Closed-form Expressions of Vector Gravity and Gravity Gradient Tensor due to a Line Segment

Closed-form expressions of vector gravity and gravity gradient tensor based on a line segment are derived. If a cylindrical object with axial symmetry is observed from a distance, it is possible to approximate it as a line segment; therefore, it is necessary to compute the gravity and the gravity gradient tensor due to a line source by using closed-form expressions. The gravitational potential for a line segment is defined as a one-dimensional integral, and this integral is differentiated with respect to the Cartesian coordinate system to derive the vector gravity. The expressions of the gravity gradient tensor are derived by differentiating the vector gravity once more in the same coordinate system.