New methodology to determine the terminal height of a fireball. Manuel Moreno-Ibáñez, Josep M. Trigo-Rodríguez & Maria Gritsevich

Transcription

1 New metodology to determine te terminal eigt of a fireball Manuel Moreno-Ibáñez, Josep M. Trigo-Rodríguez & Maria Gritsevic

2 Summary Summary - Background - Equations of motion - Simplifications - Database - Results - Discussion - Conclusions - References 7

3 Background (I) Asteroid: diameter > 10 m. Meteoroid: diameter < 10 m. Meteor: meteoroid tat interacts wit te Eart atmospere. Fireball: meteor tat is able to get deep in te atmospere. Brigtness similar to Venus. Great Fireball: bigger fireball tat is able to get to lower altitudes and can reac a brigtness similar to te Moon. Meteorites: meteor tat survives to its atmosperic fligt and reaces te ground. Micrometeorites: small grains tat get te atmospere at low velocities and are deposited on te ground. Fireballs and Meteorites Adapted from Rendtel et al. (1995) 8

4 Background (II) Cepleca y McCrosky (1976) Study of te Prairie Network to find similar meteorites to te Lost City meteorite. Tey used four criteria: End eigt agrees wit te single-body teoretical value, calculated using dynamic mass, as well as wit tat of Lost City too witin ±1.5km, wen scaled for mass, velocity and entry angle in accordance wit classic meteor teory. Stulov et al. (1995), Stulov (1997) and Gritsevic (007) Study of te Prairie Network to distinguis between ordinary and carbonaceous condrites. Te end eigt as te principal discrimating observational parameter in teir discussion (potometric mass). Empirical Criterium: PE log Alog m E BlogV A, B and C obtained by Least Squared fit on PN data. Weterill and Revelle (1981) C log(cos Z Instead of using te average values as input parameters, tey gatered all te unknowns into two new variables, α and β (ballistic coefficient and mass loss parameter). Adjusting te equation to te registered values tese new variables can be obtained. Tis describes in detail te meteoroid trajectory and allow to invent a classification for possible impacts. 9 R )

5 Equations of motion (I) 1 Te equations of motion for a meteoroid entering te atmospere projected onto te tangent and to te normal to te trajectory Variation of te mass H * dm dt 1 c av 3 Extra equations Isotermal atmospere exp / 0 Levin (1956) 3 S / S Equations of motion S ( M / e M e ) Drag force dv 1 M cd av S Psin dt Lifting force d MV 1 MV P cos cos c LaV S dt R d V sin dt 4 Use of dimensionless parameters M M m; V V v; S S s; y Were index e indicates values at te entry of te atmospere. 0 is te scale eigt (7.16 km) e e e 0 ;a 0 10

6 Equations of motion(ii) Analytical solution of system : Initial conditions : y ; v 1; m 1 1 v m exp 1 y ln ln, [1] Ei( ) Ei( v ) [] Ei( x) x z e dz z In tis metodology we gater all te unknown values of te meteoroid s atmospere fligt motion equations into two new variables (Gritsevic, 009): Ballistic Coefficient 0 Se sin 1 0 c d M e Mass loss parameter c V c H e 1 * d 11

7 Simplifications 1 Simplifications For quick meteors, a strong evaporation process takes place so β becomes ig (β >> 1), te deceleration can be neglected and te velocity tus assumed constant. Stulov (1998, 004) developed te following asymptotic solution: v 1, m 1 1 e y, ln y However, te meteor velocity begins to decrease in a certain vicinity of m=0. In order to account for tis cange in velocity we combine te Eq.[1] (valid for arbitrary β values) wit te Eq. [3] suitable for ig β values: [3] v y e 1, ln y [4] ln 1 1 1

8 Database Database In order to test tis metodology, we compare our derived terminal eigts results wit te fireball terminal eigts registered by te Meteorite Observation and Recovery Project operated in Canada between 1970 and 1985 (MORP) (Halliday et al. 1996). We use previous α and β values derived by Gritsevic (009). Halliday et al., 1996 Gritsevic,

9 Resolution Adjusting te (vi, yi) values of Eq. [] to te trajectory observed (vi, yi) values by means of a weigted least-squares metod. Assigning manually te weigted factors may be quite complicated, so, since te eigt and velocity of a meteor decrease wile it gets closer to te surface, te solution was proved to perform better if we take an exponential form of eq. [] (see Gritsevic, 008 for furter details): exp( y) exp( ) 0, Ei( x) We can derive tese new variables (α, β) for eac meteoroid by minimizing tis expression. From Eq.[3], at te point were m=0 we ave: I 0 yt 0 ln [5] x z e dz z Q(, ) ( Fi ( yi, vi,, )) i1 F ( y, v,, ) exp( y i i i Resolution n i ) i exp( ) 0 Ei( ) Ei( v ) If we reorder Eq.[4] we ave: II 0 yt 0 ln 1 1 v e t [6] 14

10 Results (I) Results I 0 yt 0 ln II 0 t 0 v 1 1 e t y ln 4.11 Km 1.5 Km 15

11 Results (II) Differences could be due to te use of eq. [4] establised for ig β. As suggested by Gritsevic et al. (015), we would rater use te modification: 1.1 III yt 0 ln vt e [7] 16

12 Results (III) I y 0 t 0 ln III y 1.1 ln 1.1 v 1 1 e t 0 t Km II y ln v 1 1 e t 0 t Km 1.5 Km 17

13 Discussion Discussion For β >5 eq. [5] sall give good results. But te decrease in v near te terminal point is not considered. Eq.[6] sows a lineal tendency. Still discrepancies in all β values. Te modification made in [7] leads to a good agreement between observed and teoretical data. However at low β, some discrepancies appear. Te inverse problem is possible for non decelerated bodies if te terminal eigt is known constraints in α and β. Meteor eigt as a function of time new problems may be scoped: - Determination of luminous efficiency based on meteor duration. - Critical Kinetic Energy to produce luminosity. Te small discrepancies at low β sall be taken into account for future planetary defense applications. Meteoroids could reac lower eigt tan tose predicted. We use dimensionless parameters instead of te empirical set A,B, C coefficients of Cepleca and McCrosky (1976). However α and β keep te same variable dependency as te PE criterium. 18

14 Conclusions We ave derived te terminal eigts for MORP fireballs using a new developed metodology. Tis metodology ad only been tested on several fully ablated fireballs wit large β values (Gritsevic and Popelnskaya, 008). We were particularly interested in determining weter tis new matematical approac works equally for fully ablated fireballs and meteorite-producing ones. We introduced a new modification in te metodology wic allows to get a iger accuracy. We foresee a calculation of terminal eigt to be useful wen te lower part of te trajectory was not instrumentally registered. It also brings critical knowledge into te problem wen one needs to predict ow long will be a total duration of te luminous fligt or at wic eigt a fireball produced by a meteoroid wit given properties would terminate. Based on our investigations we can igly recommend te use of equation [7] also to solve inverse problem wen terminal eigt and velocity are available from te observations, and parameters α and β need to be derived. 19

15 References References M. Moreno-Ibáñez, et al., Icarus 50, (015). Z. Cepleca and R.E. McCrosky, J.Geopys. Res. 81, (1976). M. Gritsevic, Solar Syst. Res. 41 (6), (007). M. Gritsevic, Solar Syst. Res. 4, (008). M. Gritsevic and N.V. Popelenskaya, Doklady Pys. 53, 88-9 (008). M. Gritsevic, Adv. Space Res (009). M. Gritsevic et al., Mat. Model. 7 () 5-33 (015). I. Halliday et al., Meteorit. Planet. Sci. 31, (1996). V.P. Stulov et al., Aerodinamika bolidov, Nauka (1995). V.P. Stulov, Appl. Mec. Rev. 50, (1997). V.P. Stulov, Planet. Space Sci. 46, (1998). V.P. Stulov, Planet. Space Sci. 5 (56), (004). G.W. Weterill and D.O. Revelle, Icarus 48, (1981). 0