[Paper Review] Are explanations of the Poynting-Robertson effect correct?

J. Klačka, Jaromír Petržala+2 more|ArXiv.org|Apr 2, 2009

Astro and Planetary Science66 references3 citations

TL;DR

This paper critiques widely accepted explanations of the Poynting-Robertson (P-R) effect, arguing that many derivations and interpretations in the literature are physically incorrect. Using a relativistically covariant formulation of the equation of motion, the authors show that the P-R effect arises from radiation pressure on a moving spherical body and that the concept of 'P-R drag' as a distinct force is nonphysical and misleading. The correct relativistic framework eliminates confusion and clarifies the role of electromagnetic versus solar wind radiation forces.

ABSTRACT

Physics of the Poynting-Robertson (P-R) effect is discussed and compared with the statements published in the past thirty years. Relativistically covariant formulation reveals the essence of the P-R effect and points out to nonphysical explanations in scientific papers and monographs. Although the final equation of motion $m$ $d\vec{v} / dt$ $=$ ($S A'\bar{Q'}_{pr}$ $ / $ $c$) ${(1 - \vec{v} \cdot \vec{e} / c) \vec{e} - \vec{v} / c}$ has been usually correctly presented and used, its derivation and explanation of its essence is frequently incorrect. The relativistically covariant form of the equation of motion yields the P-R effect as an action of the radiation pressure force on a moving spherical body. No "P-R drag", as a particular relativistically covariant equation of motion, exists. Omission of the nonphysical term "P-R drag" excludes any confusion in the published definitions. The difference between the effects of solar electromagnetic and corpuscular (solar wind) radiation is stressed. The force acting on the particle due to the solar wind (the simple case of radial solar wind velocity is considered) is $\vec{F}_{sw}$ $=$ $F_{sw}$ [ (1 $-$ $\vec{v} \cdot \vec{e} / v_{sw}$) $\vec{e}$ $-$ $x'$ $\vec{v} / v_{sw}$ ], where $F_{sw}$ is the force on the stationary particle, $v_{sw}$ is the heliocentric solar-wind speed, and, the value of $x'$ depends on material properties of the particle (1 $

Motivation & Objective

• To identify and correct widespread physical inaccuracies in the explanation of the Poynting-Robertson effect found in scientific literature over the past thirty years.
• To demonstrate that the term 'Poynting-Robertson drag' is not a valid relativistically covariant force component and should be excluded from physical descriptions.
• To clarify the distinction between electromagnetic radiation pressure and solar wind forces on dust particles using relativistic mechanics.
• To provide a physically consistent, relativistically covariant derivation of the equation of motion for dust grains under stellar radiation and gravity.
• To promote the use of correct physical interpretations in textbooks, encyclopedias, and scientific literature to prevent the propagation of misconceptions.

Proposed method

• Use of a relativistically covariant formulation of the equation of motion for a moving spherical dust particle under electromagnetic radiation.
• Derivation of the force expression $ \vec{F} = \frac{SA'\bar{Q}'_{pr}}{c} \left\{ \left(1 - \frac{\vec{v} \cdot \vec{e}}{c}\right)\vec{e} - \frac{\vec{v}}{c} \right\} $, which correctly describes the P-R effect as a whole radiation force.
• Comparison of the P-R effect with the solar wind force, given by $ \vec{F}_{sw} = F_{sw} \left[ \left(1 - \frac{\vec{v} \cdot \vec{e}}{v_{sw}}\right)\vec{e} - x' \frac{\vec{v}}{v_{sw}} \right] $, where $ 1 < x' < 3 $ depends on particle material properties.
• Application of relativistic corrections to the aberration of light and radiation pressure, showing that classical explanations are insufficient.
• Secular evolution of orbital elements (semi-major axis, eccentricity) is derived using relativistically consistent equations, including initial conditions and time-to-spiral-in estimates.
• Use of Mie theory solutions to Maxwell’s equations to derive the dimensionless efficiency factors $ \bar{Q}'_{pr} $ and $ \bar{Q}'_{ext} $, ensuring relativistic consistency.

Experimental results

Research questions

• RQ1 Why are many standard explanations of the Poynting-Robertson effect physically incorrect despite decades of use?
• RQ2 Does the concept of 'Poynting-Robertson drag' as a distinct force term have a basis in relativistic physics?
• RQ3 How does the relativistically covariant formulation resolve inconsistencies in the derivation and interpretation of the P-R effect?
• RQ4 What is the correct relativistic expression for the force due to solar electromagnetic radiation on a moving dust grain?
• RQ5 How do the effects of electromagnetic radiation and solar wind differ in their influence on dust grain orbital evolution?

Key findings

• The term 'Poynting-Robertson drag' does not correspond to any physically meaningful, relativistically covariant force component and should be abandoned in scientific literature.
• The correct equation of motion for the Poynting-Robertson effect is a single, fully relativistically covariant expression that describes radiation pressure on a moving body, not a decomposition into 'drag' and 'radiation' terms.
• The force due to solar electromagnetic radiation is given by $ \vec{F} = \frac{SA'\bar{Q}'_{pr}}{c} \left\{ \left(1 - \frac{\vec{v} \cdot \vec{e}}{c}\right)\vec{e} - \frac{\vec{v}}{c} \right\} $, which is derived from relativistic electrodynamics and correctly accounts for aberration and Doppler shifts.
• The solar wind force on a stationary particle is $ F_{sw} $, and for a moving particle, it is $ \vec{F}_{sw} = F_{sw} \left[ \left(1 - \frac{\vec{v} \cdot \vec{e}}{v_{sw}}\right)\vec{e} - x' \frac{\vec{v}}{v_{sw}} \right] $, with $ x' $ dependent on particle material (1 < x' < 3).
• Secular evolution of orbital elements shows that semi-major axis and eccentricity decrease over time, with the time to spiral into the star given by $ T[\text{yrs}] = \frac{6.4 \times 10^2}{\beta} \frac{M_{\odot}}{M} \frac{(a_{\beta\text{ in}}[AU])^2 (1 - e_{\beta\text{ in}}^2)^2}{e_{\beta\text{ in}}^{8/5}} \int_0^{e_{\beta\text{ in}}} \frac{z^{3/5}}{(1 - z^2)^{3/2}} dz $.
• As the orbit decays, the eccentricity $ e_{\beta} $ asymptotically approaches $ \beta $, the ratio of particle speed to light speed, confirming relativistic consistency.