# What is the period of Jupiter being visible in the sky?

For more than 3 months now, we can enjoy seeing Jupiter in the sky, and this will be the case until end of December.

This means that Jupiter move slowly in the sky every day, but it makes me wonder when we'll be able to see it again after December 2020?

Or, put it differently: how long does it takes for Jupiter to do a full "rotation" in the sky?

Thank you !

You can make a ballpark estimate of Jupiter's synodic period if you know that Jupiter orbits the sun once every twelve years, while Earth orbits in the same direction in one year. So when your Earth calendar has completed a year, Jupiter has moved approximately one-twelfth of the way around its orbit, and Earth has to move approximately another month to catch up. That gives you a synodic period of about thirteen months, consistent with the more careful calculation by Mike G.

The ballpark estimate doesn't work very well if the periods are too similar (e.g. for Mars or Venus), but it's fine for the outer planets.

As to when you can see it again, Jupiter's next solar conjunction is on 2021-01-28. So if it disappears into your evening twilight at the end of December, you should expect to find it in the morning twilight around the beginning of March.

• You can get a more accurate estimate by going further: in one year Jupiter has moved about $1/12$ of an orbit ahead, then in $1/12$ of a year Jupiter has moved another $1/12^2 = 1/144$ of an orbit ahead, and so on. In fact, if you keep going, the geometric series $1 + 1/12 + 1/12^2 + 1/12^3 + \dots$ converges to $12/11$ years, or $398.8$ days. And if you use Jupiter's true orbital period of $11.862$ years, you'll get the true synodic period of $1 + 1/(11.862 - 1) \approx 1.0921$ years, or $398.87$ days. – Ilmari Karonen Sep 14 '20 at 23:47
• Well, sure, but if you're going to do an infinite sum, you might as well do the harmonic difference like in Mike G's answer. – rob Sep 15 '20 at 0:31

The midpoint of an outer planet apparition is opposition, when it is directly opposite the Sun as seen from Earth. Jupiter is at opposition on 2019-06-11, 2020-07-14, 2021-08-20, and 2022-09-26.

The average time between oppositions or solar conjunctions of another planet is its synodic period. Jupiter's synodic period is $$\mathrm{\frac{1}{\left|\frac{1}{365.25~d} - \frac{1}{4332.6~d}\right|} = 398.9~d}$$ or 13.1 months.

• Thank you. I liked your precise response, but @rob's answer was more explanatory, that's why I accepted his. If I could have accepted both, I would have. – Cyril N. Sep 15 '20 at 11:55