The change in the motions of the Earth and spacecraft launching: a college physics level analysis

• Main Author: Gengmin Zhang
• Format: Article
• Language: Portuguese
• Published: Sociedade Brasileira de Física
• Series: Revista Brasileira de Ensino de Física
• Subjects: segunda velocidade cósmica; terceira velocidade cósmica; movimento da Terra; conservação do momento; conservação do momento angular; energia cinética da Terra
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300015&lng=en&tlng=en

Both the translational velocity and the angular velocity of the Earth change during a spacecraft launching process, in which a spacecraft is accelerated from the ground and eventually sent into space. This article presents a systematic study of the role played by the changes in the translation and rotation of the Earth in spacecraft launching. Neglecting these changes, which inevitably arise in the interaction between the Earth and the spacecraft, there is an obvious conflict with the conservation laws of momentum and angular momentum. Nevertheless, this flaw in principle is not accompanied by any technically erroneous answers when college students solve the often-encountered exercise problems, thanks to the special reference frames students use. It is pointed out that the technical validity of the Earth-in-constant-motion approximation cannot be generalized to arbitrary reference frames. For example, the correct values of the second and third cosmic velocities cannot be found in an arbitrary reference frame if the velocity of the Earth is treated as a constant. In an arbitrary reference frame, the increase in the translational kinetic energy of the Earth, which is caused by the work done by the gravitational pull by the spacecraft, is not negligible if compared with the increase in the kinetic energy of the spacecraft. It is also demonstrated that the disparity in the energy consumed in launching a spacecraft from the ground along different directions cannot be well interpreted if the angular velocity of the Earth is treated as a constant. When the spacecraft is launched eastwards, the increase in its kinetic energy is partly gained, either directly or indirectly, at the expense of a decrease in the rotational kinetic energy of the Earth.