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There is conjunction of Jupiter and Saturn on Dec 21. And there is another celestial event on that day the winter solstice.

So I'm just wondering that are these two events are related or not?

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Not in any way, no.

The December solstice is the moment when the Sun reaches its southernmost point in its daily path in the sky (the June solstice, when the Sun reaches its northernmost point). It only depends on the tilt of the Earth on its orbit and the Sun.

On the other hand, Jupiter and Saturn being in conjunction is a phenomenon that doesn’t depend at all on the Earth’s axial tilt. It does involve the Earth, though, as it’s our vantage point. From Earth, Jupiter and Saturn appear close in the sky then. Seen from Mars, for example, they may or may not appear close together in the sky at the same moment.

The last time a Jupiter–Saturn conjunction happened near a solstice was in June 2000. You can find a list of Jupiter–Saturn conjunctions happening within ±24 hr of a solstice at https://astronomie.quebec/conjsols.html.

Solstices, on the other hand, happen twice a year (one in June, one in December).

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    $\begingroup$ Excellent answer. To summarize in a different way: solstices happen often, and conjunctions (from Earth's point of view) happen occasionally. In rare cases they happen close together, but that is just a coincidence of timing. $\endgroup$
    – Nate Barbettini
    Commented Dec 15, 2020 at 14:18
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    $\begingroup$ If the orbital periods of the 3 planets had a low common multiple, these coincidences would be frequent. $\endgroup$
    – Barmar
    Commented Dec 15, 2020 at 16:18
  • $\begingroup$ The link doesn't really show when solstices happen within 24hr of a solstice, but what the separation was on the solstice closest to a conjunction. Great conjunctions (between Saturn and Jupiter) are rare, happening about every 20 years, and the link seems to show them, but always the solstice date instead of the conjunction date. For example the conjunction in 2000 actually happened on May 28 with a 69 arcminute separation, but your list shows June 21 and a 148 arcminute separation. Or am I reading it wrong? $\endgroup$
    – Jason Goemaat
    Commented Dec 16, 2020 at 14:06
  • $\begingroup$ @JasonGoemaat: My calculation may not have been perfect. Also, I used the dates of conjunction in ecliptic longitude, whereas your dates might be those of conjunction in right ascension instead. $\endgroup$
    – Pierre Paquette
    Commented Dec 17, 2020 at 1:37

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