<p>If you go to <a href="https://en.wikipedia.org/wiki/Conjunction_(astronomy)" rel="noreferrer">Wikipedia article of conjunction</a>, there is a formula given for the average time between two conjunctions between a planet pair in siderial years.</p>
<p><span class="math-container">$$\mathrm{p_{conjunction} = \frac{1}{\frac{1}{p_{1}}-\frac{1}{p_{2}}}}$$</span></p>
<p>where p1 and p2 are the orbital time periods of two planets respectively.</p>
<p>The orbital time periods of Uranus and Neptune are 84.012 and 164.782 years respectively. Plugging the numbers, you get the value of 171.396 years.</p>

CC BY-SA 4.0
2021-11-07T03:42:10.707Z
Thx. Put that formula into a scientific calculator just now and got the same answer as you did.
Constantthin
CC BY-SA 4.0
2021-11-07T03:10:32.650Z
2021-11-07T03:10:32.650Z
Nilay Ghosh
<p>I am trying to figure out how often Neptune and Uranus align.
Internet sources says that Neptune's orbit around the sun is 165 years, and that Uranus' is 84 years. It also claims that the two planets align every 170 years. Is 170 years really accurate? It sounds too long.</p>
<p>I am therefore searching for a planet alignment calculator. One that is non-astrological. Are they to be found somewhere on the net, or in an app?</p>
<p>Alternatively, is there a simple formula one can use to calculate this with paper and pen?
Or, alternatively a brain-twist way of getting to the right answer.</p>

CC BY-SA 4.0
2021-11-07T01:38:03.687Z
See https://en.wikipedia.org/wiki/Orbital_period#Synodic_period There's a formula in that article.
PM 2Ring
CC BY-SA 4.0
2021-11-07T02:25:21.867Z
You are asking multiple questions at once. Try to stick with one question per post.
Nilay Ghosh
CC BY-SA 4.0
2021-11-07T02:38:43.860Z
@PM 2Ring. That formula is too much for my limited math knowledge. I think I prefer a calculator. The internet is full of various calculators. Why wouldn’t there be one for this too. A straight answer to my problem would otherwise be helpful.
Constantthin
CC BY-SA 4.0
2021-11-07T09:07:51.193Z
Sorry. That's one of the simplest formulas in celestial mechanics. It can also be written as $\frac{p_1p_2}{p_2-p_1}$. Here's a [synodic period calculator](https://sagecell.sagemath.org/?z=eJxzyMwrSS1KTC7hSklNU4jXKDC0NdRRKDCyNda0UuBSAIKCIqASDaXgyrz8lMxkhYLUosz8FCslHYW0nPzEEqAGBS2gegV9hcSkYg0gQ1ehwFBTUxMAqboZcw==&lang=sage)
PM 2Ring
CC BY-SA 4.0
2021-11-07T09:11:34.607Z
@PM 2Ring. I tried the formula that the answer below provided and it worked nicely. Your formula looks a bit different. Will it do the same job?
Constantthin
CC BY-SA 4.0
2021-11-07T09:16:38.160Z
It's mathematically *identical* to Nilay's formula. Try the calculator I just wrote, which basically use the same formula (adapted slightly so that it doesn't matter whether $p_1$ is larger or smaller than $p_2$).
PM 2Ring
CC BY-SA 4.0
2021-11-07T10:34:48.717Z
Like $$p_1 × p_2 ÷ (p_2 - p_1)$$ But Nilay's version is probably easier on a calculator, since you only have to enter each number once.
PM 2Ring
CC BY-SA 4.0
2021-11-14T10:18:21.090Z
There's only one question here and it's been nicely answered, so closing for "This question currently includes multiple questions in one. It should focus on one problem only." seems counterproductive. **voting to leave open**
uhoh
<planet><alignment>
How does one find out how often planets align?
Constantthin
# How does one find out how often planets align?

(Asked by: username_0 on 2021-11-06)

I am trying to figure out how often Neptune and Uranus align.
Internet sources says that Neptune's orbit around the sun is 165 years, and that Uranus' is 84 years. It also claims that the two planets align every 170 years. Is 170 years really accurate? It sounds too long.

I am therefore searching for a planet alignment calculator. One that is non-astrological. Are they to be found somewhere on the net, or in an app?

Alternatively, is there a simple formula one can use to calculate this with paper and pen?
Or, alternatively a brain-twist way of getting to the right answer.

**Tags:** planet, alignment
> **Comments:**
> **username_1**: See https://en.wikipedia.org/wiki/Orbital_period#Synodic_period There's a formula in that article.  
> **username_2**: You are asking multiple questions at once. Try to stick with one question per post.  
> **username_0**: @PM 2Ring. That formula is too much for my limited math knowledge. I think I prefer a calculator. The internet is full of various calculators. Why wouldn’t there be one for this too. A straight answer to my problem would otherwise be helpful.  
> **username_1**: Sorry. That's one of the simplest formulas in celestial mechanics. It can also be written as $\frac{p_1p_2}{p_2-p_1}$. Here's a [synodic period calculator](https://sagecell.sagemath.org/?z=eJxzyMwrSS1KTC7hSklNU4jXKDC0NdRRKDCyNda0UuBSAIKCIqASDaXgyrz8lMxkhYLUosz8FCslHYW0nPzEEqAGBS2gegV9hcSkYg0gQ1ehwFBTUxMAqboZcw==&lang=sage)  
> **username_0**: @PM 2Ring. I tried the formula that the answer below provided and it worked nicely. Your formula looks a bit different. Will it do the same job?  
> **username_1**: It's mathematically *identical* to Nilay's formula. Try the calculator I just wrote, which basically use the same formula (adapted slightly so that it doesn't matter whether $p_1$ is larger or smaller than $p_2$).  
> **username_1**: Like $$p_1 × p_2 ÷ (p_2 - p_1)$$ But Nilay's version is probably easier on a calculator, since you only have to enter each number once.  
> **username_3**: There's only one question here and it's been nicely answered, so closing for "This question currently includes multiple questions in one. It should focus on one problem only." seems counterproductive. **voting to leave open**  

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## 1 answers

### Answer by username_2 on 2021-11-07. Score: 5 | Accepted answer

If you go to [Wikipedia article of conjunction](https://en.wikipedia.org/wiki/Conjunction_(astronomy)), there is a formula given for the average time between two conjunctions between a planet pair in siderial years.

$$\mathrm{p\_{conjunction} = \frac{1}{\frac{1}{p\_{1}}-\frac{1}{p\_{2}}}}$$

where p1 and p2 are the orbital time periods of two planets respectively.

The orbital time periods of Uranus and Neptune are 84.012 and 164.782 years respectively. Plugging the numbers, you get the value of 171.396 years.

> **Comments:**
> **username_0**: Thx. Put that formula into a scientific calculator just now and got the same answer as you did.  

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