Write a function integrate$\_$earth $($ tmax,$dt=1e-3$ that returns the trajectory of the Earth, assuming that the Earth only feels the attraction from the Sun.

Produce a trajectory for time $0t$ tmax in steps of $dt.$

$dt$ is an optional argument with default value $1{10}^{-3}yr.$

Return a $(N,3)$ numpy array for the $x,y,z$ coordinates of the earth.

$($Note: numpy arrays are containers, so if you are changing a numpy array $r$ in place with $r+=v^{**}dt$ in your code then you need to copy them when appending to your results list, e$.$g$.,$

r$\_$values.append$($r$.$copy$())$

Otherwise you'll find that your list contains $N$ times the same three numbers. If you don't use inplace operations then that's not a problem for you, but the copy is still safe.$)$

TEST: $1-$year Trajectory

Compute and visualize the trajectory for $1yr$ :

Run integrate$\_$earth$(1).$

Plot the $x$ and $y$ coordinates.

Label the axes $"x(AU)"$ and $"$y $($AU$)".$

Write the figure to the file "orbit$\_$earth$\_$only.png$".$