So Savvy . . . the answer to your first question is, "yes it is possible to build this Orrery project using an Arduino to control the mechanism.”
The answer to your second as to how to do it is a little more complicated and is best simply summed up in Webmeister's suggestion that you, “First buy an Arduino board and learn how to use it.”
It is not that this forum does not want to help you, it's just that they just don't want to do all of the tough work for you so that you can essentially kit build your project based on their hard work and experience without you contributing to the process.
The nature of this forum and the open source community in general is that everyone is willing to share what they learned, but in most cases no one is willing to do all your work for you.
Believe the forum members when they tell you that your project can be done using an Arduino, then follow through on the purchase of an Arduino (the Duemilanove is the recommended first board) and a protoshield and some generic electrical components, . . . then download a copy of the “Earthshine Design Arduino Starters Kit Manual - A Complete Beginners Guide to the Arduino” from the following locations and get to work on learning how to make this obey your every wish.
Here is the required Code for working with the E-Manual (unless you like to do a lot of typing)http://www.earthshineelectronics.com/files/EDASKCode.zip
Along your way, post your questions and issues and the community will in all likelihood jump in with the help you need, then once you have gone that far on your own you will find your pursuit of your Orrery a lot easier and the group very willing to help.
You will find with a little bit of searching that there is a large number of Arduino projects including their code that have been posted for reference by others. The nature of the open source community is also that in most cases you will ultimately post project information about your Orrery including code for reference by others in the future who are also traveling down this road of discovery.
PS. Even a standard hobby servo can be easily modified for continuous rotation.