## Gravitational forces and moments on spacecraft, Volume 2618 |

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arbitrary constant attitude dynamics center of gravity centrobaric body collection of terms confirming Eq defined in Eq degree in rJ/R Derivations dextral differential element differentiation with respect distance earth exceeds the greatest expressed as F F exerted force F force function forces and moments given by Eq gravitational attraction gravitational forces exerted Hence inertia dyadic inertia ellipsoid Legendre polynomials Legendre's equation line joining line of action mass center mass density moments of inertia necessarily rigid obtained orthogonal unit vectors parallel particle particular solution position vector potential energy principal axes products of inertia quantity relative replaced rigid body satisfies Laplace's equation scalar function shown in Fig small body spacecraft spherical coordinates spherical harmonic substituted into Eq symmetry axis system of forces system of gravitational tr(I unit vector directed universal gravitational constant validity of Eq vector basis VVV(R zero