I made a Desmos Graph following the most voted answer of this question, but I'm not sure if it is correct, because it suggest that the formation of the Sun happened shortly after it would have crossed the galactic plane, but the Sun did not exist before that. Is that possible?

The line is part of a cosine function

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    $\begingroup$ First, your $x$ is wrong. The universe isn't even $\sim 57$ billion years old. Please edit your question to correct it. $\endgroup$ May 28 at 0:28
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    $\begingroup$ Probably not. The sun is executing radial epicyclic motion around the galactic center, so its distance increases and decreases periodically. The question you are referring to does not say anything about radial motion, so anything you have plotted on that basis must be wrong. $\endgroup$ May 28 at 0:34
  • $\begingroup$ See desmos.com/calculator/exeupoixbq $\endgroup$ May 28 at 0:38
  • $\begingroup$ @fasterthanlight ok, but where is the Sun now? if I mark x=4.6*10^9 the graph show that the Sun is going down, towards the galactic plane, where the post I mentioned states that the Sun is currently going up. $\endgroup$ May 28 at 1:16
  • $\begingroup$ @fasterthanlight again, and I quote "As the Sun is currently above the plane and moving upwards, and each cycle takes about 70 million years with an amplitude of 100pc, it will be roughly 30 million years before we cross the plane again" The "correction" you made marks the sun as going down. $\endgroup$ May 28 at 1:48

Unfortunately, what you are trying to do is not possible. We do not know the details of the Sun's motion or the Galactic potential precisely enough to make a prediction of exactly where the Sun was 4.5 billion years ago.

The amplitude and period of the oscillatory motion that I specified in my answer to the previous question is known now to of order 10%. If you extrapolate backwards for more than a few cycles then the phase could be anything.

In addition, the Sun has likely changed its radial position in the Galaxy during its life. If so, then the amplitude and period of the vertical oscillatory motion will also have evolved.

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    $\begingroup$ Since you are the authority from which I based my graph, I guess that I will take my defeat with dignity. Thank you. $\endgroup$ May 28 at 12:42

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