IOAA 2021, Теория — Задача 3. Mars (10 points).

Theory — Q3-1 English (Official) — Mars (10 points). · 10 т.

Standard Table of Constants — values used in this problem

Universal gravitational constant: $G=6.674\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

Standard Table of Constants — values used in this problem

Mars: mean radius $3\ 390\ km$; mass $6.417\times10^{23}\ kg$.

Условие

A spacecraft of mass $m=5.0\times10^{4}\ \mathrm{kg}$ approaches in a parabolic orbit $AB$, with respect to Mars. When the spacecraft reaches point $B$ of least distance to the center of Mars, $r_B = 6.8\times10^{6}\ \mathrm{m}$, 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 $(km\ s^{-1})$ of the spacecraft at point $B$ just before the deceleration. [3 т.]

3.2 Calculate the total energy $(J)$ of the spacecraft as it is moving between points B and C. [4 т.]

3.3 Calculate the speed $(km\ s^{-1})$ of the spacecraft at point $C$. [3 т.]

Отговори

Решение

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Оригинал в Архива: TQ-3-Q.pdf · официални решения: TQ3.pdf · допълнителни данни: TQ-3-A.pdf · допълнителни данни: Standard-Table-of-constants.docx.pdf · допълнителни данни: TQ-G.pdf · допълнителни данни: data.pdf