**Investigation of the Magnetosphere
of Ganymede with Galileo's Energetic Particle Detector**

*Ph.D. dissertation by Shawn M. Stone, University of Kansas,
1999.*

*Copyright 1999 by Shawn M. Stone. Used with
permission.*

*4.8.2 Solving and Mapping the Boundary*

The external multipole model given in Section
4.3 is unphysical outside the magnetopause
boundary, as unphysical as an image dipole, since the terms
are directly proportional to r. It is essential, then,
to map the boundary of the magnetopause and tail field so
that it can be turned off when the particles exit the
magnetosphere of Ganymede. The ideal method to
approach this problem would have been to propose a boundary
and then impose currents upon this boundary and integrate
via the Biot-Savart law. Unfortunately, the magnetic field
geometry of Ganymede is more complicated than a dipole.
However, it is satisfactory to take the solution in Tables
4.8 and 4.9 and trace field lines until a balance is reached
between the internal and external field lines, thus tracing
out the boundary where the tangential components of the
magnetic field vanish. The first guess boundary is based on
a dipole with magnetic moment of the g_{1}^{0} of the
respective encounter. Figure 4.27 shows a trace for
the G2 model. The function that is used for the fit is

where z_{o} is the offset distance of the
boundary on an axis where the boundary is completely axially
symmetric, denoted here as axial coordinates. This boundary
is then rotated about the GSII X axis by α and
GSII Z axis by β (Figure 4.28)
until the inbound and outbound crossings reach a minimum,
thus attaining the preliminary abberation angles from
corotation. The boundary is then refit in the same
manner as above and the process repeated until there is no
significant change in the aberration angles (less than a
degree). Table 4.10 lists the coefficients of Equation
[4.35] for G2 and G7 along with the aberration angles that
were derived from this process.

**Figure 4.27** Magnetic
line trace for the G2 encounter where r_{o}=2.0 R_{g}. The
magnetic field from the internal Ganymede sources and the
external Jovian field combine to define the boundary which
is then sampled, and the data gathered from this sampling is
fit to Equation [4.35].

**Figure 4.28** Diagram
representing the variation of the preliminary boundary by
the aberration angles α and β.

**Table 4.10** The
boundary parameters for G2 and G7 derived from the fit of
Equation [4.35]. The offset distance r_{o} was
defined as 2.0 R_{g} for the G2 encounter.

G2Boundary Parameters |
Mean |
RMS Error |

ρ_{0} |
0.0 R_{g} |
0.0 R_{g} |

ρ_{1} |
1.552 R_{g} |
±0.002 R_{g} |

ρ_{2} |
2.436 R_{g} |
±0.006 R_{g} |

ρ_{3} |
-6.992 R_{g} |
±0.007 R_{g} |

ρ_{4} |
9.527 R_{g} |
±0.001 R_{g} |

ρ_{5} |
-10.515 R_{g} |
±0.002 R_{g} |

ρ_{6} |
7.891 R_{g} |
±0.005 R_{g} |

z_{o} |
2.0 R_{g} |
±0.0 R_{g} |

α | 10º | ±1.0º |

β | -35º | ±1.0º |

G7Boundary Parameters |
Mean |
RMS Error |

ρ_{0} |
0.0 R_{g} |
0.0 R_{g} |

ρ_{1} |
2.429 R_{g} |
±0.005 R_{g} |

ρ_{2} |
0.524 R_{g} |
±0.003 R_{g} |

ρ_{3} |
-1.180 R_{g} |
±0.009 R_{g} |

ρ_{4} |
-2.790 R_{g} |
±0.003 R_{g} |

ρ_{5} |
6.579 R_{g} |
±0.004 R_{g} |

ρ_{6} |
-4.525 R_{g} |
±0.002 R_{g} |

z_{o} |
2.6 R_{g} |
±.1 R_{g} |

α | 30º | ±1.0º |

β | 40º | ±1.0º |

Next: 4.8.3 Adding Finite Thickness to the Boundary

Return to dissertation table of contents page.

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Galileo Table of Contents Page.

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Technologies Home Page.

Updated 8/23/19, Cameron Crane

## QUICK FACTS

**Manufacturer:**The Galileo Spacecraft was manufactured by the Jet Propulsion Laboratory, Messerschmitt-Bölkow-Blohm, General Electric, and the Hughes Aircraft Company.

**Mission Duration:**Galileo was planned to have a mission duration of around 8 years, but was kept in operation for 13 years, 11 months, and 3 days, until it was destroyed in a controlled impact with Jupiter on September 21, 2003.

**Destination:**Galileo's destination was Jupiter and its moons, which it orbitted for 7 years, 9 months, and 13 days.