I havent played the game, but just from looking at the picture, it looks like on the touch screen grab either the Satlites on the Outside circle and line then up with the Dots on the coloured lines or grab the dots and pull them in line with the satilites
yep, you can hold the stylus at each of the orbiting satellites, then wait for its corresponding "dot" with its own color to line up with the satellite before releasing. the inner orbit revolve slowly than the outer ones, so line them up first. do it fast though, since unaligned satellites lose fuel.
there's a third minigame after that before you resume on first-person view.