We analyze spacecraft formation establishment and reconfiguration problems for two-body orbits. The desired formations are characterized by nonsingular orbital-elemental differences. An analytical, two-impulse solution is proposed for achieving the desired orbital-elemental differences. Gauss's variational equations are used to compute the corresponding impulse magnitudes analytically and the resulting solutions can be easily implemented using onboard computational resources. It is also shown that the cost obtained from the analytical solution differs by less than 1 % from that obtained by numerical optimization.