Closest Planet to Earth?

Which planet is closet to Earth?  Most kids and adults will know the order of the planets from the Sun, but which is closet to Earth?  Is it Venus or is it Mars?  According to a book my 4 year old checked out of the library on Mars, the closet planet to Earth is Mars.  Unfortunately this is not true.  In fact, the planet closest to Earth changes over the course of the year depending on where Mercury, Venus, Earth, and Mars are at in their orbits around the Sun relative to each other.

Mercury is located 0.387 AU (astronomical units) from the Sun on average.  Venus's average distance is 0.722 AU, Earth's average distance is 1.0 AU, and Mars's average distance is 1.52 AU from the Sun.  Adding in the fact the orbits are not circles, but ellipses, complicates this further, but let's just assume the orbits are circles for an easier discussion.  If Earth and Mars are at closest approach, they are approximately 0.5 AU from each other.  Venus, however, gets closer, with a distance of approximately 0.3 AU at closest approach.  Therefore it is NOT correct to say Mars is the closest planet.  At times it could be, but not always.  If Mars is at closest approach and Venus is on the other side of the Sun, Mars is closer.  In this case, Earth would be about 1.7 AU from Venus.

Now let's toss in Mercury.  If Mars and Venus are both on the other side of the Sun, Mercury is the closest planet to Earth (assuming on our side of the Sun), at a distance of approximately 0.6 AU.  Thus it's not as simple as saying a specific planet is always the closest.  It depends on the locations relative to each other.  The closest planet could be Mercury, Venus, or Mars, although Jupiter can never be closer than the others.  

The book we checked out was a good one, but it was wrong on this one detail.