Methods Remote Sensing of Saturn’s Bow Shock Chrystal Moser & Charles Stine UNIVERSITY OF NEW HAMPSHIRE Introduction Results As the planet Saturn orbits the sun, it's magnetic field carves a wake through the solar wind. This wake is similar to that of a speed boat across a calm lake: the solar wind particles collide with the magnetic field of the planet and pile up until they fall to the side. This is the planet's bow shock. Changes in speed and density of the solar wind cause the shape of the shock to change over the course of time. When a certain set of solar wind conditions happen to occur, a Langmuir wave is released along a tangential trajectory to the shock. These waves can be intercepted by satellites such as the Voyager 1 and 2 probes. From that information, and knowing the position of the satellite when it picked up the Langmuir wave, it is possible to calculate the exact shape of the shock. We seek to use the data from multiple Langmuir waves to find the shape of the bow shock for different sets of solar wind conditions, and find correlations between the two. The result will make it possible to predict the shape of Saturn's bow shock from the characteristics of the solar wind, which is what we are looking for. To state the problem mathematically we consider the general formula for a parabolic shock in terms of two parameters, and the equation for the path of the Langmuir wave, which is a tangent line to the shock: For our first approach in solving this problem we use an numerical method. Combining the above equations results in a quadratic equation in terms of t: In order to ensure that we have a tangent point, t can only have one solution, which occurs when the value under the square root in the quadratic formula is equal to zero: The numerical program takes this equation, which contains both As and Bs, and starts by picking a small As value and evaluating the equation for many different Bs values; then it increases As by a small amount and repeats the process. Thus it tests every combination of the two over a plausible range for each, and it writes down those combinations which make the equation close to zero. Our second approach is analytical, when the above equation is fully expanded and the known quantities are grouped it looks like this: Where: That is a single equation with two unknowns, which cannot be solved. We deal with this by pairing up lines in the data table that have the same solar wind conditions. Each line gives us a version of that equation, and because the conditions are the same in each line of the pair, we know that the As and Bs values are the same as well. That leaves us with two equations and two unknowns. We then perform elimination, and use the quadratic formula to get a pair of solutions: The analytical approach leaves us with two solutions, however we see that one of the two solutions is trivial to discount. The remaining solution matches the with the solution from the numerical method precisely. In the end, by comparing the sets of possible answers each method produced, we are able to find a single common answer, one that makes physical sense. By doing this for each pairing, we hope to find correlations between the ram- pressure at a certain time, and the shape of the bow shock at the same time. Average RamPAsBs Having produced a table of average ram pressure across each pair, we proceed to plot our results. It becomes apparent that there is quite a poor correlation. We think this is because our tolerance for choosing similar ram pressures, while pairing our events, was too high. We intend to continue working on finding different approaches to our calculations, and how we represent our data, in the hope that a useful correlation may yet arise. A S [R S ] B S [R S -1 ] P RAM [Pa]