Question re: Planets Facing Each Other

[JorgeMedinero]

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.

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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.

 

[mgb_phys]

The rotation rate (ie. length of a day) of planets is fairly constant but its value is random in that it depends on the precise arragement of particles at their creation - there is no law to predict the rotation rate from the mass or position of the planet.

The rotation rate of venus for instance was only measured once it was possible to detect mountains under the constant clouds using radar, the rotation rate of Jupiter is very easy to measure because you can watch the red spot go round.

 

[sir-pinski]

First of all, it's great that you are thinking about these concepts and exploring them through thought experiments. It's always important to question assumptions and think critically about our understanding of the world.

To answer your question, there are a few things to consider. Firstly, the alignment of two points on different planets depends on their orbital periods and the angle between their orbital planes. For example, if Planet A and Planet B have the same orbital period and their orbital planes are perfectly aligned, then Point 1 and Point 2 will align every time the planets complete one orbit. However, this scenario is highly unlikely as each planet has its own unique orbital period and the angle between their orbital planes can vary.

Additionally, the rotation of each planet on its axis also plays a role in the alignment of two points. If Planet A rotates faster than Planet B, then the alignment between Point 1 and Point 2 will occur more frequently, but it may not be a perfect alignment as the planets will have moved slightly in their orbits.

So, to answer your question, there is no simple equation to determine when Point 1 and Point 2 will align again, as it depends on multiple factors such as orbital periods, orbital planes, and rotation rates. However, you could use mathematical models and simulations to make predictions about when these alignments might occur.

Furthermore, it's important to note that the concept of an unobstructed vector is not entirely accurate in this scenario. The planets are constantly moving and their positions are not fixed in space, so even if you were able to fire a laser from Point 1 to Point 2 at a specific time, it's possible that the laser would miss its target due to the movement of the planets.

In conclusion, while it is an interesting thought experiment, there is no easy way to determine when Point 1 and Point 2 will align again. It would require a complex understanding of orbital mechanics and precise calculations to make accurate predictions. I hope this helps to answer your question!