### Abstract

A novel analytical formula is developed for the second order approximation of the potential function of a pair of charged spacecraft assuming either particle-body or body-body interactions. These approximations use the center of charge (CoCh) as the center of expansions provided that the charge distribution is known. The generated formulas for the potential function are then used to analytically find Coulomb force and corresponding moment about the center of mass (CoM) of the interacting bodies. The resulting expressions are presented in terms of the entire charge and the quadrupole charge tensor (QCT) of each individual body about the corresponding CoCh, as well as the relative distance between the centers of charge of the two charged spacecraft. Because of using expansions about the CoCh, dipole moments of each individual spacecraft do not explicitly appear in the resulting equations. Closed-form approximations of the force and moment are also obtained from the potential function using the CoM expansions. As it is shown, the CoCh expansions are generally more accurate when the distance between the CoCh and the CoM is a significant fraction of the separation distance.

Original language | English (US) |
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Pages (from-to) | 829-862 |

Number of pages | 34 |

Journal | Journal of the Astronautical Sciences |

Volume | 67 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 2020 |

### Keywords

- Center of charge
- Charged spacecraft
- Coulomb
- Dipole moment
- Force
- Moment
- Quadrupole charge tensor

### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science