Problem 2 define a repeating ground-track orbit whose period of repetition is two orbits per day (we = 7.2921151467-10-5 rad/s), has an eccentricity of 0.74, an inclination of 63.4349 deg, a right ascension of the ascending node of -86.915798 deg, and argument of perigee of 270 deg. Provide the following results using 100 points equally distributed in time over an orbital period with a starting position of true anomaly equal to 0 degrees: a) Semi-major axis of the orbit in kilometers. b) 3D representation of the orbit. Include the Earth (as a simple sphere) in the center of the plot for a size comparison. Make sure that the axis have the same scale. c) Evolution of the radial distance over time. d) Evolution of the magnitude of the velocity over time. e) Evolution of the Keplerian orbital elements over time. This must be done using the transformation from cartesian coordinates to Keplerian elements Problem 3 We are interested in studying the coverage that the previous orbit provides to the ARMS building (40.43094 N, 86.915798 W). We will assume that the satellite has a field of view (complete cone angle) of 10 degrees pointing at Nadir. Additionally, at the initial time, the true anomaly is equal to zero, and the Greenwich meridian points to the Aries point. Under these conditions, determine: a) The ground-track of the orbit. Represent that ground-track in a 2D plot in longitude and latitude and include, with a different colour, the position of the ARMS building in the same plot. b) How much time, in hours, does the ARMS building have coverage from this satellite every day. c) The azimuth and elevation of the satellite observed from the ARMS build- ing as a function of time. Assume that we only have vision when the elevation is larger than 15 degrees.