Fermi questions and orders of magnitude - science on the envelope

How high can a mountain get on earth? How long does it take for a 3cm thick layer of ice to melt when the refrigerator is open and switched off? How big must a space telescope be designed so that it can observe a certain astronomical phenomenon and is it then still realistic to transport it into space? The exact answer to these and similar questions requires extensive analyzes, often based on complex models or information that seems difficult to access. In many cases, however, it is possible to give an approximate answer to the above questions with relatively little effort using an estimate based on simplifying assumptions, i.e. estimate the magnitude of the answer. Using examples from different areas of science (energy, materials, economics, ...), the lecture is intended to give an insight into the elementary methods (divide and rule, dimensional analysis, scaling, ...) that are necessary for this type of problems.