I understand that we don't know the exact trajectory of the object, but there should be relatively little play on the time of (potential) impact, and the direct

I understand that we don't know the exact trajectory of the object, but there should be relatively little play on the time of (potential) impact, and the direction it would come from, so we should already know the orientation of the earth, and the spot on the earth where it would hit if we assumed the trajectory to pass through the center of the earth. The hemisphere centered around this position on the earth surface is then effectively candidate for the future potential impact, the rest of the earth surface would be obscured by the front hemispherical earth surface from the perspective of the object. Do you know where this center is?