A spacecraft at Saturn is initially in an orbit with the following orbital elements: a = 500 × 103 km, e = 0.9, and an inclination i = 15◦. The ascending node (point A) of the orbit has a radius of 240 ×103 km. Denote initial orbit as 1 and final orbit as 2 in your notations. 1. What is the true anomaly at the ascending node (point A)? Use the value from 0 to 180 deg. 2. What is the velocity and flight-path angle at this ascending node? 3. Without changing a and e of the orbit, what is the ∆V required at this ascending node to enter the spacecraft into an equatorial orbit (with 0◦ inclination)? 4. Draw three schematics, for each, show the radial, tangential and normal directions denoted as ˆur, ˆut, and ˆun respectively. (i.) Velocity at point A for the initial orbit, V A,1, viewed above the orbital plane. (ii.) Velocity at point A for the final orbit, V A,2, viewed above the orbital plane. (iii.) Velocities at points A for BOTH the initial and final orbit, as viewed directly into the radial direction (showing tangential and normal components).