. α=2.3∗log(χ) (4) χ, the meteor distribution index with a typical range between 2.4 and 3.5 is given in Table 1. The value 2.3 reflects the relationship between meteoroid mass and meteor visual magnitude. This relationship is also described in Annex 1. k=N(0)/M-α

m=0.5 (5) N(0) is the cumulative flux for zero magnitude meteors. N(0) depends on ZHRmax and the probabilities to observe meteors at certain magnitudes (see Annex 1 for full explanation). Mm=0.5 describes the meteoroid mass for the given magnitude of 0.5. b= -(log(0.5)/t) (6) t=(FWHM/(360/365)/2) (7) t represents the storm duration. Calculated with a given FWHM in [days]. b describes the meteoroid stream slopes of the log-lin activity profiles. Most streams have symmetrical profiles and the slopes are described by a single value of b. Further information see Annex 1. Because b is changing with the storm duration it has to be calculated here. The new parameters α, k and b can now be changed in the stream_change.dat for further use.

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Equator Earth

Sun

S*

VE

AE

P

A

SS WS

A= AphelionAE= Autumnal EquinoxS*= Intersection Ecliptic/EquatorplaneSS= Summer SolsticeVE= Vernal EquinoxWS= Winter Solsticeλ = Solar LongitudeP= Perihelion λ

Figure 2: Schematic, geometrical Solar Longitude Description (the Earth orbit eccentricity is largely enhanced in this figure)

For some useful references data concerning the annual earth orbit the see Annex 8.

Name λ max

[degrees] RAmax

[degrees] ZHR max

v [km/s]

α k b χ

Bootids 283.3 232 133 43 0.92 8.40E-17 1.84 2.5 gVelids 285.7 124 2.4 35 1.1 5.80E-19 0.12 3 aCrucids 294.5 193 3 50 1.06 1.90E-19 0.11 2.9 aHydrusids 300 138 2 44 1.03 3.40E-19 0.2 2.8 aCarinids 311.2 99 2.3 25 0.92 1.30E-17 0.16 2.5 dVelids 318 127 1.3 35 1.1 3.10E-19 0.2 3 aCentaurids 319.4 210 7.3 57 0.83 3.70E-18 0.18 2.3 oCentaurids 323.4 176 2.2 51 1.03 1.90E-19 0.15 2.8 thCentaurid 334 220 4.5 60 0.95 4.40E-19 0.2 2.6 dLeonids 335 169 1.1 23 1.1 1.90E-18 0.049 3 Virginids 340 165 1.5 26 1.1 1.50E-18 0.2 3 gNormids 353 285 5.8 56 0.87 1.90E-18 0.19 2.4 dPavonids 11.1 311 5.3 60 0.95 5.10E-19 0.075 2.6 Lyrids 32.4 274 12.8 49 0.99 2.00E-18 0.22 2.7 mVirginids 40 230 2.2 30 1.1 1.10E-18 0.045 3 eAquarids 46.5 340 36.7 66 0.99 1.50E-18 0.08 2.7 bCoronaAu 56 284 3 45 1.13 1.50E-19 0.2 3.1 aScorpiids 55.9 252 3.2 35 0.92 4.70E-18 0.13 2.5 oScorpiids 72.6 241 5.2 21 1.1 1.40E-17 0.15 3 da.Arietids 77 47 54 38 0.99 2.60E-17 0.1 2.7 gSagitarids 89.2 286 2.4 29 1.06 1.90E-18 0.037 2.9 tCetids 95.7 24 3.6 66 0.92 3.70E-19 0.18 2.5 thOphiuchid 98 292 2.3 27 1.03 3.50E-18 0.037 2.8 tAquarids 98 342 7.1 63 0.92 8.90E-19 0.24 2.5 nPhoenicids 111.2 28 5 48 1.1 2.60E-19 0.25 3

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oCynids 116.7 305 2.5 37 0.99 1.40E-18 0.13 2.7 Capricornid 122.4 302 2.2 25 0.69 8.30E-17 0.041 2 dAquaridsN 124.1 324 1 42 1.19 3.60E-20 0.063 3.3 PiscesAus. 124.4 339 2.9 42 1.16 1.50E-19 0.26 3.2 dAquaridsS 125.6 340 11.4 43 1.19 3.60E-19 0.091 3.3 lAquaridsS 131.7 335 1.5 36 1.19 1.20E-19 0.07 3.3 Perseids 140.2 47 84 61 0.92 1.20E-17 0.2 2.5 kCygnids 146.7 290 2.3 27 0.79 3.00E-17 0.069 2.2 pEridanids 153 51 40 59 1.03 1.70E-18 0.2 2.8 gDoradids 155.7 60 4.8 41 1.03 1.10E-18 0.18 2.8 Aurigids 158.2 73 9 69 0.99 2.90E-19 0.19 2.7 kAquarids 177.2 339 2.7 19 1.03 1.90E-17 0.11 2.8 eGeminids 206.7 104 2.9 71 1.1 2.10E-20 0.082 3 Orionids 208.6 96 25 67 1.13 1.60E-19 0.12 3.1 LeoMinorids 209.7 161 1.9 61 0.99 1.10E-19 0.14 2.7 Taurids 223.6 50 7.3 30 0.83 4.30E-17 0.026 2.3 dEridanids 229 54 0.9 31 1.03 7.50E-19 0.2 2.8 zPuppids 232.2 117 3.2 41 1.22 9.50E-20 0.13 3.4 Leonids 235.1 154 23 71 1.22 3.40E-20 0.39 3.4 Puppids/Vel 252 128 4.5 40 1.06 8.20E-19 0.034 2.9 Phoenicids 252.4 19 2.8 18 1.03 2.50E-17 0.3 2.8 Monocerotid 260.9 100 2 43 1.25 3.30E-20 0.25 3.5 Geminids 262.1 113 88 36 0.95 7.80E-17 0.555 2.6 sHydrusids 265.5 133 2.5 59 1.1 4.70E-20 0.1 3 Ursids 271 224 11.8 35 1.22 8.10E-19 0.61 3.4

Table 1: Main Meteoroid Stream Parameters used in the new tools

3.3.2 Zenithal Hourly Rate (ZHR) As explained before, the Zenithal Hourly Rate (ZHR) is a main parameter for meteoroid stream flux calculations. Typical values are displayed in Table 1. For normal stream activities the STREAM.PRO tool provides the result in Figure 3. It is a summation of the contributions from the 50 given meteoroid streams with a background reference value of 10, which is the same in all ZHR plots. For an assumed Leonid storm with the changed storm parameters ZHRmax=1000 b=4.88, α=1.22, k=1.44*10-18, and FWHM=0.125 (3 hours), the STREAM.PRO program delivers Figure 4. The increased ZHRmax peak at a solar longitude of 235.1 degrees can easily be seen. Figure 5 gives a close up for the solar longitude range between 200 and 280 degrees. If one compare Figure 3 and Figure 4 , it can be seen, that the storm model considers only the storm rate but does not use the common stream activity as well.

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Figure 3: Zenithal Hourly Rate summation for the 50 given meteoroid streams with normal activities for a whole year and a background reference value of 10.

Figure 4: Zenithal Hourly Rate summation for the 50 given meteoroid streams, for a whole year with an assumed Leonid storm (ZHRmax=1000) and a background reference value of 10.

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With a defined solar longitude range between 200 and 280 degrees, the sharp peek for the Leonid storm is shown in Figure 5.

Figure 5: Zenithal Hourly Rate summation with an assumed Leonid storm (ZHRmax=1000), a solar longitude plot range between 200 and 280 degrees and a background reference value of 10.

3.3.3 Mass Dependent Stream Flux As shown in Equation (2) the flux depends on the particle mass. For a given particle density and the assumption of spherical shape, the particle diameter is related to mass by: d=(6∗m/(π∗ρ))1/3 (8) In Table 2 the flux in (particles/m2/s) is presented for given masses in [kg], together with the relevant stream parameters and at the end of table 1 the minimum particle diameter in [cm]. Grün Model reference values are also presented.

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Name ref. α k V [km/s]

ZHRmax

F(1E-10kg)m-2 ∗s-1

F(1E-8kg)m-2 ∗s-1

F(1E-6kg) m-2 ∗s-1

F(1E-4kg) m-2 ∗s-1

F(1E-2kg)m-2 ∗s-1

Bootids 0.92 8.40E-17 43 133 1.331E-07 1.92E-09 2.78E-11 4.02E-13 5.81E-15gVelids 1.1 5.80E-19 35 2.4 5.8E-08 3.66E-10 2.31E-12 1.46E-14 9.19E-17aCrucids 1.06 1.90E-19 50 3 7.564E-09 5.74E-11 4.35E-13 3.30E-15 2.50E-17aHydrusids 1.03 3.40E-19 44 2 6.784E-09 5.91E-11 5.15E-13 4.48E-15 3.90E-17aCarinids 0.92 1.30E-17 25 2.3 2.06E-08 2.98E-10 4.30E-12 6.22E-14 8.99E-16dVelids 1.1 3.10E-19 35 1.3 3.1E-08 1.96E-10 1.23E-12 7.79E-15 4.91E-17aCentaurids 0.83 3.70E-18 57 7.3 7.382E-10 1.62E-11 3.53E-13 7.73E-15 1.69E-16oCentaurids 1.03 1.90E-19 51 2.2 3.791E-09 3.30E-11 2.88E-13 2.50E-15 2.18E-17thCentaurid 0.95 4.40E-19 60 4.5 1.391E-09 1.75E-11 2.21E-13 2.78E-15 3.50E-17dLeonids 1.1 1.90E-18 23 1.1 1.9E-07 1.20E-09 7.56E-12 4.77E-14 3.01E-16Virginids 1.1 1.50E-18 26 1.5 1.5E-07 9.46E-10 5.97E-12 3.77E-14 2.38E-16gNormids 0.87 1.90E-18 56 5.8 9.523E-10 1.73E-11 3.15E-13 5.74E-15 1.04E-16dPavonids 0.95 5.10E-19 60 5.3 1.613E-09 2.03E-11 2.56E-13 3.22E-15 4.05E-17Lyrids 0.99 2.00E-18 49 12.8 1.589E-08 1.66E-10 1.74E-12 1.82E-14 1.91E-16mVirginids 1.1 1.10E-18 30 2.2 1.1E-07 6.94E-10 4.38E-12 2.76E-14 1.74E-16eAquarids 0.99 1.50E-18 66 36.7 1.191E-08 1.25E-10 1.31E-12 1.37E-14 1.43E-16bCorona Au. 1.13 1.50E-19 45 3 2.993E-08 1.64E-10 9.04E-13 4.97E-15 2.73E-17aScorpiids 0.92 4.70E-18 35 3.2 7.449E-09 1.08E-10 1.56E-12 2.25E-14 3.25E-16oScorpiids 1.1 1.40E-17 21 5.2 0.0000014 8.83E-09 5.57E-11 3.52E-13 2.22E-15da.Arietids 0.99 2.60E-17 38 54 2.065E-07 2.16E-09 2.26E-11 2.37E-13 2.48E-15gSagitarids 1.06 1.90E-18 29 2.4 7.564E-08 5.74E-10 4.35E-12 3.30E-14 2.50E-16tCetids 0.92 3.70E-19 66 3.6 5.864E-10 8.48E-12 1.23E-13 1.77E-15 2.56E-17thOphiuchid 1.03 3.50E-18 27 2.3 6.983E-08 6.08E-10 5.30E-12 4.61E-14 4.02E-16tAquarids 0.92 8.90E-19 63 7.1 1.411E-09 2.04E-11 2.95E-13 4.26E-15 6.16E-17nPhoenicids 1.1 2.60E-19 48 5 2.6E-08 1.64E-10 1.04E-12 6.53E-15 4.12E-17oCygnids 0.99 1.40E-18 37 2.5 1.112E-08 1.16E-10 1.22E-12 1.28E-14 1.34E-16Capricornid 0.69 8.30E-17 25 2.2 6.593E-10 2.75E-11 1.15E-12 4.78E-14 1.99E-15dAquarids N 1.19 3.60E-20 42 1 2.86E-08 1.19E-10 4.97E-13 2.07E-15 8.64E-18Pisces Aus. 1.16 1.50E-19 42 2.9 5.972E-08 2.86E-10 1.37E-12 6.55E-15 3.13E-17dAquarids S 1.19 3.60E-19 43 11.4 2.86E-07 1.19E-09 4.97E-12 2.07E-14 8.64E-17lAquarids S 1.19 1.20E-19 36 1.5 9.532E-08 3.97E-10 1.66E-12 6.91E-15 2.88E-17Perseids 0.92 1.20E-17 61 84 1.902E-08 2.75E-10 3.97E-12 5.74E-14 8.30E-16kCygnids 0.79 3.00E-17 27 2.3 2.383E-09 6.27E-11 1.65E-12 4.34E-14 1.14E-15pEridanids 1.03 1.70E-18 59 40 3.392E-08 2.95E-10 2.57E-12 2.24E-14 1.95E-16gDoradids 1.03 1.10E-18 41 4.8 2.195E-08 1.91E-10 1.66E-12 1.45E-14 1.26E-16Aurigids 0.99 2.90E-19 69 9 2.304E-09 2.41E-11 2.53E-13 2.64E-15 2.77E-17kAquarids 1.03 1.90E-17 19 2.7 3.791E-07 3.30E-09 2.88E-11 2.50E-13 2.18E-15eGeminids 1.1 2.10E-20 71 2.9 2.1E-09 1.33E-11 8.36E-14 5.27E-16 3.33E-18Orionids 1.13 1.60E-19 67 25 3.192E-08 1.75E-10 9.64E-13 5.30E-15 2.91E-17LeoMinorids 0.99 1.10E-19 61 1.9 8.738E-10 9.15E-12 9.58E-14 1.00E-15 1.05E-17Taurids 0.83 4.30E-17 30 7.3 8.58E-09 1.88E-10 4.11E-12 8.98E-14 1.97E-15dEridanids 1.03 7.50E-19 31 0.9 1.496E-08 1.30E-10 1.14E-12 9.89E-15 8.61E-17zPuppids 1.22 9.50E-20 41 3.2 1.506E-07 5.47E-10 1.98E-12 7.21E-15 2.62E-17Leonids 1.22 3.40E-20 71 23 5.389E-08 1.96E-10 7.10E-13 2.58E-15 9.36E-18Puppids/Vel 1.06 8.20E-19 40 4.5 3.264E-08 2.48E-10 1.88E-12 1.42E-14 1.08E-16Phoenicids 1.03 2.50E-17 18 2.8 4.988E-07 4.34E-09 3.78E-11 3.30E-13 2.87E-15Monocerotid 1.25 3.30E-20 43 2 1.044E-07 3.30E-10 1.04E-12 3.30E-15 1.04E-17Geminids 0.95 7.80E-17 36 88 2.467E-07 3.11E-09 3.91E-11 4.92E-13 6.20E-15sHydrusids 1.1 4.70E-20 59 2.5 4.7E-09 2.97E-11 1.87E-13 1.18E-15 7.45E-18Ursids 1.22 8.10E-19 35 11.8 1.284E-06 4.66E-09 1.69E-11 6.14E-14 2.23E-16

Diameter in cm: d=(6*m/(π∗ρ))^(1/3) ; ρ=1(g/cm3) =>d[cm] : 0.00576 0.02673 0.12407 0.57588 2.67301

; ρ=2(g/cm3) =>d[cm] : 0.00457 0.02122 0.09847 0.45708 2.12157

Grün-Model: Flux in (particle/m2/yr) : 9.54E+00 1.46E-01 5.97E-04 1.49E-06 3.26E-09

Flux in (particle/m2/s) : 3.03E-07 4.64E-09 1.89E-11 4.73E-14 1.03E-16

Table 2: Mass Dependent Stream Flux for several minimum masses and diameters. Grün Model values for reference and the needed equation values are also included.

Figure 6 shows qualitative each stream flux for masses equal or larger then 10-8 kg during the year. Sequencing Figures 7 - 11 present the summation for the meteoroid stream fluxes in [particles/m2/s] with different minimum particle masses. In each plot a Grün Model straight line gives the corresponding fluxes from the Grün Model as reference.

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Figure 6: All Meteoroid Stream Flux from Table 1, qualitative, with a minimum particle mass of 10-8 kg for a whole year and with linear scales.

Figure 7: Annual Meteoroid Stream Flux with particle masses equal or larger than 10-10 kg and a Grün reference line

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Figure 12 shows the Meteoroid Stream Flux within a solar longitude plot range between 200 and 280 degrees. The minimum particle mass in this case was 10-6 kg. Figure 13 in contrast to Figure 12, gives the Meteoroid Stream Flux including a Leonid storm with the changed storm parameters b=4.88, α=1.22 , k=1.44*10-18, ZHRmax=1000 and FWHM=0.125 (a 3 hour storm duration). The minimum particle mass is again 10-6 kg Figure 14 is an overlapping plot, where the additional flux from the storm is clearly visible (at Solar Longitude 235.1).

Figure 12: Meteoroid Stream Flux for particle masses equal or larger than 10-6 kg in a solar longitude range of 200 and 280 degrees, a Grün reference line and normal stream activity.

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Figure 13: Meteoroid Stream Flux for masses equal or larger than 10-6 kg in a solar longitude range of 200 and 280 degrees and a Leonid storm with a ZHRmax value of 1000 a FWHM=0.125 (3 hours), b=4.88, α=1.22 and k=1.44∗10-18. A Grün reference line is given as well.

Figure 14: Meteoroid Stream Flux for masses equal or larger than 10-6 kg in a solar longitude range between 200 and 280 degrees. Overlapping the Leonid storm and the normal stream flux curves. The additional storm flux contribution is shown at solar longitude 235.1.

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Note: The stream flux contributions are believed to be for masses between 10-4 kg and 10-10 kg. For masses above 10-4 kg and below 10-10 kg, a cut-off for the stream fluxes has to be considered.

3.3.4 Penetration Stream Flux Penetration Stream fluxes depend on the given target thickness and the impact angle, where 0 degrees means a perpendicular impact. Both parameters are taken into account in the ESABASE Thin Plate damage equation, which is shown below in Equation 9. This equation, which is described in Annex 2, yields the critical diameter for penetration. d=(tt/(0.45∗ρ0.519∗v0.875∗cos(α)0.875))0.947 (9) A density of ρ=1.0g/cm3 is assumed. d: Lowest, impacting particle diameter [cm] v: Stream velocity in [km/s] tt: Threshold thickness for penetration [cm] α: Impact Angle [degrees] With equation 8 the minimum particle mass is obtained from the diameter. Equation 2 is used to compute the penetration stream flux. Figure 15 – 26 show the Penetration Stream Flux (summed over all streams) for different target thicknesses (tt=0.2, 0.1 and 0.01 cm), impact angles (α=0 and 45), for normal stream activity as well as for a assumed Leonid storm with the parameters b=4.88, α=1.22 , k=1.44∗10-18, ZHRmax=1000 and FWHM=0.125 (a 3 hour storm duration). It is also postulated that particles from all streams impact with the same, user defined, angle.

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Figure 15: Annual Penetration Stream Flux for a given 0.2 cm target thickness and an 0o impact angle. Also a Grün Model reference line is given.


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Figure 17: Annual Penetration Stream Flux, including a Leonid Storm with a ZHRmax of 1000 and a FWHM of 3 hours is assumed. All for a given 0.2cm target thickness and an 0o impact angle. Also a Grün Model reference line is given.


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Figure 20: Annual Penetration Stream Flux for a given 0.1cm target thickness and an 45o impact angle. Also a Grün Model reference line is given.

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23



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For an assumed Leonid stream or storm with λ max=235o and RA=154o the impact angle for a sun-pointed solar arrays is 81o. An schematic explanation is given in Figure 27. No consideration of the angle between the ecliptic or the equator plane and the stream is made. Figure 28 and Figure 29 give the Penetration Stream Flux (summed over all streams) for 0.1 cm target thickness and an 81o impact angle. Figure 28 represents normal stream activity and Figure 29 includes the Leonid storm with the same values as used before: b=4.88, α=1.22 , k=1.44∗10-18, ZHRmax=1000 and FWHM=0.125 (a 3 hour storm duration). A closer look for that storm gives Figure 30 within a solar longitude plot range between 200 and 280 degrees.

Earth(t=0)

Sun

λ

Leonids

RA

Earth (t>0)

Figure 27: Schematic description for Leonid Stream or Storm direction, in the Earth-Sun system with λ max=235 o and RA=154 o.

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Figure 30: Annual Penetration Stream Flux in a solar longitude range between 200 and 280 degrees. A Leonid Storm with a ZHRmax of 1000 and a FWHM for 3 hours is assumed. All for a given 0.1cm target thickness and an 81o impact angle. Also a Grün Model reference line is given.

4. First Test of ESABASE/DEBRIS Tool

4.1 Deficiencies in the ESABASE/DEBRIS Tool 1) If the ESABASE DEBRIS Tool calculates with the meteoroid model mode, an “upper

mass limit error” message appears. This problem was solved with an implemented cut off.

2) Within the .dmi file the particle size and mass limit had the wrong unit of measurement.

For the given diameter it was corrected into cm and the mass into g.

4.2 Deficiencies in the ESABASE/DEBRIS Tool-Documentation Document Page Mistake Correction

TD 8 brackets around “1+p” g2(t,p)=1+p*(t-1988) TD 28 no opening bracket before c1*m… F(m)=c0{(c1*m… TD 32 unperformed oScorpiids in table2.2.3.1-1

EDM 18 no opening bracket before c1*m… F(m)=c0{(c1*m…

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EDM stands for: ESABASE/DEBRIS release2, Final Report, Enhanced Debris/Micrometeoroid Environment Models and 3D Software Tools TD stands for: ESABASE/DEBRIS Release2, Technical Description

5. Suggestions for future enhancements and applications For further investigations, the following suggestion should be considered: 1. Multiple Wall Ballistic Limit Equation could be used for Penetration Stream Flux

calculations. 2. With the plots, the highest value for certain solar longitude ranges could be given. 3. The physical relevance for the storm model could be investigated. 4. A model for a sun pointed surface should be developed, which considers each stream

direction. 5. One could implement AKC.PRO in STRESM.PRO

REFERENCES [1] HTS

ESABASE/DEBRIS Release2, Technical Description, Aug. 1998 [2] Jenniskens P.

Meteor Stream Activity I, The annual streams, J. Astronomy and Astrophysics 287, 990-1013), 1994

[3] Grün E., Zook H.A., Fechtig H., Giese R.H. Collisional Balance of the Meteorotic Complex, ICARUS 62, pp 244-277, 1985

[4] McBride Neil Modelling the Meteoroid Environment, Version 3, 1998, ESA contract 11540/NL/JG/95

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Documents

TEST OF ESABASE/DEBRIS - Space Environmentspace-env.esa.int/Reports/Final_Report_149_98_BIELER.pdf3) The Zenithal Hourly Rate (ZHR) Output is a PostScript file and/or a screen-plot,