Lab for Ch. 13 - Vector-Valued Functions The last situation (i.e. Ch. 12 Lab) was pretty scary, Earth could have been hit! So, in order to spot these objects in space sooner, it was decided to launch a satellite into deep space. This satellite would observe the space outside of our solar plane, looking for anomalies. In order to get the right angle, a gravity slingshot around Jupiter has been proposed. Describe what type of graph would be used if the satellite were to stop its hyperbolic trajectory but instead orbit Jupiter. Can you find an exact function? What would its eccentricity be? Are there multiple solutions? A hyperbolic trajectory is then considered. A basic shape of the equation started as: 12 Find the velocity and curvature at t = 0. What is different about your findings r? Why would this be used over the function r ? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Seeing that this function is too simplistic, a new hyperbolic trajectory is now considered. 13 = , 22 -- What is different about your findings 2? Why would this be used over the function 12 ? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). To try and adjust the velocity of the trajectory, an alteration was made: r4 , T Discussion question: What is missing from the velocity calculations of the four proposed trajectories? Or, are they accurate to a real-life model? If not, what could possibly be done to alter these trajectories? (Heavy math is not required to get this answer correct, this is simply a discussion question)