This is tricky to do in 9 days. I would suggest trying to come up with an experiment which would determine how many days in a year there are, since you cant wait a whole year to see if it works.

Ask your son how you could determine that the earth is in the exact same place it was with respect to the sun? This is much harder than it sounds.

The earth revolves on its axis once every 24 hours, this is a day. The earth revolves around the sun once every 365 days, 5 hours, 49minutes and 12 seconds. It is important to know that the earths axis is tilted, and as it revolves around the sun the tilt causes the sun's relative position to move- this is why we have seasons, and why in the winter there is so little day light. If you could figure out which day the least sunlight (winter solstice) or most (summer solstice) or equal daylight and darkness (this happens twice a year: vernal and autumnal equinox). Knowing these points would give you a method of determining how long a year is- by measuring how many days past between solstices. You will not get to hour precision with this method, but it would get you 365 most likely.

Making a sun dial is one way to detect an equinox, but this takes careful measurement, at a precision that will be hard at 4th grade. Another, easier method is to look from a fixed point at the sun set or rise (with appropriate warnings about looking into the sun), and mark this spot each day- over time your son will notice this point moves. When the movement stops, and starts going back the other way, you have the solstice.

Hi salair,

Good question!  The revolution of the earth around the sun is how we define 1 year.  It is actually 365.25, this is why we have a leap year every 4 years.  Each planet moves around the sun at different rates.  

Idea 1:
You could possibly make a model of our solar system.  I believe I would make a stationary base using cardboard and in the center, place a ball to represent the sun.

Next, on another piece of cardboard, use balls to represent each planet, maybe attach this board to a string so that it could be mobile.

Holding the board with the planets above the still board of the sun and gently twisting the string so that the board will rotate around the sun, would demonstrate the revolutions.

On poster board, document each planet and make note of how long it takes for each planet to rotate the sun.  I've attached a link with that information.  For visual interest, you could always use a flashlight with the sun to represent day & night as the model revolves.  For a matter of interest include trivia about how old you would be if you lived on other planets.  On the same link provided below, is a calculator that figures this for you.

Idea 2:
If it's acceptable to the school, you may could just draw or use construction paper to represent the planets and the sun and place on a poster board and just include the information on the poster.

Idea 3:
Another idea, possibly easier than the first would be to cut two large circles from cardboard, one bigger than the other.  On the smaller circle, connect a ball to represent the sun.  On the larger board connect the planets.  Now placing a rivet of some sort, attach the two together, so that the board with the planets can turn to represent the revolutions.  Still use a poster board to show the revolution period of each planet as listed in the site below.

This is a few thoughts that I hope is useful, if nothing else, I'm hopeful that it will get the creative juices flowing.  Good luck with the science fair!