A space satellite is orbiting Earth in an elliptical low orbit. The satellite positions (x, y spatial coordinates) are recorded every 5 minutes and are given for one orbit rotation

in the table below (the time of one orbit rotation is approximately 90 minutes). The goal of this problem is to determine the semi-axes a and b of the elliptical orbit, and its eccentricity e=\sqrt{1-\frac{b^{2}}{a^{2}}} NOTE: The equation of an ellipse is \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 1) The problem can be formulated as finding the least squares solution for a system Aââ = b. What are A and b (give symbolic forms)? HINT: The vector is \hat{\boldsymbol{x}}=\left[\begin{array}{l} 1 / a^{2} \\ 1 / b^{2} \end{array}\right] Solve the least squares problem using python. You are allowed to use built-in solvers for linear equations. Built-in data fitting functions are NOT allowed. Give the values for a, b, and e. On the same plot, plot the original data as points alongside a curve representing the least squares model of the ellipse.