This is another branch of my previous question.
Currently, in real life, space agencies around the world charts and tracks asteroids and other objects that orbit the sun. They project the object's orbits and basically do simulations of their future orbits to determine whether or not the object will intersect with the Earth in the future. That's how their "prediction" works.
However, in my scenario, the 20-km object appears out of nowhere (a dimensional rift that closes soon after, so no one knows about it) as shown in the diagram below. The Earth and the asteroid are both traveling counter-clockwise.
More Asteroid Information: The asteroid has a reddish crystalline surface, with a mass of approximately 2.5 times Chicxulub despite being double the diameter.
Question: Given current technology, around how long would it take the Earth to realize that they will be hit?
To be more generally applicable, given no past orbital data, how long would it take astronomers to figure out whether or not a given object will strike Earth in the near future?
Accepted answers will give a rough time-frame and justification.
Optional but Relevant Question: If the above question addresses the combined capabilities of the agencies of the world, how would the answer change as access to information decreases? Say, a stargazing guru or some guy with a telescope.
(This might belong in Space exchange, but given the sudden appearance of the meteor and the dimensional rift, I thought I might try here first. Vote to close if it doesn't belong here.)