What term describes asteroids that cross and spend most of their time in Earth's orbit?

The term that describes asteroids which cross and spend most of their time in Earth's orbit is "Apollos." Apollos are a class of asteroids whose orbits bring them into close proximity to Earth, often crossing its orbital path. They are characterized by having semi-major axes greater than that of Earth's orbit and perihelion distances that are less than Earth's aphelion, allowing them to intersect with Earth’s orbit.

Atens, on the other hand, are asteroids that orbit the sun in a path that is generally inside Earth's orbit, crossing it at certain points, but most of the time they are not in Earth's orbital zone. Amors are a group of asteroids that have orbits that are outside of Earth's orbit and do not cross it, which places them in a different category. Astronomers are simply those who study celestial bodies and do not refer to any specific type of asteroid.

In summary, Apollos are the correct description for those asteroids that spend a significant amount of time crossing Earth's orbit due to their orbital characteristics.