(Solved): equation of motion of a particle in a gravitational field. (Hint: use reaction rate by \( 50 \% \) ...

equation of motion of a particle in a gravitational field. (Hint: use reaction rate by \( 50 \% \) (but that is irrelevant for this problem.) \( { }^{2} \) Or your favorite software, \( { }^{3} \) I had to use the command iiGraphics 'Graphics' to load PolarPloL. (a) Plot the orbits for several values of \( c \equiv l^{2} / \gamma \mu \) ( \( \gamma \) is the force constant) on the same graph. [Hint: the Show command combines multiple graphs. I (b) Check analytically that the circular orbit occurs for the expected value of \( c \) (c) For a single value of \( c \), investigate the effect of deviations from Newton's Law of Gravitation. Plot an eccentric orbit for \( F \propto r^{-2.1} \) and for \( F \propto r^{-1.9} \). (Hint: selecting \( \phi \) between 0 and \( 6 \pi \) gives a nice looking graph.) 3. ThP Precession. Starting Irom Eq. \( (8.41) \), use Mathematica- to find the equation of motion of a particle in a gravitational field. (Hint: use In his latest projecti polarizang the nuclear spin of the collfoling particles mighi increase the reaction rate by \( 50 \% \) (but that is irrelevant for this problem.) \( { }^{2} \) Or your favorite software. \( { }^{3} \) I had to use the command ¿iGraphics'Graphic' to load PolarPlot.