$[$Using Matlab$]$

This time, Space G would like you to conduct an analysis for all planets in the solar system. As you may know, in $2006$ Pluto was demoted to dwarf planet status, but we still include it here in the grouping of "all planets". You should not include the Sun or Moon as Space G has no plans to colonize these objects.

Surface Gravity of the Planets and the Sun

Again, you will use the equation:

$\backslash [$

h$=$V$\_\{$i$\}$ t$-\backslash$frac$\{1\}\{2\}$ g t$^\{2\}$

$\backslash ]$

$-$ where $\backslash (\backslash$mathrm$\{$h$\}=\backslash )$ height. $\backslash (\backslash$mathrm$\{$Vi$\}=\backslash )$ initial velocity,

$-$ Use an initial velocity $\backslash (=25\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Space $\backslash ($ G $\backslash )$ has asked for the following improvements to your initial work:

$-$ Space G would like the analysis of the above equation performed for all planets in the solar system.

$-$ Space G would like each planet's lines representing height over time do be presented on the same axis, ie the same plot includes all planets.

$-$ A single plot should include a line for all planets. Each line should be visually distinguished in some way.

$-$ Plots should show sufficient time such that all paths strike the ground $($surface$,$ height $\backslash (=0\backslash ))$

$-$ Plots should exclude heights $<mtext></mtext><mn>0</mn>$

$-$ Plot should include informative axis labels and title.

$-$ BONUS: plot should include text, specifically the planet's name, at the spot on the curve that corresponds to the max. Along with the text, place a circular marker at the max height point. Note: These features should not be positioned manually, but rather using variables, indexing, and matlab builtins.

$-$ BONUS $2$: Create three subplots, one that shows all the inner rocky planets, one that shows all the gas giants, and one that shows the sun. Then consider the engineering justification for visualizing the way proposed in Bonus $2?$ Consider the draw backs?

$-$ Space G also wants results displayed to the console, clearly and concisely, that show the projectile's max height on each planet.

Hints:

$-$ You really should solve this using for loops. Please avoid writing the same code over and over in your script.

$-$ You may choose to use a single or several for loops. Either is acceptable.

$-$ The plotting should also be something you can accomplish with the for loops and the application of special plot and plot related commands we have discussed.

$-$ You may need to use MATLAB's built in: max, text, hold

Outputs:

Your m$-$script should provide several outputs:

$1.$ Use disp to show the maximum value in the vector height for each planet. The output should clearly indicate which value is for which planet.

$2.$ A plot of height against time as described above.