Dark matter and gravitational lensing as teaching tools for physics and astronomy

In this work, mainly aimed at teachers of physics, mathematics and astronomy, it is illustrated how two important topics of cosmology can be introduced as valuable teaching aids: the dark matter problem and gravitational lensing. These complex and articulated topics have been treated with appropriate elementarisation and the use of simplified models, that made them suitable for introduction into the classroom in the form of exercises and/or extracurricular projects for students in their final years of secondary school or first years of university. In the first part of this thesis, the concepts of radial and rotational velocity, together with those of spider diagram and rotation curve, are introduced and applied to the solar system and a spiral galaxy. The inclusion of the spider diagram in this educational context is innovative. All this is discussed while working with real data and using the dynamic mathematical software Geogebra. Finally, we estimate the amount of non-visible mass that apparently influences the motion of all matter in a spiral galaxy. This provides evidence for the possible existence of dark matter. In the second part, we discuss the phenomenon of strong gravitational lensing, which can produce optical illusions observable in the universe. This effect is investigated for several examples of mass distributions acting as lenses. By examining the geometry of the gravitational lens system, we deduce size, distances and alignment of the components. Using this information and thanks to the software Geogebra, visualisations and interactive simulations of the images resulting from the gravitational lensing effect are created. Finally, the form to be given to lenses made of glass, to recreate the same effects produced by gravitational lenses, is studied. We have designed and produced five models of plexiglass lenses, that add an experimental part to the teaching of this subject, as they reproduce the gravitational lens effect directly in the classroom.