Making the Planets and the Sun
There are several possible objects you can use to make your planet forms before you cover them in paper mache. Round balloons, balls of tinfoil, Styrofoam balls, or anything else that is round and sturdy enough to surround with paper mache can provide an ideal form to work with. Just make sure to have several sizes for your different planets. You don't want a gas giant looking the same size as a planet like Mercury!
You can make your Sun the same way, but, if you're feeling particularly creative, you can purchase a small battery powered light to serve as the Sun. Some craft stores even sell light orbs which are ideal for a glowing Sun. This can make your Solar System really come alive; just make sure the light isn't so hot that it will interfere with the paper mache paste.
Once you have your planet molds ready, cut the newspaper into strips about an inch and a half to two inches wide; dip them in your paste and start applying the strips to each form. Keep the newspaper as tight to the form as you can to avoid too many wrinkles or bulges. Once you've covered all your planets, you'll need to wait around 24 hours for the first layer of paper mache to dry.
Adding another layer will make your model stronger and better able to withstand being handled. Apply the next layer and wait another 24 hours for it to dry. If you wish, you can apply a third layer for even more strength, but at this point you and your child may be too tired out from applying layers to eight planets and a Sun to want to do a third layer. It is ultimately up to you.