Hello Universe

The James Webb Space Telescope (JWST) and its high resolution images of the universe has captured the imagination of people around the world since 2022. Before that most people have only a vague recollection of the images captured by the Hubble telescope which still operates today. If you haven’t had the chance to view any of the images captured by either Hubble or JWST I highly recommend that you access them via their respective NASA webpages: https://hubblesite.org/home and https://webb.nasa.gov/

In addition to the NASA website for JWST there are other great resources which discuss some of the engineering challenges encountered along the journey to where we are today. The Netflix documentary “Unknown: Cosmic Time Machine” describes the multi-decade journey of developing the next space telescope as well as some of the major engineering challenges of deploying such an intricate system into space and eventually the sun’s orbit.

In a recent issue of Radiations magazine (Fall 2023 Vol 29 Issue 2) there was a very interesting article authored by Professor Dwight E. Neuenschwander of Southern Nazarene University. The article, entitled “The Five Lagrange Points: Parking Places in Space”, does an excellent job reviewing the mathematical steps required to calculate the so-called Lagrange Points for a two-body system. The article’s primary motivation was to help the reader develop a mathematical understand the various Lagrange Points which exist between the earth and sun two body system.

The mathematical development described by Prof. Neuenschwander is quite detailed and I highly encourage you to read it. One of the most interesting aspects of the development, to me, is that there comes a point when the gravitational potential of the two-body system is given explicitly:

Using the gravitational potential described above one should be able to generate a plot and visualize the local extrema in the gravitational potential which would correspond to the five Lagrange points. There are a few things we should keep in mind as we attempt this.

• The distance between the sun and the earth (center to center) is approximately 149.6e06 kilometers
• The Lagrange points are local “wells” in the gravitational potential field between the sun and the earth. They are “local” phenomena which will need to be resolved when we map the gravitational potential (above) into space