Closed JulienPeloton closed 13 hours ago
In order to gain intuition, we should estimate parameters using several initial vectors:
00
01
10
11
where
$$ P{sidereal}^{\pm} = P{synodic} \dfrac{2\pi}{2\pi \pm \beta} $$
with $\beta$ being the median angle between the unit vectors for the asteroid at position $t$ and position $t + P_{synodic}$ (phase shift). Note that $\alpha_0^{alt}, \delta_0^{alt} = (\alpha_0 + \pi) \% 2\pi, -\delta_0$ (the symmetric solution).
In order to gain intuition, we should estimate parameters using several initial vectors:
00: $\alpha_0, \delta0, P{sidereal}^{+}$01: $\alpha_0, \delta0, P{sidereal}^{-}$10: $\alpha_0^{alt}, \delta0^{alt}, P{sidereal}^{+}$11: $\alpha_0^{alt}, \delta0^{alt}, P{sidereal}^{-}$where
$$ P{sidereal}^{\pm} = P{synodic} \dfrac{2\pi}{2\pi \pm \beta} $$
with $\beta$ being the median angle between the unit vectors for the asteroid at position $t$ and position $t + P_{synodic}$ (phase shift). Note that $\alpha_0^{alt}, \delta_0^{alt} = (\alpha_0 + \pi) \% 2\pi, -\delta_0$ (the symmetric solution).