Abstract
In this paper, we will review recent research on numerous aspects of bolide entry into a planetary atmosphere, including such topics as the entry dynamics, energetics, ablation, deceleration, fragmentation, luminosity, mechanical wave generation processes, a total (panchromatic) power budget including differential and integral efficiencies versus time, etc. Fragmentation, triggered by stagnation pressures exceeding the bolide breaking strength, has been subsequently included in either a collective or non-collective wake behavior limit. We have also utilized the differential panchromatic luminous efficiency of ReVelle and Ceplecha (2002) to compute bolide luminosity. In addition we also introduce the concept of the differential and integral acoustic/infrasonic efficiency and generalized it to the case of mechanical wave efficiency including internal atmospheric gravity waves generated during entry. Unlike the other efficiencies which are assumed to be a constant multiple of the luminous efficiency, the acoustic efficiency is calculated independently using a “first principles” approach. All of these topics have been pursued using either a homogeneous or a porous meteoroid model with great success. As a direct result, porosity seems to be a rather good possibility for explaining anomalous meteoroid behavior in the atmosphere.
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Acknowledgements
I would like to thank the ISR-DR Program Office at Los Alamos National Laboratory for their continuous support throughout the course of this work, especially, Mr. Mark Hodgson. I would also like to thank DOE HQ in NA-22 for their continuing support as well. Finally, I would like to dedicate this paper to the memory of my beloved father, Mark A. Revelle.
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An erratum to this article is available at http://dx.doi.org/10.1007/s11038-007-9142-x.
Appendix A: Energetics End Height Single-body Equation Equivalence
Appendix A: Energetics End Height Single-body Equation Equivalence
where \(Ei(\sigma\cdot F\))=the exponential integral function; \(F=(1-\mu)/2\); −2(*) \(\le\mu\le\sim \mu\)=2/3 is the self-similar value (no shape change); p *∞ = mg·sin \(\theta\)/(C D A)=modified ballistic entry parameter; \(p_{\infty}^{\ast}= 4\cdot\rho_{m}\cdot r<$> <$>\cdot g \cdot \sin\theta /(3C_{D})\) for a sphere; p 0=surface pressure; D=4.605 for 99 % kinetic energy depletion at the end height.
(*): Effective “pancake” model limits for \({\mu}0\)
Starting from the classical (geopotential) end height equation using standard notation as given in ReVelle (1979, 1980, 1987) written assuming \(\mu= 2/3\) so that \(F=(1-\mu)/2=1/6\) for simplicity with \(\sigma\)=constant, i.e., the so-called simple ablation theory:
where
As shown in ReVelle (1980), ΔEi can be expanded in an infinite length power series form that can also be expressed as the difference between two very simple functions in (A.9):
Also, from (A.5) and (A.6) we can write:
Combining these two expressions in (A.10) and (A.11), we can also write:
Rearranging (A.4) into a form solved for the velocity and as the natural logarithm of the velocity as a function of z, we also have:
Equating (A.12) and (A.14), we can solve again for z(V) in the form:
Defining:
where
Equation (A.17) and (A.18) are the desired results. Thus the classical end height equation has been shown to be totally equivalent to the energetics approach used throughout this paper written in terms of the D parameter of ReVelle. The solutions that we have used to make predictions use the variable ablation parameter form of these equations developed in ReVelle (1979). Thus, all solutions are numerical results in thin vertical layers over small velocity change intervals rather than the simple analytic results developed above.
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ReVelle, D.O. Recent Advances in Bolide Entry Modeling: A Bolide Potpourri. Earth Moon Planet 95, 441–476 (2004). https://doi.org/10.1007/s11038-005-9064-4
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DOI: https://doi.org/10.1007/s11038-005-9064-4