# How does one find out how often planets align?

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.

• See en.wikipedia.org/wiki/Orbital_period#Synodic_period There's a formula in that article. Nov 7, 2021 at 1:38
• You are asking multiple questions at once. Try to stick with one question per post. Nov 7, 2021 at 2:25
• @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. Nov 7, 2021 at 2:38
• 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 Nov 7, 2021 at 9:07
• 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 $p_2$). Nov 7, 2021 at 9:16

$$\mathrm{p_{conjunction} = \frac{1}{\frac{1}{p_{1}}-\frac{1}{p_{2}}}}$$