Abstract: In the college classroom teaching of the orbital mechanism, students easily confuse Jacobi constant of the circular restricted three-body problem with the orbital energy of the spacecraft. To solve this issue, in this paper, we derive the expression of the derivation of orbital energy, and uncover the mechanism of the gravity assist or flyby. Then, a new and concise approach to derive Jacobi constant is proposed. Finally, the difference between the orbital energy and Jacobi constant is clarified. The result in this paper can help students figure out the key point in the orbital dynamics.