Assessing the Meteoroid Risk in Near Earth Space

Open Astron. 2018; 27: 144–149

Review Article

Andrey K. Murtazov* Assessing the meteoroid risk in near earth space

https://doi.org/10.1515/astro-2018-0025 Received Oct 01, 2017; accepted Jan 03, 2018

Abstract: The meteoroid risk in circumterrestrial space is basically caused by 1-10 mm meteoroid bodies. Meteoroid particles of such dimensions cannot be registered by modern monitoring astronomical instruments. Observable are only meteor phenomena they cause. This work analyses the activity of main meteor showers over several years and assesses the danger from meteoroids with a size of more than 1 mm. The results of calculating the meteoroid risk during these showers’ maximum activity periods have shown that despite its low values it is sufficiently close to the maximum allowable risk. This already constitutes a recognizable danger, and such a danger needs to be taken into consideration.

Keywords: circumterrestrial space, meteoroids, risk 1 Introduction (Cooke 2010). So, the meteoroid hazard should be taken into consideration in the design of space vehicles and long- term space missions (Foschini 1998; Cooke 2010; Wiegert The technogenic object and meteoroid particles collision and Vaubaillon 2009). risk has recently become notably urgent in relation to the We developed the meteoroid risk theory (Murtazov increased concentration of satellites and space debris in 2014; Mironov and Murtazov 2015) wherein the risk is the near Earth space. mainly determined by the flux of hazardous meteoroids. The meteoroid risk is calculated based on models of The most active of the constant periodic meteor show- meteoroid environment in near Earth space (Drolshagen ers are Quadrantids (QUA, early January), ETA-Aquariids et al. 2008; NASA 1970, 2011). The Meteoroid Environment (ETA, late April - early May), Perseids (PER, August), Gemi- Model (NASA 1970, 2011) includes the meteoroid environ- nids (GEM, mid-December). For these showers, the average ment in the following areas: over ~10 years (2006-2017) risk during its peaks of activity (1) meteoroid velocity distributions as a function of from hazardous meteoroids seen in the atmosphere as me- mass; teors brighter than 0m. (2) flux of meteoroids of larger sizes (>100 microns); (3) effects of plasma during impacts, including impacts of very small but high-velocity particles; and (4) variations in meteoroid bulk density with impact ve- 2 Model of meteoroid risk in near locity. Earth space We considered as hazardous the particles over 1 mm in size. Although the concentration of such particles in the Meteoroid risk is the probability (a measure of hazard) that near Earth space is considerably low as compared to the a spacecraft will collide with hazardous meteoroids capa- concentration of technogenic space debris, their energy is ble of having a destructive effect on the spacecraft and stop sufficient to break the space vehicles’ envelopes (Beech et (fully or partly) its operation for a certain number of colli- al. 1997). The probability of meteoroid impacting an astro- sions. naut’s spacesuit during his space walk at the maximum Our physical model of meteoroid risk consists of the of such a meteor shower like the Perseids may reach 15% following components (Mironov and Murtazov 2015): (1) hazardous directions, i.e., distribution of meteor streams and sporadic meteors in space; Corresponding Author: Andrey K. Murtazov: The Ryazan State (2) distribution of meteor streams by seasons and by the University, Ryazan, 46 Svobody St., 390000, Russia; duration of action within these seasons; Email: [email protected]

Open Access. © 2018 A. K. Murtazov et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 License A. K. Murtazov et al., Assessing the meteoroid risk in near earth space Ë 145

(3) distribution of meteor streams by velocities and 3 Calculations masses; (4) spatial distribution of meteoric particles in the For calculations, the data of the Visual Meteor Database of stream itself; International Meteor Organization (IMO) has been used. (5) effect of the gravitational attraction of meteoric par- It should be noted that this data is valid only for vi- ticles by the Earth; sual meteors, as the moments and intervals of the meteor (6) effect of shading of meteoroids by the Earth fromthe shower maximum activity differ depending on monitoring observer; methods. For instance, the discrepancies in maximum ac- (7) orientation of the entire spacecraft as well as its con- tivity moments of Quadrantids-2016 for the visual, video, structive elements relative to the meteoroid arrival and radar monitoring reached ∆λ = 0.2∘ (Rendtel et al. direction; 2017). (8) time of spacecraft residence on the orbit and time of The particle density D is the approximate number of meteoric stream influence on the spacecraft. dangerous particles (meteoroids) causing meteors brighter On the celestial sphere of the spacecraft in a satellite than magnitude 0 per billion cubic kilometer (i.e., a cube centered coordinate system (Murtazov 2014), the Earth’s with 1000 km edge length). The meteoroid flux F depends disc moves along the equator of the spacecraft orbit (Fig- on this density (which can be variable) and the velocity ure 1), and the radiant of a meteor stream describes a small (which is roughly constant) of the meteoroid stream. circle, the plane of which is parallel to the equatorial plane The population indices of the showers in question are of the system. Here, R, E, ⊙, , are the directions to the quite close to each other (2.1 ± 2.6), therefore the average meteor stream radiant, the Earth, the Sun, and the vernal proportion of dangerous meteors in the shower was taken equinox, respectively; b is the ecliptic latitude; and is as- as 5%, in case the distribution of meteoroids in the stream cending node of the spacecraft orbit. This means that the is uniform. For example, the proportion of dangerous me- Earth’s coordinates are characterized by the spacecraft’s teoroids in the flux of 2007–2013 Perseids was 0.051 ± 0.008 position on the orbit. (Murtazov 2013, 2014). The shower maximum period was broken into intervals ∆λ = 0,100∘, which corresponds to 8640 mean solar seconds. Within the intervals we summed up annual spatial densities D, (km−3) of bright meteors. The bright meteors flux density −(km 2s−1) is

Fλ = vD (1)

where v (km·s−1) – the shower geocentric velocity. The risk is determined by the number of collisions of dangerous meteoroids within the shower maximum interval ∆λ = (λ1, λ2):

λ2 λ ∫︁ ∑︁2 R = N = Fλ dλ ≈ Fi ∆λ (2)

λ1 λ1

The processing was conducted in Statistica-6.1. The flux of sporadic meteors having a mass− over10 2g for different Meteoroid Flux Models in Near Earth Space does not go above 10−12 m−2s−1 (Drolshagen et al. 2008). In Figure 1. Satellite-centric reference system for calculation the number of collisions. some cases, it is fairly close to the flux of bright dangerous meteoroids, but we did not take this into account in our calculations. 146 Ë A. K. Murtazov et al., Assessing the meteoroid risk in near earth space

Table 1. Activity peak spatial density of dangerous Quadrantids 2006-2016.

Year Spatial density of dangerous Meteoroid risk, Year Spatial density of dangerous Meteoroid risk, meteoroids in near-Earth space, 10−6 km−2 meteoroids in near-Earth space, 10−6 m−2 10−9 km−3 10−9 km−3 2006 5.3 0.04 2011 4.4 0.1 2007 4.4 0.002 2012 5.8 0.2 2008 4.9 0.01 2013 8.5 0.1 2009 9.4 0.3 2015 4.0 0.01 2010 6.7 0.002 2016 5.3 0.2

4 Results

Quadrantids (QUA) 2006-2017

The activity period is from December 28 to January 12. The activity maximum year after year shifted near the inter- ∘ ∘ val λ⊙ = 282.45 - 283.75 . The particle density D herein takes on the value from 4·10−9 km−3 to nearly 9.4·10−9 km−3, which means that the dangerous meteoroids collision number varied from 0.002·10−6 m−2 (2007) to 0.3·10−6 m−2 (2009). The 10-years meteoroid risk in the near Earth space during this time period was R = (0.3±0.1)·10−6 m−2.

η-Aquariids (ETA) 2008-2017

Activity: April 19-May 28. Contrary to Geminids and Per- seids, the activity peak moment significantly varies from year to year; therefore it seems to be impossible to obtain the average risk values years to date. Table 1 contains the results of calculating the meteoroid risk for ETA in the peak activity periods. The meteoroid risk average value in the activity periods of ETA 2008-2017 was R = (2.2±1.2)·10−6 m−2.

Perseids (PER) 2006-2017

Activity: July 17-August 24. The activity peak consistently ∘ ∘ belonged to the interval λ⊙ = 139.50 - 140.65 , but the spatial density of meteoroid particles notably varied from year to year from ~3.5·10−9 km−3 to 7.1·10−9 km−3 (Figure 3). Number of dangerous collisions varied from 0.2·10−7 −2 −6 −2 m (2011, 2014) to 0.5·10 m (2007). Figure 2. The average 2006-2017 spatial density of dangerous The meteoroid risk value during the activity peak of Quadrantids during their activity peak and scattering histogram PER 2006-2017 was R = (0.4±0.2)·10−6 m−2. of processing results. A. K. Murtazov et al., Assessing the meteoroid risk in near earth space Ë 147

Table 2. 2008-2017 bright η-Aquariids activity and meteoroid risk.

Year Period of peak activity, dd/solar Spatial density of dangerous meteoroids Average flux density, Meteororid risk, longitude (2000.0) in near-Earth space, 10−9 km−3 10−6 km−2s−1 10−6 m−2 2008 02.05-11.05 90.5 5.97 4.4 42.515-51.007 2009 03.05-07.05 49.3 3.25 1.1 42.773-46.629 2010 22.04-10.05 38.0 2.51 3.3 32.200-47.486 2011 03.05-10.05 83.0 5.48 3.7 42.117-49.910 2012 04.05-09.05 17.4 1.15 0.4 43.881-48.666 2013 03.05-11.05 76.8 5.07 2.0 43.139-51.048 2014 03.05-11.05 40.7 2.69 1.8 42.714-50.459 2015 20.04-06.05 22.6 1.49 2.0 29.471-54.073 2016 01.05-07.05 49.8 3.29 1.7 40.923-46.811 2017 02.05-07.05 47.6 3.14 1.4 42.199-47-299

Table 3. Activity peak spatial density of dangerous Perseids 2006-2017.

Year Spatial density of dangerous Meteoroid risk, Year Spatial density of dangerous Meteoroid risk, meteoroids in near-Earth space, 10−6 m−2 meteoroids in near-Earth space, 10−6 m−2 10−9 km−3 10−9 km−3 2006 3.9 0.3 2012 5.3 0.3 2007 6.0 0.5 2013 4.3 0.2 2008 5.9 0.4 2014 3.5 0.02 2009 7.1 0.3 2015 4.1 0.08 2010 5.8 0.4 2016 4.7 0.02 2011 3.5 0.02 2017 6.9 0.007

Table 4. Activity peak spatial density of dangerous Geminids 2007-2016.

Year Spatial density of dangerous Meteoroid risk, Year Spatial density of dangerous Meteoroid risk, meteoroids in near-Earth space, 10−6 m−2 meteoroids in near-Earth space, 10−6 m−2 10−9 km−3 10−9 km−3 2007 21.6 2.6 2012 6.0 0.4 2008 13.3 0.04 2013 6.9 0.4 2009 19.7 2.7 2014 6.7 0.5 2010 7.0 0.8 2015 6.6 0.4 2011 8.1 0.4 2016 6.8 0.2

Geminids (GEM) 2007-2016 The meteoroid risk value during the activity peak of GEM 2007-2016 was R = (0.9±0.3)·10−6 m−2. The Geminids are observed on December 4-17, the activity peak in those years consistently fell within December 13- ∘ ∘ 15 (λ⊙ = 261.00 - 263.10 ). The average 10-years particle density D varies from ~5·10−9 km−3 to nearly 20·10−9 km−3. The number of dangerous collisions during activity peak varied from 0.4·10−7 m−2 (2008) to 2.6·10−6 m−2 (2007). 148 Ë A. K. Murtazov et al., Assessing the meteoroid risk in near earth space

Table 5. Meteoroid risk during activity peak of main meteor streams.

Meteor Period of peak activity, Average 10-years −6 shower solar longitude λ⊙ meteoroid risk, 10 (2000.0), arc deg. m−2 Quadrantids 282.45 - 283.75 0.3±0,1 η-Aquariids 29.47 - 54.073 2.2±1.2 Perseids 139.50 - 140.65 0.4±0.2 Geminids 261.00 - 263.10 0.9±0.3

Figure 4. The average 2007-2016 spatial density of dangerous Gem- inids during their activity peak and scattering histogram of processing results.

5 Conclusions

The calculations have shown that the meteoroid risk in near Earth space is not high. Its value for the most active meteor showers does not go above 5·10−6 m−2 during their peak activity (Table 5). The results that are close to the above ones can be ac- quired from the Models of Meteoroid Environment (NASA 1970, 2011) or, for instance, from the index of meteor activity (IMA) (Kartashova 2013), which is basically similar to the spatial density of meteoroids in the near Earth space. For the Orionids-2007 maximum, the collision number Figure 3. The average 2006-2017 spatial density of dangerous Per- which we calculated according to the IMO data is approxi- seids during their activity peak and scattering histogram of pro- mately 5 times as many as the collisions calculated accord- cessing results. ing to the IMA values, whereas the results for Orionids- 2008 for the above two methods are virtually the same. A. K. Murtazov et al., Assessing the meteoroid risk in near earth space Ë 149

The most accurate are the risk factors calculated from Drolshagen, G., Dikarev, V., Landgraf, M., Krag, H., & Kuiper, W. the direct all-sky observations of bright meteors, like those 2008, In: Trigo-Rodriguez, J.M., Rietmeijer, F. J. M., Llorca, J., & presented in the author’s paper (Murtazov 2014). Janches, D. (Eds.), Advances in Meteoroid and Meteor Science, Springer, 191-197. Of course, the risk from dangerous meteoroids in Foschini, L. 1998, https://arxiv.org/pdf/physics/9804026.pdf. space is not very high. However, it is noticeably dangerous Kartashova, A. P. & Bolgova, G. T. 2013, Solar System Research, 47, because the maximum allowable risk is defined as RLim. = 213–218. 10−6, and such danger should not be neglected. Limiting Future Collision Risk to Spacecraft: An Assessment of Besides, near Earth space is densely populated with NASA’s Meteoroid and Orbital Debris Programs, 2011, National satellites; therefore their total area of collisions is rather Academies Press. Meteoroid Damage Assessment, 1970, NASA SP-8042, https://ntrs. large. So the total risk for the whole of the satellite popu- nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710015594.pdf. lation may become significant. Mironov, V. V. & Murtazov A. K. 2015, Cosmic Research, 53, 430-436. Murtazov, A. K. 2013, In: EPSC-2013 Abstracts (2013, London, UK), 8, EPSC2013-346-1– EPSC2013-346-2. Murtazov, A. K. 2014, WGN, The Journal of the International Meteor References Organization, 42, 65-67. Murtazov A. K. 2015, In: Rault, J.-L. & Roggemans P. (Ed.), Proceed- Beech, M., Brown, P., Jones, J., & Webster, A. R. 1997, Adv. Space ings of the International Meteor Conference (27–30 August Res., 20, 1509-1512. 2015, Mistelbach, Austria), 155-156. Cooke, W. 2010. In: International Meteor Conference (16-19 Sept. Rendtel, J., Ogawa, H., & Sugimoto, H. 2017, WGN, The Journal of the 2010, Armagh, UK), https://www.imo.net/imcs/imc2010/talks/ International Meteor Organization, 45, 49-55. Cooke.pdf. Wiegert, P. & Vaubaillon, J. 2009. In: Kleiman, J.I. (Ed.), Proceedings Cooke, W. J. & Moser, D. E., 2012, The status of the NASA All Sky of the 9th International Conference “Protection of Materials Fireball Network, WGN, Proceedings of IMC 2011, 9-12. and Structured from Space Environment” (2009, American Institute of Physics), 567-571.