### Abstract

Increasing interest is growing within the space industry to design missions capable of sending unmanned objects (e.g. food supplies, instruments, experiment equipments, etc.) to our neighbouring planets. This has motivated the need for the development of low-cost technologies to make these missions ever more frequent and accessible. In this paper, an uncertainty study is conducted in response to the challenge of sending an unmanned object out to space as formulated in this year’s Mathematical Competitive Games challenge (2016-2017). The object is launched from the Earth’s surface towards the Moon and is given an initial thrust that lasts only for a few seconds. Given the intensity and duration of the thrust and all of the other parameters, such as the Earth’s mass, air density, mass of the object, etc. The challengers ask what is the probability of landing the object on the Moon surface given all the uncertainties in the parameters and the model? A Monte Carlo approach is proposed to efficiently estimate the probability of the object landing on the Moon, complying with the assumptions provided by the challengers on the probability density functions. Different physical models and different underpinning assumptions are proposed to simulate the launch. It has been found that, once all uncertainties have been considered, about 37 % of the simulations lead to a successful landing on the Moon’s surface. Conversely, the likelihood of successful landing on a specific area resulted fairly low. In addition, complementary sensitivity analyses are proposed which reveal the projectile motion is most affected by drag uncertainty and least affected by mass uncertainties.

Original language | English |
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Number of pages | 27 |

DOIs | |

Publication status | Published - 30 Apr 2017 |

Externally published | Yes |

### Keywords

- Uncertainty Quantification, Epistemic Uncertainty, Monte 8 Carlo Simulation, Mathematical Competitive Game

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## Cite this

Sadeghi, J., Rocchetta, R., George-Williams, H., & de Angelis, M. (2017, Apr 30). Monte Carlo approach to compute the success probability of sending objects to the Moon. https://doi.org/10.13140/RG.2.2.34247.60325