1 PM Mon Ja 5, Bonus Question + 20pt Part of my research involves the dynamical evolution of hierarchical triple systems. For example. we can consider a star orbited by a planet on a tight conguration and a companion star 011 a much wider orbit (See Figure 2 for a cartoon of the system). As another example, consider a binary star system orbited by a far away companion. In particular, I showed that the orbits (both the tight and the wide) undergoes eccentricity and inclination oscillations, Adding tidal friction between the two inner objects (just like the tides between the earth and the moon - they convert orbital energy to heat), and general relativity (not important for the question) I have calculated the evolution of triple stars. In Figure 2 I am showing two different examoles of the evolution of hierarchical triple systems, The left column shows a system that resulted in merger l ** Hicrarclucal tnple system \"3% L_I|2 9"\" humour: L Li a \"outer . mm ' ' 'inner' _' o 10- axio- 5x107 10' 1 [W] t [yr] Figure 2: Left: Cartoon of the system. Right: The evolution of hierarchical stellar systems, The left column shows a system that resulted in merger while the right column is of an inner binary that shirnked its separation to a stable tight conguration In the top panel we show the eccentricity (a value between 1 and 0 which measures how elliptical an orbit is. if its 0 its circular and if e = 1 its a radial orbit) for the inner binary (red lines), Bottom panel shown the inner binary separation (red lines) and the pericenter distance, closest approach in an orbit (blue lines). Figure adopted (and somewhat reconfigured) from N202 and Fabrycky (2014). while the right column is of an inner binary that shirnked its separation to a stable tight conguration. Both had different initial conditions that resulted in these dierent fates. Look at the gure and the oscillations of the eccentricity of each system [eccentricity is A a value between 1 and 0 that measures how elliptical an orbit is. If its 8 = 0 the orbit 5 is circular and if e = 1 its a radial orbit - we will learn more about eccentricity later / in the course, but its easy to understand it already now]. Can you relate these two 8 examples to the subject learned in class? How would you classify those two examples V in relation to what we discussed in class