A few days ago, the BA blog concerned the IAU planet proposal. One of the BA's objections was that the moon's increasing distance from the Earth would eventually move their barycenter outside of the Earth in about 40 million years, making the moon a planet under the proposed definition.
Today, he corrected his math, and the figure is now over 3 billion years.
However, that is still incorrect, and not because it might be longer than the age of the sun.
The moon is moving away from the earth because of the tidal interaction between the earth and moon, which slows the earth's rotation, and transfers its angular momentum to the moon. At a certain distance, the rotation of the earth will match the revolution of the moon, and the process will stop--in fact, it would reverse itself, because of the solar tidal effect, and the moon would start to move closer. At that distance, the earth/moon barycenter will still be within the interior of the earth. In other words, the conservation of angular momentum insures that it will never happen.