March 21, 2011 | By Brian Clark | 1 Comment »
Categories: Physics, Space sciences
Tags: astronomy, Brian Charles Clark, Joseph-Louis Lagrange, Julian Smith, Kenneth Dorrance, Kyle Welch, Neptune, Science, space, University Physics Competition Lagrangian mechanics
Next time you’re in a pub with a dart board, pick up a dart, stand at the regulation distance, and toss a bull’s eye. Piece of cake, right? Now, stand in that same pub but throw the dart so that it goes into a nice, near orbit around Neptune. Not so easy this time, eh?
But we’re not done. To make things a little trickier, figure on using Neptune’s atmosphere to brake your dart’s velocity. While you’re at it, calculate the path your dart took to get from the pub to Neptune. Write that path out in a series of differential equations. Write a 500-word abstract. Do all this is 48 hours under the auspices of your faculty mentor. You’re almost done! Last step: enter the paper you’ve just written in the University Physics Competition.
With slight variations on the process above (like, they didn’t actually throw a dart), that’s what three WSU physics majors did. Julian Smith, Kyle Welch and Ken Dorrance spent a recent weekend bravely battling the complexities of Lagrangian mechanics to calculate just what it would take to get a rocket from Earth to Neptune. Their efforts won them a bronze award in the competition.
A couple centuries ago, mathematician Joseph-Louis Lagrange made significant contributions to celestial mechanics, the area of math that deals with the movements of planets, moons and various other objects in space – including rockets. “Newton’s second law–force equals mass times acceleration–beautifully describes many simple physical systems when forces are known,” says Dorrance, a junior majoring in physics with the nanotechnology option. “Lagrangian mechanics lets you solve some less-than-simple systems without knowing the forces.”
All three of the young physicists agreed that the mechanics involved in aerobraking a probe in the atmosphere of Neptune is a complex business. “Julian and I spent a lot of time staring at the white board, looking for analytical solutions, while Ken worked on coding methods for finding numerical solutions,” says Welch, a senior from Olympia majoring in physics and neuroscience.
“Being someone who focuses on theory, I often like to believe that there will be a clean analytical solution for everything,” says Welch. “However, the complexity introduced by the drag of aerobraking showed me that sometimes you have to give up on finding an exact solution.”
Not only was the problem complex, but the three-person team had only 48 hours in which to formulate their solution. This involved investigating the composition of the upper reaches of Neptune’s atmosphere where the probe would experience frictional resistance and be slowed enough from its interplanetary velocity to go into orbit around the gas giant. Between the three of them, they hammered out a solution that satisfied them.
The University Physics Competition annually offers teams a choice between two problems.
“We chose the problem we thought would be the most interesting, and opted out of the one we thought would be easier to solve,” says Smith a senior in physics from Vashon Island. “The aerobraking problem was exciting for all of us but we really had to think outside the box. This contest taught us to be creative and to think quick.”
Michael Allen, the students’ mentor and competition advisor, says the competition problems are unlike what they would find in a textbook.
“The problems do not have a single approach, and do not have a single correct answer,” he says. “Also, the students are allowed Internet access whilst solving the problem, hence they have a lot of information available to them and must pick that tiny, relevant bit of it to use. In other words, there is scope for being creative, but there is also a need for discipline.”