2021年IOAA理论第3题-火星

英文题目

A spacecraft of mass $$m=5.0\times 10^{4} kg$$ approaches in a parabolic orbit 𝐴𝐵, with respect to Mars. When the spacecraft reaches point 𝐵 of least distance to the center of Mars,$$r_{B} =6.8\times 10^{6} m$$, it undergoes an instantaneous deceleration using its rockets and goes into a perfectly calculated orbit so that it will touch the Martian surface exactly at point 𝐶, diametrically opposite 𝐵, as shown in the figure.

3.1 Determine the speed ($$km\cdot s^{-1} $$) of the spacecraft at point 𝐵 just before the deceleration.

3.2 Calculate the total energy (𝐽) of the spacecraft as it is moving between points B and C.

3.3 Calculate the speed ($$km\cdot s^{-1} $$) of the spacecraft at point 𝐶.