It may be that this question makes assumptions that are themselves invalid -- I am less than an amateur. But here goes. Is there any easy way to determine how often Point 1 on Planet A and Point 2 on Planet B will align? That is, if at Time X you could draw a straight, unobstructed vector from Point 1 to Point 2, is there a simple equation for figuring out when the same vector will connect the same two points. Is there any assurance it will occur again? Here is the thought experiment: Thank you for the welcome! Let us say that the vector is relative to the planetary surface -- imagine that I have a laser device (on Earth, Planet A) that shoots a perfectly straight, instantaneous beam (I know, impossible per Einstein). The device is fixed in place, angle, and so forth, save for the fact that the Earth rotates and orbits and so forth. The laser has a targeting scope. It is located at Point 1. At Time X Mercury comes into my targeting scope and I fire, burning a spot at Point 2 on Mercury's surface. Astronauts then travel to Mercury. They put a bullseye at Point 2. My question is whether there will ever be a Time Y at which my laser can shoot the bullseye, and if so, how it can be predicted. --- Alternatively, is there any easy way to determine how often *any* unobstructed vector can be drawn from Point 1 to Point 2? In this case, the laser device can be re-aimed, but cannot be moved.