Le coin des amatheurs de sciences version 2

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Tintin on the Moon |

Several scientists have checked the journey of the rocket in *Destination Moon* and *Explorers on the Moon*. Here is one of them, made by Charles de Granrut.

First check

*Destination Moon*, page 60 : a man says that the rocket is situated 800 km (497 miles) from the Earth and that the atomic motor is running. Using the relation s^{2} = 2ax (where s is the speed, a is the acceleration and x the position) and taking a = 20 m/s/s (chosen by making a compromise between the needed acceleration to separe the rocket from the Earth and the acceleration that human can bear), we find a speed of 5,7 km/s (3.5 miles/s). Moreover, the relation s = at (where t is the time) shows that the rocket has been travelled for 4 min 43 s.

By doing similar arithmetics, we can find the rocket's speed and the passed time at different moments :

- Page 61 : the rocket is 1500 km (932 miles) from the Earth.

- *Explorers on the Moon*, page 2 : the rocket is 4000 km (2,486 miles) from the Earth.

- Page 3 : the Thompson learn that the rocket is 8000 km (4,972 miles) from the Earth and has a speed of 11 km/s (6.8 miles/s).

- Page 5 : the rocket has a speed of 13 km/s (8.1 miles/s) and isn't submitted anymore to the Earth's attraction.

- Page 13 : the speed is 45 km/s (28 miles/s).

The results can be sum up :

Distance | Speed | Passed time |

800 km (497 miles) | 5,7 km/s (3.5 miles/s) | 4 min 43 s |

1 500 km (932 miles) | 6,4 km/s (4 miles/s) | 6 min 40 s |

4 000 km (2,486 miles) | 8,4 km/s (5.2 miles/s) | 12 min 19 s |

8 000 km (4,972 miles) | 10,9 km/s (6.8 miles/s) | 19 min 14 s |

12 200 km (7,582 miles) | 13 km/s (8.1 miles/s) | 25 min 7 s |

166 876 km (103,714 miles) | 45 km/s (28 miles/s) | 1 h 49 min 17 s |

Conclusions

- At 8000 km (4,972 miles), the professor Calculus round the passed time to a half-hour. The calculated speed (6.77 miles/s) correspond to the announced speed (6.84 miles/s), because we haven't considered the loss of rocket's weight (loss of fuel).

- Little mistake at 12 200 km (7,582 miles) : the rocket is submitted to the earth attraction (it will always, even on the Moon). The right thing is, that with a speed of 13 km/s (8.1 miles/s), the rocket passed the needed speed not to fall in direction of Earth if the motor was ctopped.

- By finishing the operations, we find that the point where the rocket turn over is situated 188 100 km (116,905 miles) from the Earth (with a speed of 47,4 km/s = 29.5 miles/s). The passed time is then 2 h 47 s. Considerating that this point is the middle of the journey, and that the rest of the travel is so long as the first part, the travel to Moon would last 4 h 1 min 34 s. Very good : the Apollo missions needed 4 days !

Second check

We can do an other calcul, made by Roland Lehoucq and Robert Mochkovitch. Published in *Mais où est donc le temple du Soleil ?* (*Where is the Temple of Sun ?*, Flammarion, 2003), it gives the following results :

Distance | Speed | Passed time |

8000 km (4,972 miles) | 11 km/s (6.8 miles/s) | 30 min |

10 000 km (6,215 miles) | 12,66 km/s (7.9 miles/s) | 32 min 49 s |

10 447 km (6,493 miles) | 13 km/s (8.1 miles/s) | 33 min 24 s> |

12 007 (7,462 miles) | 13 km/s (8.1 miles/s) | 35 min 24 s> |

16 348 km (10,160 miles) | 15,94 km/s (9.9 miles/s) | 40 min 24 s |

25 914 km (16,106 miles) | 15,94 km/s (9.9 miles/s) | 50 min 24 s |

116 171 km (72,201 miles) | 45 km/s (28 miles/s) | 1 h 39 min 46 s> |

196 579 km (122,175 miles) | 60,02 km/s (37.3 miles/s) | 2 h 5 min 17 s) |

240 000 km (149,161 miles) | 52,45 km/s (32.6 miles/s) | 2 h 18 min 9 s |

326 200 km (202,735 miles) | 32,55 km/s (20.2 miles/s) | 2 h 51 min 57 s |

370 200 km (230,081 miles) | 14,01 km/s (8.71 miles/s) | 3 h 23 min 28 s |

375 200 km (233,188 miles) | 9,9 km/s (6.2 miles/s) | 3 h 30 min 26 s |

376 200 km (233,810 miles) | 0 | 3 h 33 min 48 s |