A computationally efficient semi-analytical model for the dust environment of comets and asteroids

Open Access

Table 1

Definition of variables.

Variable	Definition	Variable	Definition
T_j	Time of dust ejection by a given source	t_now	Time at which the dust number density is computed
r	Heliocentric position vector of the point in space where the density is calculated (“spacecraft position”, “point of interest”)	r_M	Heliocentric position vector of the source
α	Polar angle of the spacecraft position	α_M	Polar angle of the source
ω	Eastern longitude of the spacecraft	ω_M	Eastern longitude of the source
Δt	Time interval from T_j to t_now	Δτ	Length of the time interval centered at T_j over which the given source ejected dust
V	Asteroid velocity vector at the time of dust ejection T_j	Δϕ	Angle between vectors r and r_M
v	Particle’s speed at the time t_now	u	Particle’s speed at the time T_j
θ	Angle between the particle’s velocity and position vectors at the time t_now	ψ	Angle between the particle’s velocity and position vectors at the time T_j
λ	Azimuth of the particle’s velocity vector, measured clockwise from local north at the time t_now	λ_M	Azimuth of the particle’s velocity at ejection (at the time T_j), measured clockwise from local north
Γ	Total number of particles ejected by one source	γ	Rate of dust-particle ejection
R	Radius of the particle	n	Number density of dust at the given point at the given time
ζ	Zenith angle of the source symmetry axis	η	Azimuth of the source symmetry axis measured clockwise from local north
μ_R	Gravitational parameter of the Sun reduced to account for solar radiation pressure	β	Ratio of the radiation pressure force to the gravitational force
a	Dust particle heliocentric acceleration at ejection

p_x, p_y, p_z	Cartesian coordinates of the vector p in the given CS	p*	The value of variable p satisfying the given conditions
$p^{A}, p^{\tilde{A}}$ $\[p^{A}, p^{\tilde{A}}\]$	Equivalents of variable p defined, respectively, in the CS A or $\tilde{A}$ $\[\tilde{A}\]$ moving in the heliocentric CS with the asteroid velocity V. (see Fig. 5)	f_p, f_{p, q}	Respectively, a differential distribution of the variable p and a combined differential distribution of the variables p and q

Notes. In Ershova & Schmidt (2021), β and β_M denote the eastern longitudes of the spacecraft and the dust source, respectively. We used a different notation to prevent confusion as β conventionally represents the ratio of the radiation pressure force to the gravitational force.

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