A finite-time observer design for translational and rotational motion states of a rigid body modeled for a spacecraft and the parameters of an asteroid is presented. This nonlinear observer presents almost global convergence of the state and the parameter estimations in finite time using the state measurements of the rigid spacecraft's pose and velocities. The states include the pose and velocities of a rigid body of a spacecraft while the parameters include the second order and degree of gravity coefficients, and the gravitational parameter of an asteroid. The observer design is based on the use of the exponential coordinates to describe rigid body pose estimation errors on SE(3), which provides an almost global description of the pose estimation error. The finite-time convergence of the state and gravity parameters estimations of the observer is verified using a Lyapunov analysis on the nonlinear state space of the motion. Numerical simulation results confirm this analytically obtained convergence property and the robustness in the presence of measurement noises.