After the engines of a \(100 \mathrm{~kg}\) spacecraft have been shut down, the spacecraft is found to be a distance \(10^{7} \mathrm{~m}\) from the center of the earth, moving with a speed of \(7000 \mathrm{~m} / \mathrm{s}\) at an angle of \(45^{\circ}\) relative to a straight line from the earth to the spacecraft.

(a) Calculate the total energy and angular momentum of the spacecraft.

(b) Determine the semi-major axis and the eccentricity of the spacecraft's geocentric trajectory.