Introduction
Mars is one of the most intriguing planets to look at. It is close to earth in relation to other planets, making it easier to look at and explore. It also allows for the closest comparisons to earth in terms of temperature, atmosphere, and make-up of the planet. Some even fantasize that Mars may be a planet that humans could possibly inhabit one day.
One of the most peculiar things on Mars is the abnormally large dust storms that can occur. Some of these storms can cover large portions of the planet at one time. It turns out that these storms have a strong relationship with the planet’s orbit and distance from the sun.
Scientists at NASA are trying to further study these dust storms. Since the storms are not going on all the time, the scientists need you to help them evaluate when these storms tend to happen and when the next chance to study them may occur.
Using a mathematical background, the scientists at NASA would like for you to develop a presentation explaining when the dust storms on Mars tend to happen and when the next chance to observe one may occur. Remember that for your ideas to be considered meaningful, your presentations should include mathematical data and models to support your thoughts (i.e. graphs and equations of the path of orbit that Mars takes).
Task
Your task is to use the following resources as well as information you already know about ellipses, specifically the characteristics of the foci of an ellipse, to predict the next most likely time that dust storms could occur on Mars?
If NASA was going to send a crew of scientists to investigate the next massive dust storm, when would they need to be ready to go?
Be ready to support any prediction with mathematical evidence. (i.e. visual diagram - graph of the orbit pattern, equation to match the graph of the elliptical orbit, etc...)
Process
Use the following resources to find the information you need in your quest. There are obviously some terms in this material that you may not understand completely. The following terms are probably things that you should pay attention to as you look at the resources.
Key Concepts:
Orbit
Ellipse -- Already Covered
Focus -- Already Covered
Eccentricity
Aphelion
Perihelion
Resources:
- Martian Dust Storms – (Relevant)
http://science.nasa.gov/science-news/science-at-nasa/2003/09jul_marsdust/
* Planets’ Distance from the Sun – (Relevant)
http://www.nasa.gov/audience/foreducators/k-4/features/F_Measuring_the_Distance_Student_Pages.html
* Elliptical Orbits – (Relevant)
http://www.windows2universe.org/physical_science/physics/mechanics/orbit/ellipse.html
* Perihelion and Aphelion – (Relevant)
http://science.nasa.gov/science-news/science-at-nasa/2001/ast04jan_1/
* Mars at Perihelion – (Relevant)
http://dcford.org.uk/news.php?id=20130124_14_100
Evaluation
Total points for this assignment will be 200 (Same as a Test Grade).
Evaluation of this assignment will be based on 3 parts:
Part I -- Participation and Effort (50 Points)
** This will not be an easy answer to come up with. There probably will be a point in which you feel like the science is overwhelming you a bit. The key is to be able to read the material as many times as needed in order to gain the relevant information to the problem at hand.
Part II -- Rightness of the Prediction (75 Points)
** I am not looking for everyone to have the exact same date. I am looking for a ballpark figure, but depending on the information gathered your answers may vary a bit
Part III -- Mathematical Support of Prediction (75 Points)
** If you were making a presentation on your prediction, the best way to win someone over is with facts and evidence supporting your solution. In this case, a sketch of the elliptical pattern along with an equation of that ellipse is needed. Possibility for Bonus points likes in this area. The more detail you go to in this visual representation, the more points you can earn.
Conclusion
The ability to use the information we talk about in Algebra II to solve a problem is important in your life whether you think so or not. Remember, the ultimate goal of math at this level is being able to solve a given problem given a certain set of parameters on the problem. This is what life is all about as you get older. It's true, you may never have to graph another ellipse in anything else you do for the rest of your life. I can guarantee that you will have problems to solve, though!