|MadSci Network: Astronomy|
Vithia, How easy it is to calculate the alignments of planets depends strongly on your mathematical background. In middle school, I assume you have not gone much past algebra. If you know at least some trigonometry (you need an understanding of angles) then you should be able to do relatively simple calculations to estimate times for alignments using known periods for the planet's orbits. The more planets you try to include, the more challenging the calculation. Also, alignments are not perfect in astronomy - to be considered and alignment it just needs to be close. For more information, see the sunspot web site given below. If you are good with computers, you may be able to write a program to do it for you. I'll give you an example to illustrate the process. In this example I've rounded the numbers for simplicity (I've also assumed circular orbits which is a close approximation). Example: Mercury goes around the Sun once every 88 days and Earth's orbital period is about 365 days. You can not simply say that every 88 days Earth and Mercury line up because while Mercury went around the Sun, Earth was also moving. Earth moves approximately 1 degree around its orbit each day. Using this simplification, by the time Mercury gets back to its starting point (after 88 days), Earth has moved an additional 88 degrees around its orbit. Mercury has to catch up before we have another alignment. Mercury moves about 360/88=4.1 degrees per day. Hence, the time it takes for Mercury to catch up to Earth after completing its 88 day orbit is given by omega_Mercury = 4.1 omega_Earth omega_Mercury * time = omega_Earth * time + 88 degrees where omega is the angular velocity or number of degrees per day traveled by a planet, and time is the time it takes for the planets to line back up. The 88 comes from the additional number of degrees traveled by Earth while Mercury went once around its orbit. Solving for time gives 28 days. This means it takes the 88 day Mercury period, plus an additional 28 days for a total of 116 days for Mercury to line back up with Earth. This is known as its synodic period and is the value you will most likely want to use in your calculations. The synodic periods of the planets are (in days) 115.9 Mercury 583.9 Venus 779.9 Mars 398.9 Jupiter 378.1 Saturn 369.7 Uranus 367.5 Neptune 366.7 Pluto Now, an alignment of both Mercury and Venus with Earth occurs about once for every 5 of Mercury's synodic periods (115.9 goes into 583.9 about 5 times) or once every 1.6 years. After working out a few examples, it should start to become obvious that the more planets you include, the longer the time period between alignments. Now you have an idea of how to calculate the times between alignments. If you would like to estimate a date for an actual alignment, you still need a starting point. You can either take the positions of planets as they currently are in their orbits (see the links below) and include those in your calculations or take the time of the last major planetary alignment and start from there. If you use the planet's current positions, you will need to add a term into your calculations to take their current positions into account. Hopefully this gives you enough information to decide if this is a feasible science fair project for you. As I said, it depends strongly on how comfortable you are with math. Good luck! Erika Links: http://www.fourmilab.ch/solar/solar.html This site has an interactive orrery, which allows you to see the orientation of the solar system at any time. You can check your time estimate for alignments here. However, since alignments are so rare, you will not be able to simply guess a time for alignments. Calculations are still necessary. http://liftoff.msfc.nasa.gov/academy/space/solarsystem/solarsystemjava.html This site shows the orbital positions of the planets at the current time, looking from above the solar system. This will give you a starting point for their positions. http://www.sunspot.noao.edu/PR/alignment.html This site has an entire article devoted to discussing planetary alignments, including how close planets have to be for it to be considered an alignment.
Try the links in the MadSci Library for more information on Astronomy.