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##### Calculating the position of the James Webb Space Telescope using Python or TI-Basic

Students calculate the position of James Webb Space Telescope (JWST) using an iterative Python program in Langrange2.tns and TI-Basic in Lagrange3.tns.

Publisher: T³ Europe

Editor: Ian Galloway

Author: Veit Berger

Topic: Mathematics , Physics , Computer Science

Tags Python , Algebra , Solving equations , Gravitation , Lagrange

Most students of advanced physics, ages 16-18 will be able to construct but not solve, the equations which contain the solutions for calculating the positions of the Lagrange points, 1, 2 and 3. These are locations in space which have a curious property. The dominant gravitational field of the Sun is altered just slightly by the Earth’s gravitational field so that an object at those points will have the same orbital period as the Earth itself. Three points are on a straight line through the Sun and Earth. Lagrange 1, between Earth and Sun and Lagrange 2 beyond the Earth from the Sun are ideal points for placing satellites as they will appear to be stationary relative to Earth as they orbit the Sun. Lagrange3 is on the other side of the Sun, and nobody has found a use for that yet!

Students will learn how an iterative technique can be used to solve these otherwise insoluble equations and calculate for themselves the position of the JWST. Lagrange2.tns uses a Python program to iterate while Lagrange3.tns uses TI-Basic and nsolve which is also an interative technique. Teachers looking for a more visual method of finding these points should look at https://resources.t3europe.eu/t3europe-home?resource_id=3487 for a dynamic method which is more qualitative method of understanding these curious Lagrange points.