<p>For X, this month in 2024, he has his 46th birthday on Earth, and, in the same day, it is his 191st birthday on Mercury. How often this happens?
Reedit: what is the relation between the orbital frequencies such it makes the two birthdays happen in the same day? In terms of astronomical data, how much time requires the orbital phases to be the same such as the birthday on the two planets be the same? For instance, What will be the next year with coincidence of these two birthdays?</p>
<p>Data: mercury year has 87.97 days and earth day has 365.25 days.</p>
<p>Remark: I know it can be done with diophantine equations and l.c.m., but can it be done with fractions only?</p>

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2024-03-07T20:37:09.543Z
As presented, this is really more of a math.stackexchange.com question.
notovny
CC BY-SA 4.0
2024-03-07T20:51:39.347Z
OK, I will ask it as it were an astronomy questions using periods and frequencies.
riemannium
CC BY-SA 4.0
2024-03-07T21:51:15.070Z
You are still asking a math question: what integer n results in the equation 365.25/87.97*n also being an integer (within plus or minus)? You should ask on math.stackexchange.com.
JohnHoltz
CC BY-SA 4.0
2024-03-07T23:45:54.687Z
NO, I am not. If it were a mathematical only question I would have posted it in the math, but, there are some interesting points in the answer related to periods of planets, resonances, AND angular velocity of planets/orbital frequency. Were I contextualizing this question for the math SE, I would have chosen another type of text...And BTW, I will post my solution in a few days...I wish...
riemannium
CC BY-SA 4.0
2024-03-08T03:26:39.980Z
I also see this as a math question. The fact that it’s related to planets has nothing to do with it. One could replace Mercury and the Earth with two runners on different tracks or two cars in different lanes of a circular racetrack or road, and have the same kind of question.
Pierre Paquette
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2024-03-09T00:06:56.087Z
I also agree that this is primarily a mathematical question. Why are you using those numbers for the year lengths? There are several types of [Astronomical year](https://en.wikipedia.org/wiki/Year#Sidereal,_tropical,_and_anomalistic_years). For this exercise, tropical years are probably the most appropriate. What does "m.c.m." mean? You don't need to solve a Diophantine equation, you can use [continued fractions](https://en.wikipedia.org/wiki/Continued_fraction).
PM 2Ring
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2024-03-09T00:07:45.847Z
https://sagecell.sagemath.org/?z=eJxlUMFqg0AQve9XPCwUTW2Mtk1Twd567K3HXoyOZKlZ14lSRPz3ToyK0GFhZ968ebyZO3xxZXWWlugo5QuqAp%5FEWcsd7vGRcnNS3RkJDq%5Fbt%5F1BdST50%5F5lGz1HkWIppBvIrLKsTeOyp1ROBbLKNAWnmQCxgoTxkfsw7Vl%2DMjK38xGObzf2f0%2D6JDHT0o1%5FjVZok%2DgM%5FZOZ0xHctHgYKWTGNF%5FmOk1lvpAXmPGYoF1KXQiSiLcYR6b0Z8VLEMqerFRRMbQP1%5FqoPbEHElXitCF3tfS09e0ohdPrIUZvh6CvB5HqbVAPjreiWGzkiCJ5%5FcWk4%5Fi4kE2cbzPxxJvGO8Jo9vYHGlp0vA==&lang=python
PM 2Ring
CC BY-SA 4.0
2024-03-09T02:31:49.370Z
My students believe the cycle is of 7 years (or six), how could I convince them of the mistake of their "naive" argument (365.25/87.97)*(7n)=m? I know what your smart program does, but for some of them, the periodicity is "approximately" exact...
riemannium
<sidereal-period><synodic-period>
Birthday question
riemannium
# Birthday question

(Asked by: username_0 on 2024-03-07)

For X, this month in 2024, he has his 46th birthday on Earth, and, in the same day, it is his 191st birthday on Mercury. How often this happens?
Reedit: what is the relation between the orbital frequencies such it makes the two birthdays happen in the same day? In terms of astronomical data, how much time requires the orbital phases to be the same such as the birthday on the two planets be the same? For instance, What will be the next year with coincidence of these two birthdays?

Data: mercury year has 87.97 days and earth day has 365.25 days.

Remark: I know it can be done with diophantine equations and l.c.m., but can it be done with fractions only?

**Tags:** sidereal-period, synodic-period

> **Comments:**
> **username_1**: As presented, this is really more of a math.stackexchange.com question.  
> **username_0**: OK, I will ask it as it were an astronomy questions using periods and frequencies.  
> **username_2**: You are still asking a math question: what integer n results in the equation 365.25/87.97*n also being an integer (within plus or minus)? You should ask on math.stackexchange.com.  
> **username_0**: NO, I am not. If it were a mathematical only question I would have posted it in the math, but, there are some interesting points in the answer related to periods of planets, resonances, AND angular velocity of planets/orbital frequency. Were I contextualizing this question for the math SE, I would have chosen another type of text...And BTW, I will post my solution in a few days...I wish...  
> **username_3**: I also see this as a math question. The fact that it’s related to planets has nothing to do with it. One could replace Mercury and the Earth with two runners on different tracks or two cars in different lanes of a circular racetrack or road, and have the same kind of question.  
> **username_4**: I also agree that this is primarily a mathematical question. Why are you using those numbers for the year lengths? There are several types of [Astronomical year](https://en.wikipedia.org/wiki/Year#Sidereal,_tropical,_and_anomalistic_years). For this exercise, tropical years are probably the most appropriate. What does "m.c.m." mean? You don't need to solve a Diophantine equation, you can use [continued fractions](https://en.wikipedia.org/wiki/Continued_fraction).  
> **username_4**: https://sagecell.sagemath.org/?z=eJxlUMFqg0AQve9XPCwUTW2Mtk1Twd567K3HXoyOZKlZ14lSRPz3ToyK0GFhZ968ebyZO3xxZXWWlugo5QuqAp%5FEWcsd7vGRcnNS3RkJDq%5Fbt%5F1BdST50%5F5lGz1HkWIppBvIrLKsTeOyp1ROBbLKNAWnmQCxgoTxkfsw7Vl%2DMjK38xGObzf2f0%2D6JDHT0o1%5FjVZok%2DgM%5FZOZ0xHctHgYKWTGNF%5FmOk1lvpAXmPGYoF1KXQiSiLcYR6b0Z8VLEMqerFRRMbQP1%5FqoPbEHElXitCF3tfS09e0ohdPrIUZvh6CvB5HqbVAPjreiWGzkiCJ5%5FcWk4%5Fi4kE2cbzPxxJvGO8Jo9vYHGlp0vA==&lang=python  
> **username_0**: My students believe the cycle is of 7 years (or six), how could I convince them of the mistake of their "naive" argument (365.25/87.97)*(7n)=m? I know what your smart program does, but for some of them, the periodicity is "approximately" exact...  

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## 0 answers

