On the Anthropogenic and Natural Injection of Matter into Earth's Atmosphere
aa r X i v : . [ phy s i c s . g e o - ph ] A ug On the Anthropogenic and Natural Injection of Matter into Earth’s Atmosphere
Leonard Schulz a, ∗ , Karl-Heinz Glassmeier a,b a Institut f¨ur Geophysik und extraterrestrische Physik, Technische Universit¨at Braunschweig, 38106 Braunschweig, Germany b Max-Planck-Institut f¨ur Sonnensystemforschung, 37077 G¨ottingen, Germany
Abstract
Every year, more and more objects are sent to space. While staying in orbit at high altitudes, objects at low altitudesreenter the atmosphere, mostly disintegrating and adding material to the upper atmosphere. The increasing number ofcountries with space programs, advancing commercialization, and ambitious satellite constellation projects raise concernsabout space debris in the future and will continuously increase the mass flux into the atmosphere. In this study, wecompare the mass influx of human-made (anthropogenic) objects to the natural mass flux into Earth’s atmosphere dueto meteoroids, originating from solar system objects like asteroids and comets. The current and near future significanceof anthropogenic mass sources is evaluated, considering planned and already partially installed large satellite constella-tions. Detailed information about the mass, composition, and ablation of natural and anthropogenic material are given,reviewing the relevant literature. Today, anthropogenic material does make up about 2.8 % compared to the annualinjected mass of natural origin, but future satellite constellations may increase this fraction to nearly 40 %. For this case,the anthropogenic injection of several metals prevails the injection by natural sources by far. Additionally, we find thatthe anthropogenic injection of aerosols into the atmosphere increases disproportionately. All this can have yet unknowneffects on Earth’s atmosphere and the terrestrial habitat.
Keywords:
Atmosphere, Satellite constellations, Mass influx, Human-made injection, Anthropogenic effect,Meteoroids, Ablation, Meteorite composition
1. Introduction
Earth’s atmosphere is subject to a constant bombard-ment by various objects from space. Most are of naturalorigin, i. e. meteoroids (in the following, the term mete-oroids refers to objects of natural origin without any sizelimit) from comets, asteroids, and even differentiated bod-ies. With the exploration of space, anthropogenic objectslike spacecraft and rocket bodies in orbit around Earthalso enter the atmosphere. Upon reentry, bodies heat upand ablate depending on their physical and chemical prop-erties. This way, matter in form of atoms and aerosols isinjected into the atmosphere.With the steady growth of spaceflight activities withevermore nations operating space programs and the in-crease of commercialization, more and more objects arelaunched into orbit around Earth. This has raised majorconcerns about space debris (Klinkrad, 2006). As a result,standards have been introduced to minimize the amountof orbital debris (ISO Central Secretary, 2019) and spaceagencies like ESA and NASA have introduced guidelinesand requirements, largely accepting those standards (seefor example ESA, 2008; NASA, 2019). A consequence ofthese guidelines is that payload launched into low Earth ∗ Corresponding author
Email addresses: [email protected] (Leonard Schulz), [email protected] (Karl-Heinz Glassmeier) orbit (LEO) has to be disposed of within 25 years afterend of operation. This is achieved by reentry into the at-mosphere. Hence, more and more anthropogenic materialis injected into the atmosphere, raising questions about itssignificance in comparison to the natural injection causedby the ablation of meteoroids, and about possible impactson the atmosphere itself.Several companies have proposed large satellite con-stellations of hundreds to thousands of small spacecraft inLEO providing global internet and other telecommunica-tion services (Liou et al., 2018). The amount of spacecraftto be launched combined with their limited lifetime willdramatically increase the anthropogenic amount of massreentering Earth’s atmosphere in the future. Thus, thefuture influx caused by those satellite constellations needsto be considered in more detail.In this study, we provide a first overview and compar-ison of the natural and anthropogenic injection of matterinto Earth’s atmosphere. We focus on the mass influx, itselemental composition, and the resulting ablation prod-ucts injected into the atmosphere. This is done separatelyfor natural injection (Section 2) and anthropogenic injec-tion (Section 3). The necessary information to qualify themass influx, the elemental composition, and the ablationprocesses has been acquired from many published studies,partly providing conflicting numbers and information. Wetry a best effort summary of all the available information.
Preprint submitted to Advances in Space Research September 1, 2020 ith this information we provide a review of the nat-ural injection and three different scenarios for the anthro-pogenic injection. These scenarios include a present dayanalysis as well as two near-future scenarios taking intoaccount different planned projects for large satellite con-stellations. This allows to compare the relative contribu-tions of human-made objects and natural objects enteringthe atmosphere.
2. Natural injection
Many meteoroids originating from asteroids, comets,material of planetary origin, interplanetary and even in-terstellar dust (see for example Jewitt, 2000; Plane et al.,2017) enter Earth’s atmosphere every day. In this section,we look at the mass, composition and ablation of these me-teoroids and estimate the resulting injection with respectto ablation products and the elemental composition.
The knowledge of the total natural mass flux into Earth’satmosphere is of high importance. The mass influx distri-bution is sort of bimodal with a maximum at a particlemass of about 10 − kg (e. g. Flynn, 2002; Carrillo-S´anchezet al., 2015; Plane et al., 2017) and a second maximum athigh particle masses, although the mass influx increasescontinuously for large objects. Objects in the size range ofa few millimeters to meters, which are the main source ofmeteorites found on Earth, only contribute a small frac-tion of the whole mass (Flynn, 2002). The mass influxdistribution used in this study is displayed in Figure 1.The distribution has two mass ranges with rather highmass input, a small dust particle contribution in the sev-eral microns to mm-size range and large meteoroids in thetens of meters range. Differentiation of these ranges iscrucial because of the different origin, composition andablation of those two groups (see Sections 2.2, 2.3). Thepeak at small meteoroid sizes of several microns to mil-limeters is caused by the large amount of interplanetarydust particles (IDPs) in the solar system. The particlesthemselves have very low masses, but are high in num-ber. They have several sources, mainly various types ofcomets and the asteroid belt, whereas the contribution ofinterstellar material is negligible (Plane et al., 2017).Dust particles are normally defined to be smaller thantenth of microns (Rubin and Grossman, 2010; Koschnyand Boroviˇcka, 2017). However, based on the analysisand modelling of the observations of the zodiacal dustcloud by the Infrared Astronomical Satellite (IRAS) andground based radars as well as various other observations(Nesvorn´y et al., 2010, 2011) we adopt a cutoff size of2 mm. Therefore, the upper mass limit of the IPD popu-lation is roughly 10 − kg (Fig. 1).In contrast, the mass flux peak at high impactor sizesis caused by their high mass, while their impact rate is quite low and decreases with increasing size. Bodies heav-ier than hundreds of tons (larger than several meters in di-ameter) hit Earth once a year, while impacts with objectsseveral ten meters in diameter occur only once in a thou-sand years (Chapman and Morrison, 1994; Zolensky et al.,2006a). However, upon entering Earth’s atmosphere, largeimpactors ablate and disintegrate, leaving behind a trailof aerosols and particles of molecular size. Ablation ma-terial in the atmosphere in form of dust particles seemsto sediment within several months (Klekociuk et al., 2005;Gorkavyi et al., 2013), while we can not rule out that ionsand particles of molecular size remain for a longer time inthe upper atmosphere. Thus, we include large bodies thatimpact Earth at least every 10 years to account for suchablation and disintegration processes.Drolshagen et al. (2017) have calculated the mass in-flux of meteoroids in a size range of 10 − to 10 kg.Their mean model for masses below 10 − kg is based onthe widely used interplanetary flux model of Gr¨un et al.(1985), which is used by NASA (Moorhead, 2020) and isclose to the newest ESA meteoroid flux model IMEM2(Soja et al., 2019). It is derived from different spacecraftin-situ measurements of meteoroids and zodiacal light aswell as lunar impact measurements. The model providesan analytic function of the particle flux at 1 AU. For theintermediate mass range, 10 − to 10 kg, the power lawmodel of Brown et al. (2002) is used, which is based onspacecraft fireball data. For large bodies heavier than 10 ,a similar power law adapted from Stokes et al. (2003) isused.Beside the named studies, Drolshagen et al. (2017) haveincluded measurements from the Hubble Space Telescopesolar array impacts of meteoroids (McDonnell, 2005) aswell as visual data from meteor entries (Koschny et al.,2017) to verify the model of Gr¨un et al. (1985). Addition-ally, studies from Halliday et al. (1996) (fireball data) andSuggs et al. (2014) (lunar impact flashes) were used to findthe best way to connect the models of Gr¨un et al. (1985)and Brown et al. (2002). As Drolshagen et al. (2017) onlybriefly reviewed other studies that also provide estimateson the annual mass influx we shortly discuss these otherstudies.For the large impactor size range, we regard the modelsby Brown et al. (2002) and Stokes et al. (2003) as the cur-rent best models. However, for the IDP mass range, thereis a large difference between the various estimates pro-posed. Plane (2012) reviews several studies, experiments,and models regarding the influx of IDPs into Earth’s at-mosphere. The mass influx estimates vary from 1,800 to100,000 t/yr for the respective mass range. Thus, the IDPmass range needs a more critical discussion to derive a suit-able estimate for the purpose of our study. Four studiesare important here.Nesvorn´y et al. (2010) modelled the zodiacal dust cloudusing IRAS data. They estimated an influx of 100,000 t/yr.A later update (Nesvorn´y et al., 2011), using refined or-bital characteristics of the IPDs based on meteor radar2 -8 -7 -6 -5 -4 -3 -2 -1 Meteoroid diameter (m) -20 -15 -10 -5 Meteoroid mass (kg) M a ss i n f l u x ( t / y r / m a ss de c ade ) IDPs Meteorites & Large impactorsLarge impactors (impactfrequency < 0.1/yr)
Grün et al. (1985) Brown et al. (2002) Stokes et al. (2003)
Figure 1: Variation of the yearly mass influx distribution of Earth’s atmosphere with meteoroid mass. The particle diameter is calculated byusing a density of 2500 kg/m and assuming a spherical shape. The blue data, mainly covering the IDP mass range, are based on the fluxlaw of Gr¨un et al. (1985). The orange data, covering the meteorite and large impactor mass range, are calculated using the power law fromBrown et al. (2002) with a mean impact velocity of 20 km/s. The grey data is calculated using the power law of Stokes et al. (2003), givenin Drolshagen et al. (2017), again using the same average velocity. It covers large impactors which impact Earth less than every 10 years.The influx distribution reflects the mean model from Drolshagen et al. (2017) and was calculated as shown in Appendix A. Exact values aregiven there, too. The annual mass input is 11,509 t for the Gr¨un et al. (1985) model, 863 t from Brown et al. (2002), and 4,349 t from Stokeset al. (2003). data, proposes a more realistic value of about 15,000 t/yr.Hughes (1978, pp. 148–157) used satellite, radar andvisual data of IDP and micrometeor entries to reach anestimate. The IDP mass influx rate of 16,100 t/yr in amass range of 10 − to 10 − kg is widely accepted andpart of the mass influx distribution presented by Flynn(2002).Mathews et al. (2001) analyzed observations of microm-eteor entries into the upper atmosphere measured by thehigh power low aperture (HPLA) radar at the Arecibo ob-servatory. They determine the mass and speed of enteringparticles, reaching estimates of 1,600 and 2,700 t/yr for themass range 10 − to 10 − kg. These are the lowest annualinflux values of all those studies reviewed in Plane (2012).Their mean geocentric velocity of 50 km/s, endorsed bylater measurements with Arecibo (Janches et al., 2006), is much higher than in other observations (Hughes, 1978,pp. 150–155; Gr¨un et al., 1985; Nesvorn´y et al., 2010, 2011;Koschny et al., 2017). Such a large velocity raises ques-tions as it implies that the majority of the dust particlesmoves retrograde in the solar system. This could be due toHPLA radars being unable to detect very slow ( <
15 km/s)and small particles. The lack of detection of smaller parti-cles could explain the quite low influx estimate. von Zahn(2005) discusses further possible shortcomings and biases.Here, we assume that Mathews et al. (2001) significantlyunderestimate the amount of incoming meteors.Love and Brownlee (1993) measured IDP and mete-oroid impacts on the Long Duration Exposure Facility(LDEF). Impact crater size, depth and number were de-termined in order to obtain information about the mass ofeach impactor. Assumptions had to be made concerning3he particle properties, velocity and impact angle. Theintegration of the derived mass distribution yields approx.27,000–40,000 t/yr (Love and Brownlee, 1993; Taylor et al.,1998; Mathews et al., 2001).The estimate of Love and Brownlee (1993) has severaluncertainties as it is based on a mean geocentric particlevelocity of 16.9 km/s. For further detail on the velocitywe refer to Gr¨un et al. (1985); Taylor (1995, 1996); Taylorand Elford (1998); Brown et al. (2005); Drolshagen et al.(2008); ECSS (2008); Nesvorn´y et al. (2010, 2011), andCarrillo-S´anchez et al. (2016). After reviewing all the men-tioned literature, we use the higher geocentric mean veloc-ity (normalized on mass) of 20 km/s for IDPs, as the eval-uations of Taylor and Elford (1998); Brown et al. (2005)seem to incorporate the best combination of relevance andexperimental falsification. A similar velocity is also usedby Drolshagen et al. (2017).Increasing the mean velocity implies a reduction of par-ticle mass. This results in a shift of the mass distribu-tion towards lower masses and reduces the mass influxvalue. Also considering Borin et al. (2009); Cremoneseet al. (2012), a realistic mass influx estimate is a valuebelow 20,000 t/yr.
Results of the studies discussed roughly agree with themass influx estimate by Drolshagen et al. (2017). TheGr¨un et al. (1985) flux model is still widely accepted, andwe use it to determine an annual mass influx for the differ-ent mass decades. For the higher mass ranges, the powerlaws by Brown et al. (2002) and Stokes et al. (2003) areused (Figure 1). For further details see Appendix A.Thus, considering the mass range of objects impact-ing Earth less than every 10 years, 10 − to 10 kg, weyield an annual mass influx of 12,372 t with most of themass (11,509 t) caused by particles with masses lower than10 − kg. The mass flux is dominated by the IDP contri-bution of 10,856 t/yr. For all the mass ranges studied con-siderable differences in the estimation of the mass influxexist. With an error factor 2 we yield a range of 6,186 to24,746 t/yr for the mass influx. IDPs and larger meteoroids have quite different compo-sitions due to different origins. The major contribution tothe IDP flux is thought to originate from Jupiter FamilyComets (JFCs) (Zolensky et al., 2006b; Nesvorn´y et al.,2010; Jenniskens, 2015, pp. 282–283; Yang and Ishiguro,2015; Carrillo-S´anchez et al., 2016). The composition ofIDPs has been examined comprehensively in two studies:Schramm et al. (1989) examined 200 IDPs on their majorelement composition and Arndt et al. (1996) gathered dataon 89 IDPs covering elemental abundances also for mi-nor elements. Both studies only give relative abundances,normalized to Si, Fe, and CI carbonaceous chondrite classabundance. The CI abundance is representative of the so-lar system abundances of elements (Anders and Ebihara, 1982; Anders and Grevesse, 1989) and used for normaliza-tion. The only element with a significant mass fractionnot determined by the two above mentioned studies is hy-drogen. Here, we use the 2.02 wt% value from Anders andGrevesse (1989). The absolute elemental mass abundancesused in following discussions are listed in Table 1. For fur-ther considerations we use mean values. To summarize,a significant fraction of the mass contribution are metal(31 %) and metalloid elements (13 %), while the majorityis nonmetallic (47 %). About 8 % of the mass could not beassigned to an element.
Table 1: Elemental composition of IDPs and meteorites.Z El. Unit Arndtet al.(1996) Schrammet al.(1989) MeanIDP Meteo-rites1 H µ g/g 20200 a µ g/g 24 Be ng/g 315 B ng/g 3776 C wt% 9.7 9.7 0.37 N µ g/g 698 O wt% 30.7 30.7 35.29 F µ g/g 9711 Na µ g/g 3747 5503 4625 593612 Mg wt% 9.3 11.0 10.1 13.613 Al wt% 1.2 0.9 1.1 1.214 Si wt% 12.9 12.9 17.115 P µ g/g 1746 1746 129216 S wt% 3.6 5.3 4.4 2.117 Cl µ g/g 1229 1229 18819 K µ g/g 540 540 76420 Ca wt% 0.3 1.0 0.6 1.321 Sc µ g/g 12 12 822 Ti µ g/g 549 549 67623 V µ g/g 74 74 7124 Cr µ g/g 2199 3590 2894 346625 Mn µ g/g 1644 1644 235526 Fe wt% 17.3 17.9 17.6 25.927 Co µ g/g 337 337 80828 Ni wt% 0.5 0.7 0.6 1.729 Cu µ g/g 186 186 9130 Zn µ g/g 405 405 5731 Ga µ g/g 18 18 732 Ge µ g/g 42 42 1333 As µ g/g 15 15 434 Se µ g/g 32 32 835 Br µ g/g 81 81 136 Rb µ g/g 6 6 237 Sr µ g/g 16 16 1039 Y µ g/g 2 2 240 Zr µ g/g 18 18 7 > µ g/g 16Total (%) 46.4 78.0 91.3 100.0Column 4 to 6 are derived from Arndt et al. (1996) and Schrammet al. (1989) with the sixth column representing the arithmetic meanof both studies. Column 7 is the meteorite composition, taking intoaccount the meteorite portion of each group (Table 2) and the re-spective meteorite group elemental mass abundances. For furtherdetails on the derivation see the text and Appendix B. a The abundance of hydrogen is estimated as described in the text.
By contrast, large meteoroids are mostly of asteroidal4rigin (Bottke et al., 2002; Binzel et al., 2015), only asmall portion originates from comets (Binzel et al., 2004;Fern´andez et al., 2005; DeMeo and Binzel, 2008) or dif-ferentiated bodies (Grady, 2000; Boroviˇcka et al., 2015, p.258; Russell et al., 2015, p. 419). A significant amount ofmaterial can survive upon entry and reaches the groundas meteorites. Therefore, we estimate the average elemen-tal mass abundance of large meteoroids by calculating thecomposition of meteorites found on Earth. Meteorites aredivided into different classes, based on their mineralogyand thus elemental composition. By weighting the com-position of each meteorite class with their respective fre-quency of finds and falls on Earth, we calculate an aver-age meteorite composition. Due to the large amount ofclassified meteorites of more than 22,000, this statisticalapproach is possible. We use the data given in Grady(2000) to yield the frequency of each meteorite class (seeTable 2). For the average elemental mass abundances weuse data from Wasson (1974); Lodders and Fegley (1998);Mittlefehldt et al. (1998); Demidova et al. (2007). The de-rived average composition of each meteorite class as wellas details on the data are provided in Appendix B. Byweighting the elemental mass abundances with the classfrequencies of Table 2, we yield the overall elemental massabundance of meteorites listed in Table 1.The metal (45 %) and metalloid (17 %) elemental abun-dance is higher than in IDPs, while the non-metallic por-tion (38 %) is lower. All in all, IDPs and meteorites showconsiderable differences, but are similar in the abundanceof some elements.The above described method of determination of thecomposition of the large meteoroids is biased, as mete-oroids show different ablation rate and behaviour depend-ing on their composition upon entry into the atmosphere.Thus, the amount of produced meteorites and the finalcomposition to some extend depends on the propertiesof the initial meteoroids. Additionally, some meteoriteclasses are easier to find, e. g. iron meteorites are easierto distinguish from the environment due to their metal-lic look. Also, the number of meteorite finds and falls forsome groups is quite low and the statistical sample mightbe insufficient in that case. Thus, there are uncertaintiesin our approach.
Results from various studies are used to derive ablationproducts of IDPs and larger meteoroids. Three ablationproducts are thought to be important: material due todeposition in the atmosphere in form of atoms, ions ormolecules; material deposited as aerosols, e.g. particles ofmicrons to nm size; material directly reaching the ground,thus not contributing to atmospheric injection.
For small meteoroids, several studies suggest that thereis a cutoff size below which no ablation is taking place,
Table 2: Frequencies of meteorite classes derived from finds and falls(Grady, 2000).
Class Portion (%)Chondrites 91.95Ordinary Chondrites 86.35
H 42.27L 37.72LL 6.36
Carbonaceous Chondrites 3.40
CH 0.08CI 0.04CK 0.54CM 1.18CO 0.62CR 0.57CV 0.36
Enstatite Chondrites 1.22
EH 0.93EL 0.28
Other Chondrites 0.99
K (Kakangari) 0.13R (Rumurutiite) 0.85
Achondrites 3.69
Acapulcoites 0.07Angrites 0.02Aubrites 0.28Brachinites 0.04Lodranites 0.09Ureilites 0.56Winonaites 0.07
From Vesta a Diogenites 0.57Eucrites 1.22Howardites 0.57
Lunar 0.11
Lunaite 0.11
Martian 0.09
Shergottites 0.03Nakhlites 0.03Chassignites 0.03
Stony Irons 0.52
Mesosiderites 0.29Pallasites 0.22
Irons 3.85
IAB 0.76IC 0.06IIAB 0.60IIC 0.05IID 0.09IIE 0.11IIF 0.03IIIAB 1.34IIICD 0.24IIIE 0.08IIIF 0.04IVA 0.37IVB 0.08
Total 100 a Expected to originate from Vesta. due to insufficient heating of the particle. This cutoff sizeranges between meteoroid masses of 10 − to 10 − kg de-pending on the study (Jones and Kaiser, 1966; Nicol et al.,1985; Popova, 2004; Vondrak et al., 2008). Meteoroids be-5ow this size can be treated as part of the aerosol massfraction as they are slowed down to cm/s velocities. Ittakes them weeks to years to reach the ground dependingon their size (Kasten, 1968; Rietmeijer and Jenniskens,1998; Rietmeijer, 2002).Looking at masses higher than the cutoff mass, thereare three models to be considered. Rogers et al. (2005)present a numerical model of the ablation of small mete-oroids in the mass range 10 − to 10 − kg for discrete ve-locities and different meteoroid densities. With the knowl-edge of the velocity distribution of meteoroids in the re-spective size range, an overall estimate of the ablation canbe made. Taylor (1996) state that the velocity distribu-tion of meteoroids from 10 − to 10 − kg is similar. Weuse the velocity distribution from Taylor (1995), tabulatedin ECSS (2008), and recalculate the distribution to an in-cident height of 100 km, thereby taking into account theacceleration due to Earth’s gravity. Values from Rogerset al. (2005) are weighted with that velocity distribution.To come closest to an IDP density of 2,200 kg/m (Carrillo-S´anchez et al., 2016), the mean of the ablated mass fortwo different particle densities of 1,000 and 3,300 kg/m is taken. Thus, we yield a final value for the fraction ofablated mass for the different mass bins (see Figure 2).Small meteoroids with masses above 10 − kg show morethan 90 % ablated mass. Towards lower masses, the frac-tion of ablated material decreases to almost zero. For thismodel, we adopt a cutoff size of 10 − kg and interpolatethe data (also shown in Figure 2). By weighting with theGr¨un et al. (1985) mass influx, an ablated mass fractionof 86 % is obtained. We assume that all of the ablatedmaterial enters the atmosphere in atomic form, as recon-densation of the vaporized material to dust is unlikely dueto the small particle masses.Love and Brownlee (1991) have performed a similarstudy, simulating the atmospheric entry of over 50,000meteoroids. Using their data on the amount of vapor-ized mass, equal to the mass of atoms ablated, and trans-forming the particle diameter to mass by using a den-sity of 3,000 kg/m , we yield the values and interpolationdepicted in Figure 2. Here, we adopt a cutoff mass of10 − kg. Weighting with the Gr¨un et al. (1985) mass in-flux, an ablated mass fraction of 69 % is obtained, whichis considerably lower than the Rogers et al. (2005) esti-mate. Both, Love and Brownlee (1991) and Rogers et al.(2005) show a very small to zero survivability of particlesin the mass range 10 − to 10 − kg. This is supported byRietmeijer (2002).A third study, Carrillo-S´anchez et al. (2016), utilizesthe chemical ablation model CABMOD, introduced byVondrak et al. (2008) incorporating differential ablationof different elements along with the model of the zodiacalcloud (Nesvorn´y et al., 2010, 2011). They use a differentmass distribution and a different velocity distribution witha lower mean velocity than used in our study. For theirmass range of 10 − kg to 10 − kg, only 18.2 % of the ma-terial are ablated atoms. Taking the same mass range, the -20 -15 -10 -5 Meteoroid mass (kg) A t o m i c m a ss f r a c t i on Rogers et al. (2005)Love and Brownlee (1991)
Figure 2: Fraction of mass ablated in atomic form in dependence ofmeteoroid mass. The crosses depict the data points derived from thestudies of Rogers et al. (2005) and Love and Brownlee (1991), whilethe line is the interpolation. two other study interpolations yield a fraction of 85 % and65 %, respectively. Thus, differences to the other two mod-els are large, partly to be explained by the slower averagevelocity and the different mass distribution. In the fol-lowing we use the simulated values of Love and Brownlee(1991).
For large meteoroids, ablation largely reduces the massof entering meteoroids. However, a substantial fractioncan survive atmospheric entry (Rietmeijer, 2002, p. 236;Boroviˇcka et al., 2015, p. 258). The survival fraction,the ratio of the meteoroid’s terminal and initial mass, ishighly dependent on velocity, density, composition and ini-tial mass itself. The dependence of the survival fractionon mass is displayed in Figure 3, which is based on resultsof Halliday et al. (1996); Klekociuk et al. (2005); Popovaet al. (2011, 2013). Data are widely scattered due to thevarious dependencies mentioned above. An average massdependent survival fraction is derived by fitting a scaledRayleigh distribution to all the given data. The startingpoint of the distribution is chosen to be at 10 − kg withno mass survival from 10 − to 10 − kg considering Bald-win and Sheaffer (1971). This fits the results by Love andBrownlee (1991); Rietmeijer (2002); Rogers et al. (2005)and also matches our model of the small meteoroid abla-tion. The resulting survival fraction model S ( m ) with S ( m ) = ( , − ≤ log m < − . log( m )+11 . e − ( log( m )+12 · . ) , − ≤ log m ≤ -2 -1 Meteoroid mass (kg) S u r v i v a l f r a c t i on Average (fitted)Halliday et al. (1996)Popova et al. (2011)Klekociuk et al. (2005)Popova et al. (2013)
Figure 3: Survival rate of large meteoroids. Shown are fireball data from different studies. Errors are depicted if available. The black linedepicts our fitted estimate; for further details see the text. where S denotes the survival fraction, and log m the decadiclogarithm of the meteoroid initial mass, is displayed in Fig-ure 3.In a further step one needs to clarify how much of theablated material is deposited in the atmosphere in atomicor aerosol form. Here, ablated material can recondense todust and also dust particles can leave the fireball as it isablated. Observations of dust clouds are very rare and in-corporate large errors. The Chelyabinsk object created adust cloud of roughly 24 % of the initial mass of approx.1 . · kg (Popova et al., 2013). Klekociuk et al. (2005)provide observational results from an entry of a massivemeteoroid (roughly 1 . · kg). The dust cloud amountedto roughly 79 % of the total meteoroid mass, at least 47 %.TC , a smaller bolide of around 5 · kg produced a dustcloud of about 20 % (at least 15 %) of the initial mete-oroid mass (Boroviˇcka and Charv´at, 2009). Detailed mod-elling of a fireball entry by Boroviˇcka et al. (2019) indi-cates that more fragmentation leads to more dust beingreleased. This would point towards an increase in the dustfraction for larger meteoroids as fragmentation events aremore likely for larger meteoroids. Therefore, we assume alinear increase in the aerosol fraction with increasing log-arithm of mass. For meteoroid masses of 10 − kg, all thematerial is ablated in atomic form in accordance with thefindings in the previous section. The aerosol mass fractionincreases to 50 % for a mass of 10 kg. The mass dependent fraction of the three different abla-tion products is displayed in Figure 4, based on the results from the previous two sections. For nearly every meteoroidmass, the material is injected into the atmosphere eitherin atomic or aerosol form. Only for a very limited massrange significant amounts of the entering meteoroids reachthe ground directly upon entry into the atmosphere.
With the estimates of the mass distribution, the com-position, and the ablation of incoming meteoroids a com-plete picture of the injection of natural matter into Earth’satmosphere is available. The following estimates emerge.12,325 t natural material are entering Earth’s atmosphereevery year. Only 48 t/yr of meteoroids are reaching theground (0.4 % of the whole mass) directly upon entry. Therest is injected into the atmosphere, 8,421 t (68 % of thewhole mass) in atomic form, 3,904 t (32 %) as aerosols.Most of the material is non-metallic (5,674 t), but metalsare also significant (4,047 t). Metalloids take the small-est portion (1,655 t). The most abundant metals are iron(2,295 t) and magnesium (1,300 t), other metals only con-tribute with minor fractions, e. g. aluminum (131 t), nickel(90 t), calcium (88 t) and sodium (59 t). Non-metallic andmetalloid elements with high injection masses are oxygen(3,851 t), silicon (1,654 t), carbon (1,054 t), sulfur (513 t)and hydrogen (220 t).
3. Anthropogenic injection
Since the beginning of the space age, anthropogenicinjection into the upper atmosphere occurs. Decommis-7 -20 -15 -10 -5 Meteoroid mass (kg) M a ss f r a c t i on Aerosol Atomic Meteorites (Ground-reaching)
Figure 4: Estimated fractional mass ablation of meteoroids in dependence of the meteoroid mass. Values are given for each mass decade. Fordetails on the derivation, see the text. Note that all of those values are rough estimates. sioned spacecraft, rocket bodies, and other debris are en-tering Earth’s atmosphere. This is due to the aerodynamicdrag of the atmosphere, which is reducing the speed of or-biting objects even at altitudes as high as 1000 km. Mostof the space components are made of metals.With the ongoing use of space, more and more spacedebris is inserted into orbits around Earth. Space debrishas become a serious problem as it is a hazard to operat-ing spacecraft and even the International Space Station.All the debris in LEO can lead to a cascade effect of de-bris impacting satellites causing even more debris and soforth, possibly rendering whole orbits unusable for decadesto hundreds of years. In order to reduce the amount of fu-ture space debris and ensure safety in space, guidelineshave been introduced (ESA, 2008; ISO Central Secretary,2019; NASA, 2019). For LEO, satellites and upper stageshave to be de-orbited within 25 years after their end oflifetime. Due to the increasing use of space, these require-ments might tighten in the following years and decades.Thus, nearly everything launched into LEO nowadays willburn up in the atmosphere, eventually.
We derive an estimate of the annual mass influx fromthe altitude depending mass distribution around Earth asprovided by Liou et al. (2018). Due to the atmosphericdrag, there is an altitude below which, on average, all ob-jects reenter the atmosphere within one year. With that,the mass entering every year is the sum of the mass of allobjects below this altitude. Using Boykin and Mc Nair(1966) together with data from Bowman (2002); Saunderset al. (2012), we come up with an average reentry altitude of 450 km, roughly matching calculations by Braun et al.(2013). As a result, the annual mass influx amounts toabout 190 t/yr, a value comparable to that one estimatedby Pardini and Anselmo (2013). About 60 % of the massare spacecraft, 40 % rocket bodies. This mass influx valuewill increase in the future as the amount of mass in orbit isrising continuously (Liou et al., 2020). It should be notedthat space debris is large in numbers but contributes onlya negligible part to the anthropogenic mass influx.In a further step, the core stages of launch vehiclesneed to be considered. Although these are accelerated toconsiderable velocities, they remain suborbital and reen-ter the atmosphere right after liftoff. These objects arenot tracked by space agencies and therefore are not in-cluded in the studies by Pardini and Anselmo (2013) andLiou et al. (2018). To estimate the mass contribution bycore stages, we consider the launch history of 2019. Fromeach orbital launch, we consider every rocket stage thatis jettisoned into a suborbital trajectory. Using availabledata on launch profiles, the approximate entry velocity ofeach stage can be calculated. Only stages with entry ve-locities higher than 3.8 km/s are taken into account as weconsider lower entry velocities to be insufficient for signif-icant ablation and contribution to the injection rate intothe atmosphere. Additionally, we neglect launch vehicleswith a payload mass lower than 1 t as well as suborbitalrocket launches. A complete list of the data and sourcesis given in Appendix C. Using the mass of each stage,we estimate about 702 t of rocket stage mass reenteringEarth’s atmosphere in 2019, with speeds from 3.8 to km/sto 7.6 km/s. This mass value will increase in the near fu-ture, too. Summarizing, today’s (2019) annual mass influx8rom anthropogenic sources amounts to about 890 t. Thelargest contribution (87 %) are rocket bodies.
With evermore companies engaging in commercial space-flight, satellite constellation projects have been proposedand some of them already started. Mostly, these projectsaim at providing global telecommunication services for theglobal internet (Liou et al., 2018). Therefore, hundreds tothousands of satellites used as relays will be brought toLEO and eventually, after reaching their end of lifetime,burn up in the atmosphere. In Table 3, proposed and(partially) realized large satellite constellation projects arelisted with additional information such as characteristicsof the satellites or the current status. In total, constella-tions of nearly 110,000 satellites have been proposed. Thetwo constellations of SpaceX and OneWeb are about to op-erate soon (Arianespace, 2020; Krebs, 2020d), others willmost certainly follow.Constellation satellites are launched into relatively loworbits because of the effective range of antennas and la-tency. Some satellites even have to raise and retain theirorbit by themselves using on-board propulsion. Most likely,due to the large number of satellites, some of the satel-lites will fail in orbit due to electronic failure or propul-sion problems. From the first Starlink launch, 3 out of60 satellites did not seem to work properly. Thus, we as-sume a failure rate of 5 % for the satellites, which haveto be replaced. This increases the mass estimate. Ad-ditionally, we expect most of the satellites at high orbits(around 1,000 km) to be de-orbited after service, as manycompanies have already vowed to do so.In order to estimate the total mass influx caused byconstellations, upper stages and core stages of the launch-ing rockets have to be incorporated, too. Depending onthe launch vehicle, the upper stage mass relative to thepayload mass is different. Typical launch vehicles are theFalcon 9 and the Soyuz 2.1 Fregat rockets. The Falcon 9payload is 15.6 t (derived from Krebs, 2020d), that one ofthe Soyuz 2.1 Fregat 5 t (Arianespace, 2020). With theirrespective upper stage and core stage mass (Kyle, 2018;Arianespace, 2012) one can estimate a typical ratio of pay-load to upper (core) stage mass of 0.24 t (0.89 t) per tonlaunched and reentering within years. This is included intothe subsequent calculations. Based on statements fromsome companies, we expect the lifetime for each satelliteto be around 5 years. This means, every 5 years a wholeconstellation has to be replaced.In the following, we consider two scenarios for a possi-ble future mass influx:
This scenario assumes today’s, 2019 based mass influx.To this influx we add that one due to satellite constella-tions most probably installed in the future (constellation projects from Table 3 with bold and normal font type num-ber of satellites). We expect all satellites in LEO to reen-ter Earth’s atmosphere. However, we do not expect thesatellites of OneWeb’s 8,500 km height constellation (seeTable 3) to enter the atmosphere; only their upper andcore stages will reenter and are taken into account. All inall, in 5 years additional 19,411 satellites as well as 585upper stages and 443 core stages will be brought to orbit.With the above mentioned lifetime, failure rate and upperstage and core stage per payload mass, every year, 960 t ofsatellites, 291 t upper stages, and 1,491 t core stages willreenter the atmosphere. All in all, the annual mass influxamounts to 2,742 t/yr. However, a significant portion ofthat material may reach the ground, as discussed furtherdown.
This scenario assumes a doubling of the 2019 mass in-flux. To this influx all of the planned satellite constellationprojects are added. However, from the projected addi-tional 30,000 Starlink and nearly 48,000 OneWeb satel-lites we merely assume 50 % of them being realized. Thus,within 5 years, nearly 75,000 additional satellites, 1,984upper stages, and 1,503 core stages are considered in thisscenario. The total mass influx is estimated at 8,114 t/yr,consisting of 3,153 t satellites, 880 t upper stages, and 4,081 tcore stages.
The composition of satellites and rocket bodies differslargely from the composition of meteoroids. Generally, themetal abundance is way higher as most structural compo-nents are made of alloys. We distinguish between rocketbodies (core stages that reenter right after launch and up-per stages which reach orbit) and spacecraft.Rocket bodies mainly consist of propulsion tanks androcket engines. For composition information of the propul-sion tanks we use the information provided by Henson(2018). Tanks have to withstand the pressure of the loadedfuel and thus are made out of durable alloys. Most com-mon is AA2219 aluminum alloy but newer rockets likeSpaceX’ Falcon 9 are also made out of Al-Li alloys likeAA2198 (Wanhill, 2014). On the other hand, the Centaurtank is manufactured out of 301 stainless steel. Thoserockets using solid rocket motors (e. g. Antares or Vegalaunch vehicles) use D6AC steel or similar for their tanks.Other parts like feedlines, other pressured vessels, and un-pressurized structure are made out of steels, Al-alloys andTi-alloys. Non-metallic materials are rare. They are, forexample, found in thermal insulation and adapters. Basedon the available information and respecting the large vari-ety of materials we assume the following relative composi-tion values as a first estimate: 80 % AA2219 Al-alloy, 5 %AA2198 Al-Li-alloy, 5 % D6AC steel, 5 % 301 steel, 5 %others.9 able 3: Satellite constellation projects with more than 100 satellites and satellite masses greater than 10 kg.
Project Country Satellitemass (kg) Proposedsat. number Height(km) Project Status SourcesStarlink(SpaceX) USA 260 +2824 a b c d +292 1000 1 prototype launched Grant (2019); FCC(2018c)Kepler(Kepler Com-munications) Canada 12–15 d
320 1000 1 prototype launched Grant (2019)Xingyun(CASIC) China 93 156 570 2 satellites launched in 2020 Grant (2019)Satellogic Argentina 37 300 500 8 satellites launched since2016 Lal et al. (2017)Boeing USA + Beside filings at theInternationalTelecommunication Union(ITU), no informationavailable Grant (2019)3ECOM-1 Lichtenstein
Beside ITU filings, noinformation available Grant (2019)
The list might not be complete as companies in this area emerge and disappear rapidly. Reliable information are hard to gather. The fontused for the proposed satellite number (column 4) indicates the probability of realization: an italic font means that the realization is not safeor improbable, normal font implies a high probability for the project realization, and a bold font means that the constellation is granted bythe FCC of the USA and will therefore most likely be materialized or is already in process. Additional information is acquired from companywebsites and satellite launch data. The projects are ordered after their probability of realization and the number of spacecraft. a SpaceX currently has approval for 1,548 satellites at 550 km altitude and 2,825 satellites at 1,110–1,325 km altitude. They have filed for amodification of the orbit altitude to 540–570 km and reduction to 2,824 satellites. As earlier modifications of this kind were successful, it islikely this gets granted. b OneWeb has authorization of the launch of 720 satellites at this altitude but company statements suggest only 648 are needed. c OneWeb filed at the FCC for a doubling of that number, but has withdrawn that request. d Prototype mass.
Spacecraft and upper stages entering the atmospherehave a much longer interaction time than meteoroids dueto their shallower entry angle and small entry velocity ofabout 7 km/s. This is due to these anthropogenic ob-jects approaching almost circular orbits during the reentryphase. Therefore, their ablation is largely different fromthat one of meteoroids. Anthropogenic material reachestemperatures of 850 to 1950 K (Rochelle et al., 1997; Ailoret al., 2005; Lips et al., 2017) while meteoroids and fireballscan reach temperatures above 3000 K (Boroviˇcka, 1993;Jenniskens, 2004). This strong difference in temperatureand the different materials imply different ratios of theatomic and aerosol ablation for meteoroids/fireballs andanthropogenic material. In need of better data, we as-sume a higher aerosol fraction (75 %) for the anthropogenicmaterial while that one of meteoroids is only about 30 %(compare with Figure 4). This is due to higher tempera-tures causing transition into the gas and/or plasma phase.Due to the lower ablation temperature and the highmass (in the order of tons) of the anthropogenic material,a significant fraction of their mass reaches the ground. To-day, survival rates of human-made objects are expected torange between 5 to 40 % (Ailor et al., 2005; Anselmo andPardini, 2005; Pardini and Anselmo, 2019). Simulationswith reentry software indicate values in this range, too(Anselmo and Pardini, 2005; Klinkrad et al., 2006; Kelleyet al., 2010). The thermal ablation of spacecraft and up-per stages differs as well due to the different structure. Forspacecraft, we assume an average survivability of 20 %, forupper stages 35 %, and for core stages 70 %. Large constel-lation satellites are estimated to burn up completely in theatmosphere (Space Exploration Technologies Corporation,2016, 2018; WorldVu Satellites Limited, 2016).
Combining all the information about the annual an-thropogenic mass influx, composition, and atmosphericprocessing provides the following estimates for today’s in-jection and the two different future scenarios emerge.
Currently, 892 t of anthropogenic material enters Earth’satmosphere every year of which 88 t are injected in atomicform; aerosols make up 263 t. The remaining material(541 t) reaches the ground. From the injected elements,aluminum is most abundant with 211 t, followed by iron(36 t), nickel (23 t), and copper (15 t). Metals make up atleast 86 % of the injected material.
For Scenario 1, the annual anthropogenic mass influxincreases drastically to 2,742 t. 1,573 t are injected intothe atmosphere, 1,180 t as aerosols, 393 t in atomic form.Again, aluminum is the largest part of the injection with807 t, followed by iron (159 t), nickel (89 t), and silicon11 able 4: Anthropogenic and natural injection for the different ablation products. Masses are given in t/yr. Numbers in parenthesis are thepercentage compared to the value of the natural material in the respective column.
Atomic Aerosol Total injection Ground-reachingAnthropogenic Today 88 (1.0) 263 (6.7) 351 (2.8) 541 (1,138)Scenario 1 393 (4.7) 1,180 (30.2) 1,573 (12.8) 1,168 (2,458)Scenario 2 1,226 (14.6) 3,678 (94.2) 4,904 (39.8) 3,210 (6,753)Natural 8,421 3,904 12,325 48
Table 5: Anthropogenic and natural injection per element group. Masses are given in t/yr. The numbers in parenthesis depict the percentagecompared to the natural injection value in the respective column.
Metals Metalloids Non-metals Not assignable Total injectionAnthropogenic Today 305 (7.5) 12 (0.7) 1 (0.02) 33 351 (2.8)Scenario 1 1,189 (29.4) 123 (7.4) 10 (0.2) 252 1,573 (12.8)Scenario 2 3,643 (90.0) 406 (24.6) 32 (0.6) 822 4,904 (39.8)Natural injection 4,047 1,655 5,674 949 12,325 (76 t). Again, most of the injected material is metal (atleast 75 %).
For Scenario 2, the annual anthropogenic mass influxincreases even more to 8,114 t from which 4,904 t are in-jected into the atmosphere. Aerosols contribute 3,678 t,material of atomic form 1,226 t. The order of the mostinjected elements is the same as in Scenario 1 with alu-minum (2,467 t), iron (496 t), nickel (272 t), and silicon(251 t). The metal portion is at least 74 %.
4. Final results and comparison
With all the available information, the natural andanthropogenic injection can be tabulated and compared.Three aspects have been evaluated in this study: the in-jection by ablation products (Table 4), by element group(Table 5), and the injection of selected elements (Table 6).Today, the injection into the atmosphere is dominated bynatural material. About 2.8 % of the mass is of humanorigin. Although metals are highly abundant in space-craft and rocket bodies, the anthropogenic metal injectionis also well below the natural metal injection. However,there are elements which are injected mainly by human-made objects, for example aluminum or copper. The an-thropogenic injection can also prevail the natural injectionfor some specific elements that are not very abundant inthe solar system and therefore in meteoroids, e. g. germa-nium.With the incorporation of large satellite constellations,the injection situation changes strongly. The near futureScenario 1 predicts 1,573 t of anthropogenic material in-jected into the atmosphere, which is already 12.8 % of thenatural injection. For the extreme Scenario 2 we inferan anthropogenic mass injection rate of about 39.8 % ofthe natural rate. For metals, the injection is even higher with 29.4 % (Scenario 1) and even 90.0 % (Scenario 2)of the natural metal injection, respectively. Additionally,there are more elements for which the anthropogenic in-jection surpasses the natural injection: for example tita-nium (2459 %), chromium (131 %), and nickel (304 %) forScenario 2. Satellite constellations also lead to a massiveenhancement of the injection of aluminum and copper.The anthropogenic injection also increases the injectionof aerosols disproportionally as we estimate the entry ofhuman-made objects to produce more aerosols than atoms.Today, human-made bodies make up 6.7 % compared tothe natural injection, while atomic material is only at1.0 %. For future satellite constellations, the aerosol frac-tion increases to 30.2 % and 94.2 % for the two scenarios.
Table 6: Anthropogenic and natural injection of some selected ele-ments. Masses are given in t/yr. The numbers in parenthesis depictthe percentage compared to the natural injection value in the respec-tive row. Note that percentages larger than 100 % indicate that theseelements are mainly of anthropogenic origin. For some elements, noanthropogenic abundances were calculated.
El. Anthropogenic NaturalinjectionToday Scenario 1 Scenario 2H 220C 0.1 (0) 0.2 (0) 0.5 (0) 1,054O 3,851Mg 0.04 (0) 0.1 (0) 0.3 (0) 1,300Al 211 (161) 807 (614) 2,467 (1,877) 131Si 8 (0) 76 (5) 251 (15) 1,654S 513Ti 7 (100) 52 (754) 171 (2,459) 7Cr 7 (20) 17 (47) 48 (131) 37Fe 36 (2) 160 (7) 496 (22) 2,295Ni 23 (25) 89 (99) 272 (304) 90Cu 15 (720) 38 (1,747) 106 (4,923) 2Ge 4 (776) 37 (7,973) 124 (26,435) 0.5 . Conclusion The extensive review, analysis, and estimates presentedin this study provide an overview on the natural and an-thropogenic injection of matter into Earth’s atmosphere.At the present time, the anthropogenic injection alreadycontributes a non-negligible amount of mass to the injec-tion. With large satellite constellations, proposed andstarted from companies all over the world, the anthro-pogenic injection will become significant compared to thenatural injection. Although many of the values used to es-timate the injection inhibit uncertainties due to differentscientific results on many topics or insufficient data, theresults of this study should raise attention and also con-cern towards the alteration of Earth’s atmosphere due tothe reentry of human-made spacecraft and rocket bodies.Especially looking at metals, the anthropogenic injectionmay well exceed 30 % of the whole material deposited inthe upper atmosphere every year. Overall, in the nearfuture we need to be prepared that the injection of an-thropogenic material will increase to 12.8 % – 39.8 % ofthe natural injection. Those values clearly show that theanthropogenic injection is not negligible in the near futureand requires further consideration with respect to theirimpact on Earth’s atmosphere.The uncertainties involved demonstrate that more re-search needs to be done to clarify the significance of theeffects of the human use of space on Earth’s habitat. Thereare many different possible effects on the atmosphere thatmay be caused by an increased injection. For example,the large amount of aerosols injected by the ablation ofanthropogenic material may have an effect on Earth’s cli-mate as aerosols in the high-altitude atmosphere have anegative radiative forcing effect Lawrence et al. (2018).Beside the intensively discussed problem of space de-bris (e. g. Klinkrad, 2006) we conclude that the re-entry ofhuman-made objects into the upper atmosphere may havea significant effect on our habitat and needs more attentionin future studies. Advances in technology and a strongerand stronger use of Earth’s environment always have sideeffects that are most often not perceived at the beginningof innovation and progress.
Acknowledgements
The authors thank Carsten Wiedemann, Martin Sippel,Sven Stappert, Gerhard Drolshagen, and J¨urgen Blum forhelpful discussions.
Appendix A.
The annual mass influx per mass decade shown in Fig-ure 1 is derived separately for the three different massranges. For masses between 10 − to 10 − kg, the inter-planetary flux model from Gr¨un et al. (1985) with the flux at 1 AU given as F ( m ) = (2 . · m . + 15) − . + 1 . · − ( m + 10 m + 10 m ) − . + 1 . · − ( m + 10 m ) − . (A.1)is used. The mass influx in a mass range between themasses m and m can be calculated by integrating overthe flux F ( m ) and multiplying with Earth’s surface S E =4 π · (6 . · m ) and the gravity enhancement factor G = 1 .
445 (see Drolshagen et al., 2017). Here, an incidentatmospheric altitude of 100 km is used. Additionally, thenumber of seconds in a year T = 3 . · has to bemultiplied to yield the annual mass influx, then given as M Gr¨un = S E · G · T · Z m m F ( m ) d m. (A.2)In the mass range from 10 − to 10 kg and 10 to10 kg, the power laws from Brown et al. (2002) andStokes et al. (2003) N Brown ( E ) = 3 . E − . (A.3) N Stokes ( E ) = 2 . E − . (A.4)are used, respectively. The latter one is obtained fromDrolshagen et al. (2017). N ( E ) represents the cumulativenumber of meteoroids with a kinetic energy greater than E impacting Earth every year, where E is in units of ktTNT equivalent. With an average meteoroid velocity of20 km/s and 1 kt TNT equivalent = 4 . · J, the en-ergy dependence can be transformed to a dependence ofmass: N Brown ( m ) = 2 . · m − . (A.5) N Stokes ( m ) = 6 . · m − . (A.6)with m the mass in kg. So N ( m ) represents the number ofmeteoroids of a mass greater than m hitting Earth everyyear.To yield the annual mass influx from these power laws,further calculations are necessary (e. g. compare with Blandet al., 1996, Appendix A). The number of meteoroids im-pacting per year in a mass range from m to m can beexpressed by N ( m ) − N ( m ) = − Z m m d N ( m )d m d m. (A.7)To yield the annual mass influx M in the respective massrange, the mass has to be incorporated in the integral bymultiplication: M = − Z m m m d N ( m )d m d m. (A.8)This way, we yield the annual mass influx for both models13 able A.7: Annual mass influx of meteoroids into Earth’s atmospherefor each mass decade (values of Figure 1). log m (kg) M (t/yr) log m (kg) M (t/yr)-21 0.02 -5 384-20 0.03 -4 184-19 0.04 -3 86-18 0.09 -2 42-17 0.26 -1 53-16 1.0 0 67-15 4.3 1 84-14 18 2 106-13 85 3 133-12 367 4 168-11 1,125 5 211-10 2,193 6 (264)-9 2,671 7 (429)-8 2,213 8 (696)-7 1,410 9 (1,129)-6 768 10 (1,831) The mass influx M is given for the interval of the object mass log m to log ( m ) + 1. For example, 384 t of meteoroids in the mass rangefrom 10 − to 10 − kg impact Earth every year. The values derivedfrom Stokes et al. (2003) are in parenthesis as they are not includedin the annual mass influx in this study. in the mass range from m to m M Brown = Z m m . · m − . d m (A.9) M Stokes = Z m m . · m − . d m. (A.10)Taking the respective valid mass ranges of each model(given above and in Figure 1), the integration yields M Gr¨un =11 ,
509 t/yr, M Brown = 863 t/yr, and M Stokes = 4 ,
349 t/yr.The values for each mass decade, depicted in Figure 1, aregiven in Table A.7. Remember that only the mass valuesfrom M Gr¨un and M Brown (so masses in a range from 10 − to 10 kg) are counted to the annual mass influx used inthis paper. Appendix B.
The elemental mass abundances of meteorites are givenin Table B.8. Compositions are derived from the follow-ing sources: Chondrites, namely ordinary chondrites (H,L, and LL), carbonaceous chondrites (CH, CI, CK, CO,CR), Kakangari and Rumurutiites chondrites (K and R),and enstatite chondrites (EH and EL) from Lodders andFegley (1998, Tables 16.10 and 16.11); most achondrites,namely Acapulcoites (Acap), Angrites (Angr), Aubrites(Aubr), Brachinites (Brac), Diogenites (Diog), Eucrites (Eucr), Howardites (How), Lodranites (Lodr), Shergot-tites (Sher), Nakhlatites (Nak), Chassignites (Chas), Ure-ilites (Ur), and Winonaites (Wino) from Lodders and Fe-gley (1998, Tables 16.11, 16.17, and 16.18) and Mittle-fehldt et al. (1998, Tables 6, 8(4), 19, 21, 22, 26, 34, 35,and 40); lunar achondrites, so called Lunaites (Luna) fromDemidova et al. (2007); stony irons, namely Mesosiderites(Meso) and Pallasites (Pal) from Mittlefehldt et al. (1998,Tables 13 (main group), 14 (main group), 15 (main group),16 (all except Eagle Station), 17 (all except Eagle Station),45(1), 46 (all except the last three)) and Wasson (1974, Ta-bles II-5 and II-7(Ni)); and for Irons (IAB to IVB) fromMittlefehldt et al. (1998, Tables 3 and 8 (1 & 9)) and Was-son (1974, Table II-5). In a few cases, some abundanceswere estimated (mainly oxygen) considering similar mete-orite subgroups to complement the data. The total massabundance of all meteorites is shown in the last column.It is the product of the meteorite abundance with the re-spective elemental composition normalized to 100 % of themass. Thus, it represents the overall elemental composi-tion of meteorites found on Earth. This is used as theaverage elemental composition of meteorites given in thelast column of Table 1.14 able B.8: Elemental compositions of meteorite groups.
Z El. Unit H L LL CH CI CK CM CO CR CV EH EL K R Acap
Fraction → wt% 42.27 37.72 6.36 0.08 0.04 0.54 1.18 0.62 0.57 0.36 0.93 0.28 0.13 0.85 0.071 H µ g/g 20200 14000 700 28003 Li µ g/g 1.7 1.85 1.8 1.5 1.4 1.5 1.8 1.7 1.9 0.74 Be ng/g 30 40 45 25 40 50 215 B ng/g 400 400 700 870 480 300 10006 C µ g/g 2100 2500 3100 7800 34500 2200 22000 4400 20000 5300 3900 4300 5807 N µ g/g 48 43 70 190 3180 1520 90 620 80 420 2408 O wt% 35.7 37.7 40
37 28 31
30 34 µ g/g 125 100 70 60 20 38 30 24 155 14011 Na µ g/g 6110 6900 6840 1800 5000 3100 3900 4200 3300 3400 6880 5770 6800 6630 661912 Mg wt% 14.1 14.9 15.3 11.3 9.7 14.7 11.5 14.5 13.7 14.3 10.73 13.75 15.4 12.9 15.813 Al wt% 1.06 1.16 1.18 1.05 0.865 1.47 1.13 1.4 1.15 1.68 0.82 1 1.3 1.06 1.2414 Si wt% 17.1 18.6 18.9 13.5 10.64 15.8 12.7 15.8 15 15.7 16.6 18.8 16.9 18 18.015 P µ g/g 1200 1030 910 950 1100 1030 1210 1030 1120 2130 1250 1400 170616 S wt% 2 2.2 2.1 0.35 5.41 1.7 2.7 2.2 1.9 2.2 5.6 3.1 5.5 4.07 2.7617 Cl µ g/g 140 270 200 700 260 430 280 250 570 230 10019 K µ g/g 780 920 880 200 550 290 370 360 315 360 840 700 710 780 51620 Ca wt% 1.22 1.33 1.32 1.3 0.926 1.7 1.29 1.58 1.29 1.84 0.85 1.02 1.22 0.914 1.2021 Sc µ g/g 7.8 8.1 8 7.5 5.9 11 8.2 9.5 7.8 10.2 6.1 7.7 7.9 7.75 8.6322 Ti µ g/g 630 670 680 650 440 940 550 730 540 870 460 550 700 900 50523 V µ g/g 73 75 76 63 55 96 75 95 74 97 56 64 73 70 8724 Cr µ g/g 3500 3690 3680 3100 2650 3530 3050 3520 3415 3480 3300 3030 3600 3640 422925 Mn µ g/g 2340 2590 2600 1020 1940 1440 1650 1620 1660 1520 2120 1580 2400 2960 285226 Fe wt% 27.2 21.75 19.8 38 18.2 23 21.3 25 23.8 23.5 30.5 24.8 24.7 24.4 22.827 Co µ g/g 830 580 480 1100 505 620 560 680 640 640 870 720 750 610 78928 Ni wt% 1.71 1.24 1.06 2.57 1.1 1.31 1.23 1.42 1.31 1.32 1.84 1.47 1.46 1.44 1.4429 Cu µ g/g 94 90 85 120 125 90 130 130 100 104 215 120 11030 Zn µ g/g 47 57 56 40 315 80 180 110 100 110 290 18 145 150 20531 Ga µ g/g 6 5.4 5.3 4.8 9.8 5.2 7.6 7.1 6 6.1 16.7 11 8.2 8.1 8.9932 Ge µ g/g 10 10 10 33 14 26 20 18 16 38 30 1633 As µ g/g 2.2 1.36 1.3 2.3 1.85 1.4 1.8 2 1.5 1.5 3.5 2.2 2.4 1.9 2.1934 Se µ g/g 8 8.5 9 3.9 21 8 12 8 8.2 8.7 25 15 20 14.1 9.7535 Br µ g/g 0.5 0.5 1 1.4 3.5 0.6 3 1.4 1 1.6 2.7 0.8 0.9 0.55 0.237 Rb µ g/g 2.3 2.8 2.2 2.3 1.6 1.3 1.1 1.2 3.1 2.3 1.7 0.238 Sr µ g/g 8.8 11 13 7.3 15 10 13 10 14.8 7 9.439 Y µ g/g 2 1.8 2 1.56 2.7 2 2.4 2.6 1.240 Zr µ g/g 7.3 6.4 7.4 3.9 8 7 9 5.4 8.9 6.6 7.241 Nb ng/g 400 400 250 400 400 500 50042 Mo µ g/g 1.4 1.2 1.1 2 0.92 0.38 1.4 1.7 1.4 1.8 0.944 Ru ng/g 1100 750 1600 710 1100 870 1080 970 1200 930 770 850 960 67045 Rh ng/g 210 155 140 180 160 17046 Pd ng/g 845 620 560 560 580 630 710 690 710 820 73047 Ag ng/g 45 50 75 200 160 100 95 100 280 85 5048 Cd ng/g 5.5 30 40 690 420 8 300 350 705 35 30 2049 In ng/g 0.8 10 10.5 80 50 25 30 32 85 4 3 450 Sn ng/g 350 540 1700 490 790 890 730 680 136051 Sb ng/g 66 78 75 90 135 60 130 110 80 85 190 90 150 72 8352 Te ng/g 520 460 380 2300 800 1300 950 1000 1000 2400 930 2000 110053 I ng/g 60 70 430 200 270 200 160 210 8055 Cs ng/g 98 240 150 190 110 80 84 90 210 125 5056 Ba µ g/g 4.4 4.1 4 3 2.35 4.7 3.1 4.3 3.4 4.55 2.4 2.857 La ng/g 301 318 330 290 235 460 320 380 310 469 240 196 320 310 46859 Ce ng/g 763 970 880 870 620 1270 940 1140 750 1190 650 580 83059 Pr ng/g 120 140 130 94 137 140 174 100 7060 Nd ng/g 581 700 650 460 990 626 850 790 919 440 37062 Sm ng/g 194 203 205 185 150 290 204 250 230 294 140 149 200 180 22363 Eu ng/g 74 80 78 76 57 110 78 96 80 105 52 54 80 72 9664 Gd ng/g 275 317 290 290 200 440 290 390 320 405 210 19665 Tb ng/g 49 59 54 50 37 51 60 50 71 34 32 5866 Dy ng/g 305 372 360 310 250 490 332 420 280 454 230 245 29 46867 Ho ng/g 74 89 82 70 56 100 77 96 100 97 50 51 5968 Er ng/g 213 252 240 160 350 221 305 277 160 16069 Tm ng/g 33 38 35 40 25 35 40 48 24 2370 Yb ng/g 203 226 230 210 160 320 215 270 220 312 154 157 215 216 24171 Lu ng/g 33 34 34 30 25 46 33 39 32 46 25 25 33 32 3672 Hf ng/g 150 170 170 140 105 250 180 220 150 230 140 210 150 16173 Ta ng/g 21 21 14 1974 W ng/g 164 138 115 150 93 180 160 150 110 160 140 140 18075 Re ng/g 78 47 32 73 38 60 50 58 50 57 55 57 43 6076 Os ng/g 835 530 410 1150 490 815 670 805 710 800 660 670 550 690 69377 Ir ng/g 770 490 380 1070 465 760 580 740 670 730 570 560 550 610 79878 Pt µ g/g 1.58 1.09 0.88 1.7 1 1.3 1.1 1.24 0.98 1.25 1.29 1.25 1 1.379 Au ng/g 220 156 146 250 145 120 150 190 160 153 330 240 220 183 21780 Hg ng/g 30 22 310 6081 Tl ng/g 0.5 2.4 15.5 142 92 40 60 58 100 7 3 2082 Pb ng/g 240 40 2500 800 1600 2150 1100 1500 24083 Bi ng/g 5 14 12.5 110 20 71 35 40 54 90 13 25 2790 Th ng/g 38 42 47 29 58 41 80 42 58 30 38 5092 U ng/g 13 15 15 8 15 12 18 13 17 9.2 7 25 Total % 101.9 100.8 101.6 99.7 100.4 99.1 100.0 100.7 99.3 99.6 97.2 96.8 98.1 98.4 100.6 able B.8 (continued) Z El. Unit Angr Aubr Brac Diog Eucr How Lodr Luna Sher Nak Chas Ur Wino Meso Pal
Fraction → wt% 0.02 0.28 0.04 0.57 1.22 0.57 0.09 0.11 0.03 0.03 0.03 0.56 0.07 0.29 0.221 H µ g/g3 Li µ g/g 5.4 3.5 3.7 3.9 1.44 Be ng/g5 B ng/g6 C µ g/g 3000 500 265 200 8507 N µ g/g8 O wt% 40.9 46.4
36 43.3
40 39 37
35 23.5 µ g/g 43.5 57 1511 Na µ g/g 179.2 3692 2805 896 3095 1568 760 2595 9700 3200 920 743 3720 1327 11312 Mg wt% 7.84 22.7 17.3 14.6 4.8 9.2 16.8 3.8 6.19 7.55 19.2 20.6 14.6 5.2 12.613 Al wt% 5.66 0.58 0.60 0.97 6.84 4.50 0.23 11.60 3.42 1.1 0.42 0.26 0.7 2.43 0.02414 Si wt% 18.8 26.8 17.4 24.4 22.9 23.3 15.1 21.0 23.8 22.3 17.5 18.2 15 12.4 8.315 P µ g/g 556 1200 724 720 1787 1484 370 2715 1230 275 1463 1035516 S wt% 0.59 0.61 1.52 0.12 0.138 0.077 0.62 0.16 0.0335 0.026 2 1.78 1.3117 Cl µ g/g 23 19 122.5 72.5 3419 K µ g/g 179 370 29.5 331 138 64 536 1305 985 300 66 337 166 5.420 Ca wt% 11.5 0.62 1.68 1.43 7.27 4.72 1.34 10.46 7.18 10.05 0.47 0.93 0.00082 2.22 0.2621 Sc µ g/g 43.8 10.9 17.5 51.8 20.7 7.2 24.5 53.5 54.5 5.3 8.1 8.1 16.5 0.6422 Ti µ g/g 7209 644 1160 862 3432 2775 320 5687 4810 2280 480 600 859 1523 V µ g/g 93 115 75 117 78 23 300 180 40 118 55 4024 Cr µ g/g 1078 182 4045 8889 2657 5490 4536 1221 1805 1525 5240 8391 1950 5992 562225 Mn µ g/g 1433 480 2565 4294 4079 4002 2739 1042 3945 3850 4120 3024 2070 2478 188726 Fe wt% 13.9 1.0 22.8 13.3 12.6 13.4 31.1 7.7 14.6 16.4 21.2 13.8 19.8 46.3 46.227 Co µ g/g 23.5 299 20.4 7.0 23.4 783 25.6 38 45.5 123 102 761 1199 3.528 Ni wt% 0.0047 0.41 0.0054 0.0012 0.0244 1.3 0.0119 0.00635 0.0093 0.05 1.02 1.21 4.52 10.0029 Cu µ g/g 2.5 8 16 12 2.630 Zn µ g/g 1.47 239 0.71 1.24 26 120 64.5 66 72 230 131 3.031 Ga µ g/g 4.9 0.18 1.7 0.75 6.0 3.6 15 3 0.7 4.9 10.932 Ge µ g/g 0.020 0.14 0.765 2.75 0.01 37.533 As µ g/g 0.37 0.197 1.5 0.0375 0.0825 0.008 269 2.5734 Se µ g/g 8.0 0.4 0.23 0.25 6.3 0.35 0.075 0.04 1.6 11.2 9.635 Br µ g/g 0.41 0.10 0.21 0.855 2.435 0.088 0.2737 Rb µ g/g 2 0.1 0.13 0.32 3.1 6 3.3 0.7338 Sr µ g/g 15 1.7 65.9 31 143 46.5 67 7.239 Y µ g/g 1.2 17.8 19 3.85 0.640 Zr µ g/g 2.7 3 30 17 80 65 9.1 2.141 Nb ng/g 2700 5050 1530 34042 Mo µ g/g 0.015 0.37 0.08644 Ru ng/g45 Rh ng/g46 Pd ng/g 2 0.4 10 1.75 15.85 0.1547 Ag ng/g 11 30.0 19 49 2.648 Cd ng/g 21 13 47 94 14 1949 In ng/g 3.2 0.92 25 20 450 Sn ng/g 10 60051 Sb ng/g 56 11 7.2 62 45 7.1 40 0.9 12152 Te ng/g 5 5.3 2.45 4.75 5053 I ng/g 25 40 97 24 140 1055 Cs ng/g 200 1.1 3.85 20 400 355 3756 Ba µ g/g 12 34.1 14 65 30 28 7.657 La ng/g 3545 365 154 2373 1214 80 5373 1835 1960 530 69 190 136659 Ce ng/g 10350 1600 315 7185 2668 14065 4600 5345 1120 469859 Pr ng/g 970 280 810 735 13060 Nd ng/g 860 110 4960 1400 9228 3475 3160 62062 Sm ng/g 2828 135 147 1440 680 58 2785 1290 805 140 26 90 30863 Eu ng/g 956 57 41 560 276 27 925 537.5 230 45 10 48 17364 Gd ng/g 240 2348 905 744 2540 890 11065 Tb ng/g 803 65.5 409 200 23 653 380 120 30 8266 Dy ng/g 175 2990 893 313 930 2850 860 20067 Ho ng/g 48 758.75 230 211 710 162.5 4468 Er ng/g 140 1740 590 1740 385 9069 Tm ng/g 50 20 280 1000 300 5270 Yb ng/g 2590 154 281 1526 790 173 2343 1450 360 110 73 157 40871 Lu ng/g 380 43 23 228 124 30 336 227.5 53.5 15 12 24 6172 Hf ng/g 1800 205 1317 1760 80 2044 1850 275 100 25573 Ta ng/g 240 29 193 84 148 225 40045 2074 W ng/g 6.5 30 558 535 260 4675 Re ng/g 0.06 0.0053 0.0375 0.033 0.06 9976 Os ng/g 0.7 0.008 460 0.26 0.3035 1.6 122077 Ir ng/g 2.4 117 3.6 4.57 14.9 194 5.1 0.045 0.155 2.1 247 1150 3578 Pt µ g/g 0.0017 0.0027 0.005379 Au ng/g 38 0.9 2.7 169 2.8 1.46 0.36 0.73 30 265 3380 Hg ng/g81 Tl ng/g 12.5 5.25 3.782 Pb ng/g83 Bi ng/g 0.2 2.1 1.2 2.9 0.490 Th ng/g 447 130 303 110 872 375 175 5792 U ng/g 4.4 109 33 211 112.5 49 18 Total % 100.2 99.2 99.0 100.0 98.7 99.8 99.6 99.6 97.9 97.8 97.1 95.6 89.2 99.8 101.3 able B.8 (continued) Z El. Unit IAB IC IIAB IIC IID IIE IIF IIIAB IIICD IIIE IIIF IVA IVB Mean
Fraction → wt% 0.76 0.06 0.60 0.05 0.09 0.11 0.03 1.34 0.24 0.08 0.04 0.37 0.08 100.001 H µ g/g 185.63 Li µ g/g 1.664 Be ng/g 315 B ng/g 3776 C µ g/g 2100 2000 140 2100 200 40 25667 N µ g/g 698 O wt% 7.2 µ g/g 9711 Na µ g/g 2151 2151 593612 Mg wt% 3.1 3.1 13.613 Al wt% 0.28 0.28 1.1614 Si wt% 4.0 4.0 17.115 P µ g/g 3400 4300 12000 5300 9800 2600 7450 3400 5600 2200 2193 1000 129216 S wt% 0.60 8.6 4.1 0.60 0.9 0.03 2.1017 Cl µ g/g 18819 K µ g/g 166 166 76420 Ca wt% 0.24 0.24 1.3221 Sc µ g/g 11.8 11.8 8.422 Ti µ g/g 120 120 67623 V µ g/g 22 22 7124 Cr µ g/g 111 70 38 87 31 40 111 40 210 140 87.7 346625 Mn µ g/g 232 232 235526 Fe wt% 74.5
90 82 86 85
84 84
88 89 88 80 µ g/g 3050 4600 5300 6500 4700 4700 7000 5000 3050 5000 3600 4000 7400 80828 Ni wt% 7.74 7.1 5.8 10.8 11.2 9.13 12.9 8.14 7.74 8.49 7.95 8.2 17.1 1.6729 Cu µ g/g 132 160 129 260 280 416 300 160 132 160 170 150 12 9130 Zn µ g/g 170 170 5731 Ga µ g/g 52 51.7 58.3 37.3 76.2 24.4 9.8 19.1 52 17.6 6.82 2.15 0.0221 6.732 Ge µ g/g 208 230 119 94.6 87 68.3 140 37.5 208 35.6 0.91 0.13 0.053 13.433 As µ g/g 11 11 9.9 8.2 10 16 16 10.5 11 10.5 11 7.6 1.1 3.534 Se µ g/g 7.935 Br µ g/g 0.5637 Rb µ g/g 2.238 Sr µ g/g 10.339 Y µ g/g 1.940 Zr µ g/g 6.841 Nb ng/g 36342 Mo µ g/g 8.2 7.7 6.9 8.4 9.4 6.8 7.2 8.2 7.2 7.2 5.9 27 1.444 Ru ng/g 79545 Rh ng/g 14946 Pd ng/g 3500 3500 2600 6000 5300 5300 3500 3500 3500 4400 4600 3000 78747 Ag ng/g 4948 Cd ng/g 3149 In ng/g 750 Sn ng/g 38551 Sb ng/g 270 98 201 150 220 300 250 265 270 265 86 9 1.5 7752 Te ng/g 47753 I ng/g 6155 Cs ng/g 14656 Ba µ g/g 4.457 La ng/g 550 550 33859 Ce ng/g 92459 Pr ng/g 12960 Nd ng/g 65762 Sm ng/g 550 550 21563 Eu ng/g 120 120 8264 Gd ng/g 30265 Tb ng/g 5666 Dy ng/g 35067 Ho ng/g 8568 Er ng/g 23369 Tm ng/g 4170 Yb ng/g 410 410 23171 Lu ng/g 45 45 3572 Hf ng/g 17873 Ta ng/g 3274 W ng/g 1600 1300 2100 2400 780 1000 1000 1600 1000 1200 600 3000 18875 Re ng/g 5576 Os ng/g 61477 Ir ng/g 1470 380 7433 6400 9900 4100 6200 4200 1470 4100 3200 1900 22000 72878 Pt µ g/g 1.279 Au ng/g 855 1140 1050 1100 1100 1600 1500 1013 855 1200 910 1550 150 21180 Hg ng/g 1381 Tl ng/g 582 Pb ng/g 17183 Bi ng/g 1190 Th ng/g 4392 U ng/g 15 Total % 98.8 98.0 98.3 98.0 97.7 99.7 97.9 97.6 98.8 97.6 97.6 97.8 98.0 100.0 ppendix C. Table C.9 provides an overview over the rocket launches of 2019 and the respective reentering core stages.18 able C.9: Rocket launches of 2019 with the mass and velocity of reentering core stages. Only stages with a significant velocity are considered.
Launch vehicle Launches(2019) Stagenumber Stagemass (t) 2019mass (t) Reentryspeed (km/s) SourcesSoyuz 2.1a,b/Soyuz-FG 7 2 6.55 45.8 4.3 SciNews (2018); Arianespace (2012)Soyuz 2.1a,b/Soyuz-FGwith Fregat upper stage 9 2 6.55 58.9 3.9 arianespace (2019b);Arianespace (2012)3 2.36 21.2 7.0Soyuz 2.1v Volga 2 2 2.36 4.7 Krebs (2020b); Arianespace (2012)Falcon 9 a
11 0Proton 5 2 11.0 55.0 4.6 International Launch Services(2009)3 3.5 17.5 7.3PSLV 5 2 5.4 27.0 4.0 Bergin and Graham (2018);Kyle (2019c)3 0.7 3.5 6.1Ariane 5 4 2 14.7 58.8 6.9 Arianespace (2016); arianespace (2019a)Falcon Heavy a b b Sum 81 (2) 702
Small rockets (launch payload < The number of launches of each launch vehicle is retrieved from Kyle (2019a), for the chinese rockets (CZ-X) also from Krebs (2020a).Numbers in parenthesis in column 2 depict the number of failures. The stage numbering in column 3 considers booster stages as first stages.The stages’ masses are retrieved mostly from data sheets and information available online. The reentry velocity is calculated from the velocityand altitude at stage separation (if data is available). Small rockets and suborbital flights are given but neglected in the calculations as thereentering mass is comparably low. a First stage (for Falcon Heavy also the second stages) perform a controlled landing, thus do not ablate in the atmosphere. b Given that the rocket is configured with boosters, otherwise this is stage 1. eferences Ailor, W., Hallman, W., Steckel, G., Weaver, M., 2005. Analysis of reentered debris and implications for survivability modeling, in: Danesy,D. 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