Electromagnetic Radiation and Motion of a Particle

Abstract

Abstract. We consider the motion of uncharged dust grains of arbitrary shape including the effects of electromagnetic radiation and thermal emission. The resulting relativistically covariant equation of motion is expressed in terms of standard optical parameters.Explicit expressions for secular changes of osculating orbital elements are derived in detail for the special case of the Poynting-Robertson effect. Two subcases are considered: (i) central acceleration due to gravity and the radial component of radiation pressure independent of the particle velocity, (ii) central acceleration given by gravity and the radiation force as the disturbing force. The latter case yields results which may be compared with secular orbital evolution in terms of orbital elements for an arbitrarily shaped dust particle. The effects of solar wind are also presented.

Poynting-Robertson effect and perihelion motion

“…The effect of electromagnetic radiation on spherical micron-sized dust particles yields, in general, a shift of perihelion, while the evolution of the semi-major axis and eccentricity may be calculated within an approximation of constant optical properties (see Eqs. (64)- (65), (102)- (103), with the corresponding initial conditions (58)- (63) in Klačka 2004). The statement about the semi-major axis and eccentricity hold when heliocentric distances are not smaller than about 0.1 AU.…”

“…where f β 0 is a true anomaly (all orbital elements relates to the central acceleration G M (1 − β 0 ), also a true anomaly; corresponding quantities are denoted by subscript β 0, to be consistent with Klačka 2004). Using the fact that the semi-major axis and eccentricity exhibit small changes during one period − 1 6.58E-3 1.89E-3 7.51E-4 −1.08E-3…”

“…The correct approach is to consider the central acceleration given by gravity only, as it is in Eq. (3) and discussed in detail in Klačka (2004). However, if we want to show that the shift of perihelion already exists when the central acceleration is given by the term G M (1 − β), then we make an approximation β = β 0 + β 0 (r − r 0 ).…”

“…(113)- (115) in Klačka 2004). Equation (7) shows that dω β 0 /dt is nonzero and positive if β 0 is positive.…”

“…Although this effect is well-known as the PoyntingRobertson (P-R) effect (Robertson 1937;Klačka 1992Klačka , 1993Klačka , 2004, it was not recognized that it may also produce a shift of pericenter/perihelion in the accuracy to the first order in u/c, where u is velocity of the particle with respect to the source of radiation and c is the speed of light (Robertson 1937;Wyatt & Whipple 1950;Lyttleton 1976). Klačka (2004) has shown that the shift of pericenter/perihelion exists if the central acceleration is given by the gravity of the central star. The general opinion is: if the central acceleration also contains a dominant part of the electromagnetic radiation pressure of the star, then no shift of pericenter exists, supposing that the equation of motion is considered within approximation to the first order in u/c.…”