A spacecraft is launched on a geosynchronous transfer orbit (GTO) with period 12 hours, inclination of 0 degrees and eccentricity of 0.75. 1. Compute the orbit semi-major axis, perigee and apogee radius. You are to store your answers in the variables named a_gto, rp_gto, and rg to , respectively. (Value: 20 points) 2. Compute the velocity at perigee and apogee. You are to store your answers in the variables named vp, and va, respectively. (Value: 15 points) 3. The spacecraft needs to be injected into an interplanetary transfer. Compute the escape velocity at apogee and perigee (use variables named v_e_p, and v_e_a for your answer, respectively). Also compute the associated v in both cases; you can store these answers in variables delta_v_p and delta_v_a. Based on the obtained results identify the best option to minimize the required propellant mass for the manoeuvre; store your choice under the variable named best_delta_v. (Value: 25 points) 3. Consider the situation where the escape trajectory needs to be inclined by 28 degrees with respect to the equatorial plane. Compute the v of a single manoeuvre that injects the spacecraft into the escape trajectory with the required inclination for both the apogee and perigee case; store your answers in variables delta_v_p_inclination and delta_v_a_inclination. Based on the obtained results identify the best option to minimize the required propellant mass for the manoeuvre; store your choice under the variable named best_delta_v_inclination . (Value: 20 points) Relevant constants - Radius of the Earth, RE=6378km - Earth gravitational parameter E=3.986105km3/s2 These constants have been defined in the variables R_E , and mu_E for you below. Please make use of these variables in your calculations. In the same code cell, we have also provided access to the constant for ( pi in computing font), and access to the sine and cosine functions ( s in and cos respectively). As an example, we also demonstrate how to use sin and pi. Lastly, we also demonstrate how to use abs to get the absolute value of a number (or function). You may find you need this in various calculations