The minor planet revolves around the Sun in a circular orbit. Although the plane of this orbit coincides with the plane of the ecliptic

The minor planet revolves around the Sun in a circular orbit. Although the plane of this orbit coincides with the plane of the ecliptic, on Earth, the covering of this planet by the Moon has never been observed. Determine the radius of the orbit of the minor planet.

This situation can take place only in one case – if the asteroid moves along the ecliptic synchronously with the nodes of the lunar orbit, never meeting with them. For this, the asteroid must move around the Sun in the opposite direction (clockwise), making one revolution, like the lunar nodes, in 18.6 years. According to Kepler’s law, the radius of its orbit is 7.02 AU.This situation can take place only in one case – if the asteroid moves along the ecliptic synchronously with the nodes of the lunar orbit, never meeting with them. For this, the asteroid must move around the Sun in the opposite direction (clockwise), making one revolution, like the lunar nodes, in 18.6 years. According to Kepler’s law, the radius of its orbit is 7.02 AU.