Shue model

The empirical model for the Earth's magnetopause proposed by Shue et al. (1998) is given by:

r (θ) = r_{0} {(\frac{2}{1 + \cos θ})}^{α}

where:

$r (θ)$ is the radial distance of the magnetopause from the Earth's center at a given colatitude $θ$ ,
$r_{0}$ is the subsolar standoff distance of the magnetopause, given by:

r_{0} = (11.4 + 0.013 B_{z}) P_{d y n}^{- \frac{1}{6.6}}, for B_{z} \geq 0

r_{0} = (11.4 + 0.14 B_{z}) P_{d y n}^{- \frac{1}{6.6}}, for B_{z} < 0

α = (0.58 - 0.01 B_{z}) (1 + 0.01 P_{d y n})

P_{d y n} = 1.15 \cdot n \cdot v_{x}^{2} \cdot 1.67 \times 10^{- 6}

The crossings used to construct this model where taken from satellites of equatorial orbit, and thus assumes a rotational symmetry over the x axis.

Evidence of dipole tilt, indentation in the near-cusp region and dawn-dusk assymetry leads to the construction of the Lin Model