[Paper Review] Electromagnetic Radiation and Motion of Dust Particle - A Simple Model

J. Klačka|arXiv (Cornell University)|May 5, 2000

Experimental and Theoretical Physics Studies3 citations

TL;DR

This paper presents an analytical model for the motion of a dust particle modeled as a rotating plane mirror under solar electromagnetic radiation pressure. It shows that orbital evolution depends critically on initial conditions: particles with low eccentricity spiral outward, while those with high eccentricity spiral inward—challenging the standard Poynting-Robertson effect assumption of universal inward spiraling.

ABSTRACT

A simple model for motion of dust particle (meteoroid) under the action of (solar) electromagnetic radiation is presented. The particle of the form of plane mirror is taken into account and exact analytical results are presented. As for long-term orbital evolution, particle may spiral outwards the central body (Sun); initial conditions are important. As a consequence, motion of real dust particles may differ from that generally considered.

Motivation & Objective

• To develop an exact analytical model for the motion of a dust particle under electromagnetic radiation pressure.
• To investigate how initial conditions, particularly eccentricity, affect long-term orbital evolution.
• To challenge the conventional assumption that all interplanetary dust particles spiral inward due to the Poynting-Robertson effect.
• To demonstrate that radiation pressure on a rotating plane mirror can lead to outward spiraling under specific conditions.
• To provide a foundation for understanding deviations in real dust particle dynamics from simplified models.

Proposed method

• Models the dust particle as a rotating plane mirror with reflective surfaces, using exact first-order relativistic transformations in the particle's rest frame.
• Derives the equation of motion in the source frame using Lorentz transformation to first order in v/c, accounting for radiation flux and momentum transfer.
• Incorporates gravitational acceleration from the central body (Sun) via Newtonian potential, combining it with radiation force terms.
• Calculates secular changes in orbital elements (semimajor axis, eccentricity, longitude of pericenter) using time-averaged perturbation theory.
• Uses trigonometric integrals and series expansions to evaluate long-term orbital evolution, including relativistic corrections.
• Applies the model to derive analytical expressions for the rates of change of orbital elements, including dependence on eccentricity and longitude of pericenter.

Experimental results

Research questions

• RQ1 How does the orbital evolution of a dust particle with a plane mirror geometry differ from the standard Poynting-Robertson effect?
• RQ2 What role do initial orbital conditions—particularly eccentricity—play in determining whether a particle spirals inward or outward?
• RQ3 Can radiation pressure on a rotating reflective particle lead to outward spiraling, contrary to the classical inward spiral prediction?
• RQ4 How do relativistic corrections affect the precession of the pericenter in this model?
• RQ5 To what extent does the particle's orientation (via angle Θ) influence the net radiation force and orbital evolution?

Key findings

• The semimajor axis increases (outward spiral) when the initial eccentricity is less than approximately √(10/33) ≈ 0.55, contrary to the Poynting-Robertson effect.
• The semimajor axis decreases (inward spiral) when the initial eccentricity exceeds √(10/33), consistent with the classical Poynting-Robertson effect.
• The eccentricity always decreases over time, as indicated by the negative time derivative of eccentricity.
• The longitude of pericenter experiences non-zero precession due to radiation pressure, with relativistic corrections shifting the stable equilibrium from ω = ±π/2.
• The model predicts a stable configuration at ω ≈ -π/2 + ε (ε small positive), where the pericenter precession rate becomes zero due to relativistic terms.
• The radiation force depends on the cosine of the angle between the Sun's direction and the particle's normal, leading to anisotropic momentum transfer that drives the observed orbital changes.