You can create a solar system mobile, whether for a school project or as a bedroom decoration, in various ways with various materials. The method that you eventually decide on using is likely to depend on the amount of time that you have to devote to the project, as well as the materials that you already have on hand.
Although paper plates aren't going to create the most professional looking mobile, or the most durable, they are perfect for a younger student or for a simple school project. Take 27 plates (30 if you decide to include Pluto) and separate them into nine (or 10) equal groups of three plates. Each group will create one planet plus the sun. Cut each group of three to represent the various sizes of the planets relative to each other. For example, the plates for Mercury would need to be cut into smaller circles than the plates that represent Jupiter. Colour the plates. Cut slits into the plates so that they will fit together to form a sphere. Consult the image from the first Resources link to see the proper cut pattern. Thread a string through each sphere and hang them to create the mobile.
Polystyrene foam (such as Styrofoam) balls make a lightweight material for a solar system mobile. Obtain foam balls in various sizes to represent each of the planets and the sun. Spray paint the balls in different colours to make them resemble the different planets. Give them plenty of time to dry and hang them with string.
Glue images to both sides of pieces of cardboard to represent each of the planets in addition to the sun. Hang them with string to a larger piece of cardboard overarching the whole structure in the appropriate positions.