Paint the whole inside of the shoebox black. You can paint small yellow dots onto the back and sides to give the appearance of other stars in the background.
Cut a Styrofoam ball in half. The largest ball should be used, because this ball is going to represent the sun.
Paint the sun yellow. Only the curved part of the ball needs to be painted.
Glue the flat side of the model sun onto one of the sides of the shoebox. This will give the effect of the sun protruding out from space.
Paint the remaining balls the appropriate colors depending on which planets are going to be used in the diorama. Use different sized balls to represent the different sizes of all of the planets.
Tape the top of each of the balls to a string. The pieces of string attached to each ball should be equal length. To tape the string onto the ball, place a part of the string flat onto the top of the ball and tape that piece to it.
Tape the other end of the string to the top of the shoe box in order of the planets you are using in your diorama.