Paint the inside of the box black and add white splatter or dots to create a starry background.
Paint the foam balls as the Sun and planets, letting each layer dry fully before handling.
Attach string lights around the interior edges and secure them with glue.
Shape aluminum foil into small clusters and glue them in place to form asteroid areas.
Hang or glue the planets along curved wire or string paths, then add labels near each one to complete the display.