<p>You can calculate conjunction year with the formula
<span class="math-container">$$
1/(1/F1 - 1/P1).  F1 
$$</span></p>
<p><span class="math-container">$P1$</span> is the revolution time of a celestial body like a planet, asteroid etc. By substituting Jupiter and Saturn data we find it's 19.8 years</p>

CC BY-SA 4.0
2020-12-22T13:18:20.997Z
Welcome to Astronomy SE! Can you make this more readable and user-friendly?
WarpPrime
CC BY-SA 4.0
2020-12-22T16:11:15.663Z
Your formula is the same as the answer by Marco. It gives the synodic period of two planets as seen from the Sun. It is reasonably accurate for Jupiter-Saturn conjunctions as seen from the Earth since those planets are much farther from the Sun than the Earth. The synodic formula would not work for Jupiter-Venus conjunctions because the view of these two planets from Earth is completely different than the view from the Sun.
JohnHoltz
CC BY-SA 4.0
2020-12-22T02:37:13.887Z
2020-12-22T16:11:41.190Z
2020-12-22T16:11:41.190Z
KISHORE KUMAR MAHATO
<p>I worked out this equation to determine the cycle length between conjunctions of two planets:</p>

<p><span class="math-container">$$t = \frac{a \cdot b}{b-a}$$</span></p>

<p>where:</p>

<p>t = length of conjunction cycle (ie time between two conjunctions), in Earth days</p>

<p>a = year length for lower-orbit planet, in Earth days</p>

<p>b = year length for higher-orbit planet, in Earth days</p>

CC BY-SA 4.0
2019-08-09T06:04:05.767Z
The [synodic period](https://en.wikipedia.org/wiki/Orbital_period#Synodic_period) is certainly important, but it's not sufficient for precise calculation of conjunctions over long time spans. Bodies with elliptical orbits don't move with constant angular speed, which makes things messy.
PM 2Ring
CC BY-SA 4.0
2019-08-08T13:03:48.880Z
2019-08-09T05:39:39.753Z
2019-08-09T05:39:39.753Z
Marco
<p>The PyEphem library allows you to create Python scripts that could calculate any conjunction you want (and many other things besides that).</p>

<p><a href="http://rhodesmill.org/pyephem/" rel="nofollow">http://rhodesmill.org/pyephem/</a></p>

<p>Here's a script that already does that:</p>

<p><a href="http://shallowsky.com/blog/science/astro/predicting-conjunctions.html" rel="nofollow">http://shallowsky.com/blog/science/astro/predicting-conjunctions.html</a></p>

<p>Here's the result of running that script now:</p>

<p><a href="http://pastebin.com/ehjxV66m" rel="nofollow">http://pastebin.com/ehjxV66m</a></p>

<p>Notable event: extremely close conjunction between Jupiter and Venus in 2016:</p>

<pre><code>Conjunction of Venus and Jupiter lasts from 2016/8/25 to 2016/8/31.
  Venus and Jupiter are closest on 2016/8/28 (0.1 deg).
</code></pre>

CC BY-SA 3.0
2015-07-01T22:45:18.103Z
Which is interesting because most sites reporting on this don't mention the 2016 conjuction and say we won't see anything like it for another 10 years or more. (It varies drastically by article)
AdamMasters
CC BY-SA 3.0
2015-07-02T00:01:20.240Z
AdamsMasters, I don't have enough reputation to answer your comment outside of an answer so well, that's because it'll be very low when it gets dark enough to see. It should be visible to the naked eye for maybe literally 5 minutes between mid-twilight and it getting too low to see, but only if the sky isn't very hazy. However, this is from midnorthern latitudes. The Southern hemisphere should see that easily. A 6 to 9 thousand foot elevation with a low western horizon would be better than sea level. A telescope or binoculars would also make it easier to see as long as you can aim.
user7583
CC BY-SA 3.0
2015-07-02T17:42:11.903Z
It will be difficult to see unless you're free of surrounding buildings and trees. At the time of the sunset, they will be only 11 deg above horizon. That's only half the altitude of the conjunction this year at sunset. But if you have an open, flat field on the western side of town, you'll be able to observe that conjunction just fine.
Florin Andrei
CC BY-SA 3.0
2015-07-01T19:57:49.050Z
2015-07-02T17:46:36.733Z
2015-07-02T17:46:36.733Z
Florin Andrei
<p>So, the recent conjunction of Jupiter and Venus seems to have spawned lots of excitement over this "rare" event. But what I can't figure out, is exactly how rare it is. And I've seen such conflicting claims and calculations that I figured I'd better calculate it myself. The only problem is I'm no astronomer. So, does anyone know of a program that can calculate all the conjunctions between a date range that are within a degree of each other? Or does smart person know how to calculate it manually? :) 
    I have a program called Stellerium which I've been using to view the various conjunctions that people have mentioned. I don't know if I can use it in the way I need it though. Any help? :)
Thanks</p>

<jupiter><venus>
How to calculate conjunctions of 2 planets
AdamMasters
# How to calculate conjunctions of 2 planets

(Asked by: username_0 on 2015-07-01)

So, the recent conjunction of Jupiter and Venus seems to have spawned lots of excitement over this "rare" event. But what I can't figure out, is exactly how rare it is. And I've seen such conflicting claims and calculations that I figured I'd better calculate it myself. The only problem is I'm no astronomer. So, does anyone know of a program that can calculate all the conjunctions between a date range that are within a degree of each other? Or does smart person know how to calculate it manually? :)
I have a program called Stellerium which I've been using to view the various conjunctions that people have mentioned. I don't know if I can use it in the way I need it though. Any help? :)
Thanks

**Tags:** jupiter, venus


---

## 3 answers

### Answer by username_6 on 2015-07-01. Score: 5 | Accepted answer

The PyEphem library allows you to create Python scripts that could calculate any conjunction you want (and many other things besides that).
http://rhodesmill.org/pyephem/
Here's a script that already does that:
http://shallowsky.com/blog/science/astro/predicting-conjunctions.html
Here's the result of running that script now:
http://pastebin.com/ehjxV66m
Notable event: extremely close conjunction between Jupiter and Venus in 2016:
Conjunction of Venus and Jupiter lasts from 2016/8/25 to 2016/8/31.
  Venus and Jupiter are closest on 2016/8/28 (0.1 deg).

> **Comments:**
> **username_0**: Which is interesting because most sites reporting on this don't mention the 2016 conjuction and say we won't see anything like it for another 10 years or more. (It varies drastically by article)  
> **username_7**: AdamsMasters, I don't have enough reputation to answer your comment outside of an answer so well, that's because it'll be very low when it gets dark enough to see. It should be visible to the naked eye for maybe literally 5 minutes between mid-twilight and it getting too low to see, but only if the sky isn't very hazy. However, this is from midnorthern latitudes. The Southern hemisphere should see that easily. A 6 to 9 thousand foot elevation with a low western horizon would be better than sea level. A telescope or binoculars would also make it easier to see as long as you can aim.  
> **username_6**: It will be difficult to see unless you're free of surrounding buildings and trees. At the time of the sunset, they will be only 11 deg above horizon. That's only half the altitude of the conjunction this year at sunset. But if you have an open, flat field on the western side of town, you'll be able to observe that conjunction just fine.  

---

### Answer by username_1 on 2020-12-22. Score: 0

You can calculate conjunction year with the formula
$$
1/(1/F1 - 1/P1). F1
$$

$P1$ is the revolution time of a celestial body like a planet, asteroid etc. By substituting Jupiter and Saturn data we find it's 19.8 years

> **Comments:**
> **username_2**: Welcome to Astronomy SE! Can you make this more readable and user-friendly?  
> **username_3**: Your formula is the same as the answer by username_4. It gives the synodic period of two planets as seen from the Sun. It is reasonably accurate for Jupiter-Saturn conjunctions as seen from the Earth since those planets are much farther from the Sun than the Earth. The synodic formula would not work for Jupiter-Venus conjunctions because the view of these two planets from Earth is completely different than the view from the Sun.  

---

### Answer by username_4 on 2019-08-08. Score: 0

I worked out this equation to determine the cycle length between conjunctions of two planets:

$$t = \frac{a \cdot b}{b-a}$$

where:

t = length of conjunction cycle (ie time between two conjunctions), in Earth days

a = year length for lower-orbit planet, in Earth days

b = year length for higher-orbit planet, in Earth days

> **Comments:**
> **username_5**: The [synodic period](https://en.wikipedia.org/wiki/Orbital_period#Synodic_period) is certainly important, but it's not sufficient for precise calculation of conjunctions over long time spans. Bodies with elliptical orbits don't move with constant angular speed, which makes things messy.  

---

