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Meteor Shower Forecasting for Spacecraft Operations METEOR SHOWER FORECASTING FOR SPACECRAFT OPERATIONS Althea V. Moorhead(1), William J. Cooke(1), and Margaret D. Campbell-Brown(2) (1)NASA Meteoroid Environment Office, Marshall Space Flight Center, Huntsville, Alabama 35812, Email: althea.moorhead, william.j.cooke @nasa.gov (2)Department of Physics and Astronomy,{ The University of Western} Ontario, London N6A3K7, Canada, Email: [email protected] ABSTRACT meteor shower, for example, can double the meteoroid flux at the time of peak activity. The Leonid meteor shower does not pose much of an impact risk on a typical Although sporadic meteoroids generally pose a much year, but has occasionally produced outbursts in which greater hazard to spacecraft than shower meteoroids, me- the number of meteors is tens to thousands of times larger teor showers can significantly increase the risk of dam- than normal [4]. In such cases, operational spacecraft age over short time periods. Because showers are brief, it sometimes choose to mitigate the risk by avoiding op- is sometimes possible to mitigate the risk operationally, erations that increase the spacecraft’s vulnerability. If the which requires accurate predictions of shower activity. risk is great enough, operators may consider re-orienting NASA’s Meteoroid Environment Office (MEO) generates the spacecraft to present its least vulnerable side to the an annual meteor shower forecast that describes the vari- shower, phasing its orbit to use the Earth as a shield, or ations in the near-Earth meteoroid flux produced by me- powering down components. teor showers, and presents the shower flux both in abso- lute terms and relative to the sporadic flux. The shower All mitigation strategies have some associated cost such forecast incorporates model predictions of annual varia- as delays, reduced functionality, or fuel. Accurate shower tions in shower activity and quotes fluxes to several limit- predictions are therefore needed for informed risk assess- ing particle kinetic energies. In this work, we describe ment. The Meteoroid Environment Office (MEO) pro- our forecasting methods and present recent improve- duces annual meteor shower forecasts that can be used ments to the temporal profiles based on flux measure- to assess the increase in the particle flux due to showers. ments from the Canadian Meteor Orbit Radar (CMOR). These forecasts are designed to be used in conjunction with an existing sporadic meteoroid risk assessment; un- Key words: meteoroids. like sporadic models, however, the annual forecast pro- vides a detailed temporal profile that takes showers into account. The forecast also takes shower variability into 1. INTRODUCTION account; any unusual activity predicted by modelers [5, 6] is incorporated. Meteoroid impacts are known to cause damage to space- While modelers can often predict the level of meteor 1 craft surfaces; their high speed (12-72 km s− ) compared shower activity, we frequently rely on past observations to orbital debris means that relatively small particles can to characterize the activity profile. For many years, the be hazardous. Most of the meteoroid flux is associated MEO (and others; [7]) used a set of activity profiles with “sporadic” meteoroids, which are those not associ- that were determined from naked-eye meteor observa- ated with any meteor shower. The sporadic complex is tions [8]. Many of the activity profiles in this set are quite present throughout the year and constitutes the vast ma- noisy due to low number statistics. Furthermore, daytime jority of microgram-or-larger meteoroids. For this rea- meteor showers were of course not visible to observers son, meteoroid environment models such as NASA’s Me- and thus the MEO had to employ a default activity pro- teoroid Engineering Model (MEM) [1, 2] and ESA’s In- file for many of these showers. terplanetary Meteoroid Environment Model (IMEM) [3] focus on the sporadic complex. Although these models Meanwhile, the Canadian Meteor Orbit Radar (CMOR) include showers in the total meteoroid flux, they do not began operation in 2001 [9]. CMOR is a patrol radar model the short-duration fluctuations caused by showers. and can detect meteor echoes during the day as well as at Such fluctuations are generally not worth modeling for a night. It is located near London, Ontario and thus moni- long-duration spacecraft mission. tors the northern hemisphere, although it can detect me- teors with declinations as low as -40◦. Meteor flux mea- Over short time spans, however, meteor showers can surements from CMOR [10] are available for the years match or even exceed the sporadic flux. The Geminid 2002-2015, providing us with a data set suitable for re- Proc. 7th European Conference on Space Debris, Darmstadt, Germany, 18–21 April 2017, published by the ESA Space Debris Office Ed. T. Flohrer & F. Schmitz, (http://spacedebris2017.sdo.esoc.esa.int, June 2017) (ZHR0), and two exponents that characterize the shape (λ0, ZHR0) B B 100 of the shower’s activity profile ( p and m). The time of peak shower activity occurs when the center of the meteoroid stream intersects the Earth’s orbit; we there- fore measure time in terms of solar longitude, λ . The zenithal hourly rate (ZHR; the rate at which meteors oc- cur when the shower radiant is directly overhead) in- ZHR 50 Bp(λ λ0) Bm(λ λ0) 10 − 10− − / / creases with time before the peak and decreases after the peak: +Bp(λ λ0) 10 − λ <λ0 ZHR = ZHR (1) 0 Bm(λ λ0) · 10− − λ >λ0 0 ⇢ 256 258 260 262 264 266 268 In some cases, such as the Perseids, the activity profile λ (◦) of a single meteor shower is constructed from two sets of parameters that describe “peak” and “base” activity. Figure 1. Sample meteor shower activity profile. The peak zenithal hourly rate is ZHR0 and the peak occurs at ZHR describes the rate at which a meteor shower pro- solar longitude λ0. On either side the activity follows an duces visible meteors. ZHR can be converted to meteor exponential function of solar longitude; the two parame- flux by taking into account observer biases and shower ters Bp and Bm are not necessarily equal. characteristics. We use the methodology of [11] to cal- culate the flux of meteoroids that have a brightness of at least magnitude 6.5: vising many shower activity profiles. 0.748 ZHR0 kavg (13.1r 16.5)(r 1.3) f6.5 = · · − − (2) This paper presents both our methodology for shower 37200 km2 forecasting (Section 2) and the improvements we’ve made to our shower activity profiles based on CMOR flux where the average perception factor, kavg, is of order measurements (Section 3). Finally, Section 4 discusses unity. The population index, r, describes the brightness the forecast and the changes in it from a spacecraft risk distribution of meteors within the shower and is also re- perspective. quired as an input for each shower. Because ZHR has 1 2 units of hr− , this equation yields flux in units of km− 1 hr− . 2. FORECASTING METHODS This magnitude-limited flux can be converted to a mass- limited (milligram or larger) flux as follows [11]: This section describes our algorithm for forecasting me- 1 f = f r9.775 log10 (29 km s− /v100) (3) teor shower fluxes. These fluxes are derived from a set mg 6.5 · of meteor shower parameters and are adjusted for an al- titude of 400 km. We also compute the appropriate spo- This equation makes use of Verniani’s relationship [12] radic meteor flux at this altitude, taking gravitational fo- between magnitude, mass, and velocity to calculate the cusing and planetary shielding into account. Finally, we meteoroid mass that produces a magnitude 6.5 meteor at compute the flux enhancement produced by these show- the shower’s speed. The shower velocity is that at the top ers over the baseline meteoroid flux. of the atmosphere. Finally, the flux can be scaled to any arbitrary limiting mass using the relation: 2.1. Shower fluxes 1 s f m − m = (4) Meteor showers do not have a well-defined duration. In- fmg 1 mg stead, peak activity occurs at a particular time each year ✓ ◆ and activity gradually increases up to the peak and de- where s =1+2.3 log10 r is the shower mass index. creases after the peak (see Fig. 1). A double exponential function has been found to be a good fit to most meteor In all annual meteor shower forecasts to date, an addi- shower activity profiles [8]. Measures of effective shower tional factor of 2 was applied to Eq. 2. This factor was duration (such as the full width at half maximum or time obtained by applying Eq. 2 to the Grun¨ interplanetary flux period over which activity exceeds a given threshold) thus [13] and comparing it with a sporadic ZHR estimate of 8. depend on the steepness of this double exponential func- A factor of 2 was found to bring them in rough agree- tion. ment. However, a separate mass-luminosity relationship was used to convert magnitude to mass in that calcula- We characterize the activity profile of each shower with tion. When Eq. 3 is used instead, the flux corresponding four parameters: peak time (λ0), peak zenithal hourly rate to a sporadic ZHR is a factor of 4 larger, obviating the we must invert the gravitational focusing effect to obtain Table 1. The four kinetic energies (KEref) to which the the slightly lower shower flux corresponding to an alti- MEO annual meteor shower forecast reports fluxes. The tude of 400 km [19]: second column lists the particle mass which, at 20 km s 1, has the listed kinetic energy. The third column lists f v 2 − 400 = 400 (6) the particle diameter which, for a bulk density of 1000 kg f v 3 100 100 m− , has the listed mass.
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