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Table 2.
Coordinate singularities of the model.
| Variable value | Physical and geometrical meaning |
|---|---|
| αM = 0° | Point source of dust is located at the north or south pole, |
| αM = 180° | its latitude is not defined, and no spherical triangle from Fig. 1 exists |
| α = 0° | Spacecraft is located directly above the north or south pole, |
| α = 180° | its latitude is not defined, no spherical triangle from Fig. 1 exists |
| β = βM | Spacecraft has the same longitude |
| (Δβ = 0°) | as the source. No spherical triangle from Fig. 1 exists |
| Δϕ = 0° | Spacecraft position, source position, and moon center |
| Δϕ = 180° | are on a straight line. No spherical triangle from Fig. 1 exists |
| and the orbit geometry (Figs. 3 and 4) is undefined | |
| ψ = z, | A particle is ejected exactly along |
| z ≠ 0° | the jet axis, the azimuth of ejection is undefined, and the Jacobian |
| in Eq. (12) diverges | |
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