Can there be a unique planet visible each different month?

Question

In my world, ten is an important number that shows up frequently. In the solar system my world belongs to, there are ten other planets beside it, and there are ten months in a year.

I know next to nothing about astronomy, but I wondered if it were possible to have people on my planet be able to see in each consecutive month a different planet and recognize it as a planet*, maybe because the planets are brighter with clear shapes rather than points of light, or maybe because the planets' orbits take them close enough to my planet that they can be recognized.

My world is similar to Earth in size and proximity to the sun, which is comparable to our sun. The sizes of the other planets are mutable.

Is it possible that every month a different planet could be identified as a planet without a telescope?

*My world has medieval-era technology, so there are no telescopes.

Answer 1

In the sense that only one planet would be in a position in the sky that made it visible, no, it is not possible.

The orbital period of a body around a center of mass depends on the mass of the body, mass of the system and the mean distance from the center of mass. In practice, stars are so much more massive and larger than planets that planetary orbital periods are proportional just to the star's mass and the mean distance involved.

As a consequence of the above, no two planets in different orbits can have the same orbital period. And if they do share an orbit, they will merge quite catastrophically in a few million years.

Since they don't all complete an orbit at the same speed, there will always be some slower and some faster, which makes it impossible to have them organized to show up at a constant rate of a single different one every month.

There is one one way to achieve the visibility you want, though. It is such a stretch and a [redacted]pull that people will stop reading your story the moment you expose this (unless it is a comedy). If each planet's rotation period is roughly 1/10 of a year, and each planet's crust is a 10% high albedo surface and 90% low albedo surface, you might just have nine of them absorbing most sunlight while one reflects it just right at your planet at any day of the year. They just happen to alternate every month.

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You could also take a page from astrology, you know. The zodiacal signs are always visible and on the ecliptic. The sun is always on top of one, and only one of them at a time. Whatever it was by the time you were born is your solar sign. There are tons over tons of mysticism around this, which might just do the trick for you.

Answer 2

I am tempted to say that's not possible.

Every day, or better every night, any observer on any point of the surface of a planet swipes about half of the visible sky.

You are asking if, each month, it is possible that only 1 out of 10 planets is visible in this half of the sky, more around the equator, less at the poles. If that was possible in a particular month, it would mean, by symmetry consideration, that there would also be months were up to all planets would be visible. Even if their relative position in the system was fixed (which would happen only if they shared the same circular orbit) the planetary rotation would make visible more than 1 per night, and some would never be visible.

Therefore my conclusion is that it can episodically happen that only 1 planet is visible at night in the sky, but not regularly. The norm would be to see more planets during the same night.

Answer 3

Maybe

So this answer is dependent on a few hypotheticals, and a lot of luck forming the star system. The first requirement is that you need the planets to be dark. The concept being that you can only see another planet when it's closest to yours.

In other words, the planet can only be seen from the green planet (that's yours) from the position of the second gray circle. Note that the drawing is not to scale, and is in fact horrible, but it's just to give you the image idea.

Why can they only be seen from that angle? Because they aren't bright planets and the distance is necessary to see them. It should be hypothetically possible, if you play around with the factors. This way the planet isn't a bright dot (like say, Venus) but is more of dull one.

The second requirement is that the 10 planets travel around the sun in the opposite orbit, albeit since they're so far away it takes them double the time that it does for your planet, thus once every month for 10 months, the planets align. Hypothetically possible.

Oh, I should note that these 10 planets all all individual orbits, they do not share orbits, but they're close enough so that this will work. The orbits won't be entirely stable, in fact, thanks to the fact they're circling the other way they'll be pretty unstable from the beginning, but it should last long enough for a book to take place.

Answer 4

1. Elliptical orbits might make this possible, like if your planet was the only one going around the sun in a normal orbit and the ten others all had comet-like orbits and came in towards the sun in synchronicity with each other. your planet could even act as part of the slingshot effect for keeping this sort of timed dance going.

More research would be needed, as I won't do the maths involved: https://en.wikipedia.org/wiki/Elliptic_orbit

2. The other option would be using orbital resonance to note the months instead of Seeing Only One At A Time. Like in the first month you have one visible, in the second you see two in a line, in the third you see one again, in the fourth there are three visible in a row, etc. This would be dramatic-looking in the sky, and certainly would inspire religious and cultural practices. https://en.wikipedia.org/wiki/Orbital_resonance

Answer 5

SHORT ANSWER:

This is a difficult problem for those the least concerned with scientific plausibility. At the end of a long discussion I come up with a reasonably plausible planetary set up - though it is so unlikely to occur naturally that a writer might want to have characters speculate that an advanced civilization actually arranged the planets that way.

LONG ANSWER:

PART ONE: A RING OF PLANETS

This looks like a job for Sean Raymond of the PlanetPlanet blog.

In this post: https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/1

Raymond mentions a paper that shows that it is possible for several astronomical bodies to share the same orbit around another body under some circumstances.

Orbital stability of systems of closely-spaced planets, II: configurations with coorbital planets Smith, Andrew W.; Lissauer, Jack J.

Celestial Mechanics and Dynamical Astronomy, Volume 107, Issue 4, pp.487-500

http://adsabs.harvard.edu/abs/2010CeMDA.107..487S2

Their calculations indicate that at least seven bodies of nearly identical mass would have to be spaced evenly along the orbit for it to be stable. So your requirement for ten would be quite possible.

If there are ten equally spaced co orbital astronomical bodies they would be spaced 36 degrees apart along the orbit.

If those planets orbit their star at a distance of 100 units, the total circumference of the orbit will be about 628.318 units. One tenth of that will be about 62.8318 units. How close can the next planetary orbit in or out be?

According to this Wikipedia list:

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes3

the smallest known ratio between the semi-major axis of two consecutive planetary orbits is about 11 percent, with Kepler-36b & Kepler-36c.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes3

So if that was close to physical lower limit of ratio the next closest inner planetary orbit would be about 90 units or fewer from the star in the system, and the next closest outer planetary orbit would be about 111 units from the star.

Thus your planet could get within ten or eleven units of a planet in the ring of planets when it passes closest to it, which would be about six times as close as the next two closest planets in the ring will be at that time.

Note that the ratio between orbits is different from the absolute difference between orbits. The smallest known difference between two consecutive planetary orbits is in the Kepler-70 system. Kepler-70c is believed to orbit only about 0.0016 Astronomical Units, or about 240,000 kilometers, beyond the orbit of Kepler-70b.

During closest approach, Kepler-70c would appear 5 times the size of the Moon in Kepler-70b's sky.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes3

So it is possible for two planets to appear as orbs in each other's sky at their closest approach while remaining mere dots in the sky at other times.

And it is suspected, but not proved, that a third planet might orbit between Kepler-70b and Kepler-70c, which would sometimes get an ever better view of Kepler-70c.

https://en.wikipedia.org/wiki/Kepler-704

Of course the planets in the Kepler-70 system don't orbit in the habitable zone of Kepler-70. But TRAPPIST-1 does have planets in its habitable zone that do orbit very close to each other.

This work used the Spitzer Space Telescope and the Very Large Telescope at Paranal, amongst others, and brought the total number of planets to seven, of which three are considered to be within its habitable zone.[20] The others could also be habitable as they may possess liquid water somewhere on their surface.[21][22][23] Depending on definition, up to six could be in the optimistic habitable zone (c, d, e, f, g, h), with estimated equilibrium temperatures of 170 to 330 K (−103 to 57 °C; −154 to 134 °F).5 In November 2018, researchers determined that planet e is the most likely Earth-like ocean world and "would be an excellent choice for further study with habitability in mind."[24]

The orbits of the TRAPPIST-1 planetary system are very flat and compact. All seven of TRAPPIST-1's planets orbit much closer than Mercury orbits the Sun. Except for b, they orbit farther than the Galilean satellites do around Jupiter,[41] but closer than most of the other moons of Jupiter. The distance between the orbits of b and c is only 1.6 times the distance between the Earth and the Moon. The planets should appear prominently in each other's skies, in some cases appearing several times larger than the Moon appears from Earth.[40] A year on the closest planet passes in only 1.5 Earth days, while the seventh planet's year passes in only 18.8 days.[37][34]

https://en.wikipedia.org/wiki/TRAPPIST-15

So the TRAPPIST-1 system is an example of a star system where planets in the habitable zone usually look like dots in the sky but sometimes pass close enough to appear as visible orbs and even appear as large as the Moon in Earth's sky or even larger.

Calculations of how close planetary orbits can be are usually based on the assumption that all planets in a system orbit their star in the same direction, which is the direction that the star rotates in. In fact, in our solar system all the planets orbit in the same direction, and they all (except for Venus & Uranus) rotate in the same direction. And many of the moons also orbit in that same direction.

The majority of discovered exoplanets orbit in the same directions as their stars rotate in, and in the same directions as any other discovered exoplanets in their systems.

So it is a safe assumption that in the majority of star systems all planets orbit in the same direction.

But how would it affect orbital stability if the planets in a star system orbited in two different direction, perhaps even alternating the orbital direction from one orbit to the next?

Sean Raymond in this post:

https://planetplanet.net/2017/05/01/the-ultimate-retrograde-solar-system/6

discusses a paper calculating the stability of planetary orbits:

Orbital stability of systems of closely-spaced planets,
Smith, Andrew W.; Lissauer, Jack J., Icarus, Volume 201, Issue 1, p. 381-394.

http://adsabs.harvard.edu/abs/2009Icar..201..381S7

Raymond mentions that Smith and Lissauer show that planetary orbits can be closer together if the orbits alternate between prograde (orbiting in the same direction as the star rotates) and retrograde (orbiting in the opposite direction).

So if the habitable planet in your story and the ring of ten planets orbit in different directions, the planet's orbit can be much closer to that of the orbital ring of planets and during the brief periods when the planet is closest to one of the planets in the ring the other planet can appear much larger in the sky.

PART TWO: A BIG PROBLEM

As planets orbit around their star, their orbital periods are different. The inner planets complete their orbits much faster than the outer planets do. Thee are two reasons for that.

1) The orbits of inner planets are much smaller than those of outer planets, so if they traveled at the same speeds the inner planets would complete their orbits sooner.

2) The necessary orbital speed is faster the closer to the star, so the inner planets have to travel much faster in their orbits.

The combination of those two factors means that inner planets travel more degrees of their orbit per day than outer planets do, and so complete their orbits before outer planets do.

So imagine that an inner planet and an outer planet happen to be lined up with the star in their system. Then as time passes, the inner planet will pull ahead of the outer planet and leave it farther and farther behind. Eventually the inner planet and the outer planet will be on opposite sides of their star. Then the inner planet will begin to catch up with the other planet.

When the inner planet catches up with the outer planet again, the time elapsed will not be exactly one year of either the inner planet or of the outer planet.

The time period for two planets to be in the same configuration with each other and their star is called the synodic period.

For planets outside the orbit of Earth, the synodic period relative to Earth gets shorter and shorter the father they are from the Sun, because they are travelling slower and slower in their obits, so once Earth completes a full circle around the Sun it has to travel shorter and shorter further distances to catch up with the slower moving planets.

Mars has a synodic period of 2.135 Earth years, the asteroid Ceres has a synodic period of 1.278 Earth years, Jupiter has a synodic period of 1.092 Earth years, Saturn has a synodic period of 1.035 Earth years, and so on.

So if the star is like the Sun, and if your main planet is at the distance of Earth, and the ring of planets is at the distance of Saturn, a tenth of the main planet's year would be about 0.100 Earth year or about 36.525 Earth days. A tenth of the synodic period of the ring of planets would 0.1035 Earth years or about 37.803375 Earth days.

So the planet would have same same problem basing their "months" on passing successive planets in the ring of planets that Earth has basing it's months on lunations, the periods between the moon having the same phase. The inner planet may pass all ten planets in the outer ring of planets in most years, but in some years it will pass nine planets or eleven planets.

To make the problem smaller the ring of planets can be farther out compared to the orbit of the main planet in your story.

The semi-major axis of the orbit of Mars is 1.5273 times that of Earth, and the synodic period is 2.136 Earth years.

The semi-major axis of the orbit of Ceres is 2.76596 times that of Earth, and the synodic period is 1.278 Earth years.

The semi-major axis of the orbit of Jupiter is 5.2028 times that of Earth, and the synodic period is 1.092 Earth years.

The semi-major axis of the orbit of Saturn is 9.5388 times that of Earth, and the synodic period is 1.035 Earth years.

The semi-major axis of the orbit of Uranus is 19.1914 times that of Earth, and the synodic period is 1.012 Earth years.

The semi-major axis of the orbit of Neptune is 30.0611 times that of Earth, and the synodic period is 1.006 Earth years.

The semi-major axis of the orbit of Pluto is 39.5294 times that of Earth, and the synodic period is 1.004 Earth years.

The semi-major axis of the orbit of 50000 Quaoar is 43.6916 times that of Earth, and the synodic period is 1.003 Earth years.

The semi-major axis of the orbit of 136199 Eris is 67.6681 times that of Earth, and the synodic period is 1.002 Earth years.

The semi-major axis of the orbit of 90377 Sedna is 506.8 times that of Earth, and the synodic period is 1.0001 Earth years.

https://www.windows2universe.org/our_solar_system/planets_orbits_table.html8

https://en.wikipedia.org/wiki/Orbital_period#Examples_of_sidereal_and_synodic_periods9

https://en.wikipedia.org/wiki/50000_Quaoar10

https://en.wikipedia.org/wiki/90377_Sedna11

Of course Saturn is the farthest naked eye planet known since ancient times. Uranus is sometimes visible to the naked eye, but was never recognized as a planet until 1781. A planet as large as Jupiter or Saturn could be recognized as a planet out to the orbits of Uranus and Neptune.

Of course planets as distant as Neptune, or even Mars, could never appear as discs as seen from Earth.

Any outer ring of ten planets that was distant enough from the main planet in the story to avoid messing up the calendar of the planet more than Earth's is messed up with months that don't fit evenly into years, would many times too distant for the planets in the ring to ever appear as orbs as seen from the main planet in the story. And at any one time most of the ten planets in the ring should be visible from the inner planet in the story, though at any moment only one of them can be close to the position opposite to the star.

PART THREE: AN INNER RING OF PLANETS

What about planets that orbit interior to the main planet in the story?

In our solar system there are two planets orbiting inferior to Earth.

The semimajor axis of Mercury's orbit is 0.3871 that of Earth's orbit, and the synodic period of Mercury is 0.317 Earth years or 155.88 Earth days.

The semimajor axis of Venus's orbit is 0.7233 that of Earth's orbit, and the synodic period of Venus is 1.559 Earth years or 583.9 Earth days.

https://www.windows2universe.org/our_solar_system/planets_orbits_table.html8

https://en.wikipedia.org/wiki/Orbital_period#Examples_of_sidereal_and_synodic_periods9

And I note that the synodic period of Mercury is a fraction of an Earth years, while the synodic period of Venus is more than one Earth year. This leads me to suspect that there is a possible orbit somewhere between those of Mercury and Venus where a planet would have a synodic period equal to an Earth year.

According to my rough calculations, if a planet orbits with an orbital period of about 182.62505 Earth days, it should have a synodic period of about 365.000 Earth days, slightly shorter than an Earth year of 365.25 Earth days which should be close enough.

That calculation should be checked by someone or some program that is better with orbital calculations, and capable of calculating the semimajor axis of the orbit a planet with an orbital period of 182.62505 Earth days.

At such a relative distance compared to the habitable main planet, the ten planets in the ring of inner planets should be hellishly hot and uninhabitable for the natives of the main planet in the story. However, if the main planet in the story orbits toward the outer edge of the star's habitable zone, the inner ring of ten planets might be within the habitable zone and some or all of the planets might be habitable.

Now the problem would be how to get the planets in the inner ring visible only part of the time, so that only one of them at a time is visible from the outer planet.

The planet Mercury can be observed with the naked eye only for relatively short periods when it is separated from the Sun by the largest angles, and only in twilight skies before the Sun rises or after the Sun sets.

So if the ring of planets orbited at the same relative distance to the main planet in the story as Mercury does to Earth, it would be quite likely that only one of the ten planets in the ring would be visible at anyone time.

But unfortunately the ring of ten planets would be at a somewhat greater relative distance and so more than one of those planets should be visible at any one time. Therefore it would be a good idea to somehow make the day sky, the twilight sky, and maybe even the night sky if possible somewhat brighter than the skie sof of Earth, drowning out the light of the inner planets except when they are at extreme maximum elongation from the star in the system, thus making only one planet visible at any one time.

Answer 6

Yes, but it requires an engineered solar system, it can't occur naturally.

1) Your central body needs to be a fairly massive black hole, not a star. Note that this means bright jets heading along it's axis of rotation--this should be vertical or close to it as those jets will sterilize your world if they should cross it. A thick atmosphere is recommended anyway to keep the radiation levels down. (This will make wind a more destructive force, but lower wind velocities and will reduce missile weapon ranges.)

2) Your world is in an orbit by itself.

3) Your 10 planets share an orbit. Only one at a time is close enough to show a disk, some of the others can still be seen in the distance, but only as points of light.

4) Note that this system does not permit a conventional year as you can't have an orbital period anywhere near a year to make this work. You still can have seasons, though--you will need two stars. The first is in a close orbit about the black hole, it provides most of the light and heat for your world. The second is in a slightly elliptical orbit well outside your orbit. When it's closer you have summer, when it's farther you have winter. Note that you will also have a small seasonal effect based on your orbit taking you closer and farther, without a lot of math I can't tell you what the period of this cycle is. This would be sort of like weather but predictable far into the future.

5) Unlike the other answer this requires that the planet ring orbit in the same direction as you do. I'm not sure if this is directly possible or not, if it's not there could also be a counter-rotating ring of dark worlds in between--their high orbital velocity would make them very hard to see, especially if they had dark surfaces.

6) Moons are problematic in this system, they are going to have to be close to your world if they are stable at all (the stability of this whole system is based on the high mass of the central black hole squeezing down the zone of control each planet exerts. On the flip side any moon passing within your planet's Roche limit is destroyed--see Saturn's rings for an example of a moon getting too close. Whether these limits leave a space in between where a moon can be I do not know) and thus they will have to be small to avoid catastrophic tides.

7) While it is probably not relevant to your story note that interplanetary spacecraft will have a very hard time reaching your special planets, doubly so if a counter-rotating ring is necessary.

8) Note that your world is moving like a flying mammal fleeing the infernal regions. This means most meteors will be far faster and brighter than what we see on Earth. (Note that they will be no more likely to survive the fire, though--do not expect any more impacts than Earth sees, but when one gets through it will likely be a far bigger bang and ones that blow in the atmosphere will do so with a far bigger bang, also. Chelyabinsk type events will be much more common.)