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One of the many tools used in Astronomy are the formulas used to determine Orbital Motion. There are two basic forms of orbits:

  • Sidereal Period
  • Synodic Period

For Jupiter:

$$\mathrm{\frac{1}{P} = \frac{1}{E} - \frac{1}{S}}$$

where

P = sidereal period in both equations
S = synodic period in both equations
E = Earth's orbit in both equations

Synodic period in this case, for Jupiter is 398.88 days.

Query: Is there any formula to calculate how many days left for Jupiter to reach its next synodic period from Earth? or how many days left until Jupiter is in opposition?

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  • $\begingroup$ I'm not sure what you mean by "reach it's next synodic period" The synodic period is a length of time, it doesn't have a fixed start point. I suppose you could mean "how many days left until Jupiter is in opposition" (since oppositions occur once in each synodic period) Can you confirm that or explain what you do mean? $\endgroup$
    – James K
    Commented May 14, 2022 at 5:47
  • $\begingroup$ okay. Opposition yea that's the point. How long does it takes to finish synodic period, or reaching opposition. Thanks for the information. $\endgroup$
    – Arcana
    Commented May 14, 2022 at 5:50

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If you know the date of the last opposition, then the next one will be about 399 days later (ie a year, a month and a bit). That is just counting days. So if you know that there was an opposition on June 1st, then the next one will be 399 days later, on about July 4th of the following year.

But this assumes circular orbits and so is good for an estimate, but is not exact It's usually out by a few days. Properly calculating the time of opposition requires you to calculate the position of the planets following elliptical orbits (and perturbed by each other's gravity etc). Fortunately, you can get a table which lists the dates of opposition:

August 20, 2021: Aquarius
September 26, 2022: Pisces
November 1, 2023: Aries
December 6, 2024: Taurus
January 9, 2026: Gemini
February 10, 2027: Leo
March 13, 2028: Virgo
April 13, 2029: Virgo
May 14, 2030: Libra
June 16, 2031: Ophiuchus
July 20, 2032: Sagittarius
August 25, 2033: Back in Aquarius (source)

The calculation of these dates is ultimately based on observation. There is no way to calculate them purely from the knowledge of the synodic or sidereal period.

So, as of 14th May 2022, there are 135 days until the next opposition.

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    $\begingroup$ Thanks. How about inner planets like Mercury, Venus? $\endgroup$
    – Arcana
    Commented May 14, 2022 at 8:11
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    $\begingroup$ Well they dont have oppositions, but you could look up the dates of their conjunctions (ie when the Earth would be in conjunction viewed from Mercury. $\endgroup$
    – James K
    Commented May 14, 2022 at 10:45
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    $\begingroup$ Thanks again. How about between Mercury-Venus, Venus-Mars, and Jupiter-Saturn? Without respecting to Sun. $\endgroup$
    – Arcana
    Commented Oct 24, 2022 at 6:08

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