Cut a cardboard circle about 14-inches in diameter, or clean off the round cardboard from under a frozen pizza. Measure from the edges of the circle to the center with a ruler to mark the center point. Draw four concentric circles spaced closely together around the center point using the compass. Leave a small gap and draw five more concentric circles.
Supervise as your child uses a nail to punch 10 holes in the cardboard. One hole in the center will hold the circle representing the Sun. Punch a hole somewhere on each of the other nine circles. Space the holes so that the planets will be balanced and hang evenly.
Cut circles of various colors to represent the planets. Vary the sizes of the planets. The actual sizes of the planets cannot be represented to scale, so make the Sun the largest and Jupiter, Saturn, Uranus and Neptune slightly smaller than the Sun. Cut five more planets smaller than the previous group. Label each planet with its name on the back.
Cut 10 pieces of 12-inch craft yarn or string. Attach one piece of string to the back of each planet with tape. Thread the other end of the string through the hole in the cardboard circle in the appropriate orbit. Place the Sun in the center. Place the rest of the planets in the following order, beginning with the smallest circle: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.
Cut three small slits equidistant from each other along the edge of the cardboard circle. Cut three pieces of craft yarn or string. Tie a knot at the bottom of each one. Slide the end of the string into each slit. Tie the tops of the strings together. Hang the Solar System mobile from the ceiling.