This is a computational homework. Answer the questions from exercise 8.25 in a document, showing the graphs you created and short discussions. Also attach your code. If you use a python notebook, you can include everything in 1 document. You can use any programming or scripting language (Python, C, C++, Fortran, Matlab, etc.). If you use a compiled language such as C++, do not try to make plots within it, but write the data to a file and use an external (easier) program to make the plots (gnuplot, xmgrace, matplotlib, etc). Since this is not a coding class, your code does not have to be the most optimized one. You can use library functions (you don't have to explicitly code any numerical algorithms). For figures, do label the axes, and use a legend when needed. If you decide to use python, but don't want to install anything on your computer, you can use Google colab (colab.research.google.com). Make sure to give me access to your code./n8.25 *** [Computer] Consider a particle with mass m and angular momentum & in the field of a central force F = −k/r5/2. To simplify your equations, choose units for which m = l = k = 1. (a) Find the value r。 of r at which Ueff is minimum and make a plot of Ueff (r) for 0 < r ≤ 5r. (Choose your scale so that your plot shows the interesting part of the curve.) (b) Assuming now that the particle has energy E = −0.1, find an accurate value of rmin, the particle's distance of closest approach to the force center. (This will require the use of a computer program to solve the relevant equation numerically.) (c) Assuming that the particle is at r = 'min When ¢ = 0, use a computer program (such as "NDSolve" in Mathematica) to solve the transformed radial equation (8.41) and find the orbit in the form r = r() for 0≤≤7л. Plot the orbit. Does it appear to be closed?

Fig: 1