Problems in physics and mathematics contexts with middle and high school classes: vertical and horizontal comparison

My thesis falls within the framework of physics education and teaching of mathematics. The objective of this report was made possible by using geometrical (in mathematics) and qualitative (in physics) problems. We have prepared four (resp. three) open answer exercises for mathematics (resp. physics). The test batch has been selected across two different school phases: end of the middle school (third year, 8\textsuperscript{th} grade) and beginning of high school (second and third year, 10\textsuperscript{th} and 11\textsuperscript{th} grades respectively). High school students achieved the best results in almost every problem, but 10\textsuperscript{th} grade students got the best overall results. Moreover, a clear tendency to not even try qualitative problems resolution has emerged from the first collection of graphs, regardless of subject and grade. In order to improve students' problem-solving skills, it is worth to invest on vertical learning and spiral curricula. It would make sense to establish a stronger and clearer connection between physics and mathematical knowledge through an interdisciplinary approach.

Spacecraft Collision Probability Calculation from Conjunction Data Message and High Precision Orbit Propagator

The increasing number of Resident Space Objects (RSOs) is a threat to spaceflight operations. Conjunction Data Messages (CDMs) are sent to satellite operators to warn for possible future collision and their probabilities. The research project described herein pushed forward an algorithm that is able to update the collision probability directly on-board starting from CDMs and the state vector of the hosting satellite which is constantly updated thanks to an onboard GNSS receiver. A large set of methods for computing the collision probability was analyzed in order to find the best ones for this application. The selected algorithm was then tested to assess and improve its performance. Finally, parts of the algorithm and external software were implemented on a Raspberry Pi 3B+ board to demonstrate the compatibility of this approach with computational resources similar to those typically available onboard modern spacecraft.