Cut the flaps off a large cardboard box -- four feet wide by three feet tall and four feet deep should be enough space. The entire solar system needs to fit inside.
Use the acrylic paint to cover the inside of the box a mixture of dark blue and black. Use a large brush to cover more area in a shorter amount of time.
Paint white stars randomly on the inside once the first coat has dried. It takes 30 minutes to an hour for acrylic paint to completely dry.
Set the planets and Sun in a line according to their correct sizes. The largest styrofoam ball belongs to the Sun, the center of the solar system. The smallest ball belongs to Mercury, the planet closest to the Sun. The next biggest ball is Venus. Earth and Mars are the next two planets. Use a slightly larger ball for Earth than Mars. Place a collection of cotton balls after Mars to represent the asteroid belt. Use the largest ball left to represent Jupiter next after the belt. Saturn is the next largest planet after Jupiter -- it also has large rings that circle it. Set the styrofoam circle by Saturn. Uranus and Neptune are similarly sized -- use the last two styrofoam balls remaining. If the kit has a tiny ball to represent Pluto, then this goes at the end of the solar system, although Pluto is no longer a planet, but a dwarf planet.
Poke each planet, excluding the cotton balls, with a wooden skewer. Secure the other end of the skewers into a cardboard box or large styrofoam block. You can also secure them in dirt or sand. This allows you to paint the entire planet without having it set on a surface to roll around. Ensure they do not easily tip over.
Paint the planets according to their reported surface colors. The Sun is bright yellow, red and orange. Mercury is a spotted brown-grey planet. Venus is a lighter red-orange-peach color. Earth is mainly blue with brown spots representing the continents. Mars is dark red and black. Jupiter has fuzzy red, orange, cream and brown lines across its surface. Saturn is a dark red-peach color with its rings being similarly colored, but slightly darker. Uranus is light blue with undefined white stripes going around its surface. Neptune is a dark blue-teal color with grey swirls. Pluto is grey and white. Be creative with painting the planets. The effort you put into the project is more important than getting the colors exactly correct.
Cut a wire three feet in length. Thread the cotton balls onto the wire until the entire piece is covered. It is OK to leave some space between each cotton ball as they are representing asteroids, which do not stay directly next to each other. Lock the ends of the wire together by twisting them around each other. If it hurts your fingers, use pliers. Dab grey and black paint onto the cotton balls to represent the asteroid belt.
Let the planets and asteroid belt dry for an hour or two before touching them again. Put the planets outside to dry if the weather permits.
Cut 15 to 20 pieces of thin wire. The wire should have its smallest piece at a size of one inch with each piece getting increasingly larger as the planets get further from the Sun. The longest piece of wire should be 18 inches.
Remove the wooden skewers from each planet. Poke each piece of wire into its corresponding planet, with Mercury getting the shortest wire and Neptune (or Pluto) getting the longest wire. Secure Saturn's ring to the planet by poking a one to two inch piece of wire through the styrofoam circle and through the planet. Wrap two pieces of wire around the asteroid belt, each being an equal distance away from the other one. Use pliers to help wrap the wire if necessary.
Poke the planets into the Sun in their correct order. Poke both pieces of wire attached to the asteroid belt into the Sun between Mars and Jupiter. If the circle is too large, unravel it and shorten the wire by retwisting it in the appropriate spot for the circle size needed.
Set the entire solar system in the center of the box. Use a small piece of double-sided tape to prevent the Sun from rolling around. Use a piece of string connecting the top of the box to the top of the Sun with glue or tape if you would like the Sun to float in the middle of the box.