Derivation of the 1st cosmic velocity

Abstract

In almost every high school physics textbook, the derivation of this velocity using centrifugal force is mentioned. Other possibilities of this derivation are given in the text. For an ordinary high school student, these are more demanding calculations, so it is appropriate to include this issue in physics seminars for students with a deeper interest in physics - it is a derivation using the Pythagorean theorem and trigonometric functions. The last two derivations (free-fall into the centre of the Earth and the law of conservation of mechanical energy) require the basics of higher mathematics (calculus, a certain integral and differential equation of harmonics) and are therefore suitable for gifted high school students with extended mathematics teaching. It is also possible to use them in the first semesters of universities as a practical example of the application of higher mathematics in astrophysics.