Problem #4: The following problem is relevant to recent news regarding the James Webb Space Telescope, where some have seen the term Lagrangian point. Students have been asking me about this, so let's figure it out together! A Lagrangian point can be simplistically defined to be a location in space where the force of gravity between two masses cancels out, i.e., Fnet = 0 Newtons. These serve practical purposes; for example, the Solar and Heliospheric Observatory (SOHO) satellite investigates properties of the Sun, such as its solar atmosphere and solar winds. The SOHO satellite is placed at a Lagrangian point known as L1. The newly launched James Webb Space Telescope is placed at a different Lagrangian point, known as L2. Using the distance between the Earth and the Sun, 1.5 x 1011 meters, calculate one location of a Langrangian point between the Earth and the Sun where a small satellite can be placed and feel no net force due to the force of gravity of the Earth and the Sun. Conceptually, should the Lagrangian point be nearer to the Earth or the Sun? Why? Explain your answer. Be sure to include any diagrams needed to arrive at any answer. As side research, you are encouraged to consider why there are multiple Lagrangian points, and if the methodology used is the only way to find these locations (or, more precisely, can the methods taught in this class be considered a general way to solve for where these locations exist?).