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Planet with a year of 13 fifty-two day months

  1. Dec 29, 2016 #1
    I want to describe a planet that has 13 fifty-two day months and a 36 hour day.
    IF someone could point me to a place where I can figure this, it would be appreciated.
    What's the math?
  2. jcsd
  3. Dec 29, 2016 #2


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    Kepler's third law should do here. The rotation velocity will only affect planetary properties, depending on number, size and distances of moons, amount of liquid water and such. How do you define month and hour? 36 hours shouldn't cause any difficulties.
  4. Dec 29, 2016 #3
    If the planet has 13 months each with 52 days, that's 676 days a year. A day is 36 hours long, so 1.5 times an Earth day. That means it would have a year of 1014 Earth Days. Mars has a year of 687 Earth days and Ceres has a year of 1680 Earth days. That means your planet would sit somewhere between the orbits of Mars and Ceres.

    For a Sunlike star, that would mean that to keep it warm it would need some kind of greenhouse effect. If the creatures there could survive in an atmosphere that is heavy on methane, it is 25 times more potent than carbon dioxide, but breaks down fairly quickly into CO2 and water. Creatures that exhale methane could potentially work with creatures that consume CO2 and produce oxygen, or even that consume methane and break it down, then consume the CO2 and produce oxygen and water.

    Methane is nontoxic, but a little corrosive and very flammable at specific concentrations. It breaks down fairly quickly so it will have to be replenished quickly - that means potentially there could be explosions if methane exhaling life forms get into places where the methane accumulates - caves?. Or if you had methane-exhaling trees, they could explode when lightning strikes. Methane is also water soluble - frozen lakes of water would regularly have methane bubbles in them.

    The 36 hour day isn't a huge issue - days would be longer, nights would be longer, but not in a way that would be incompatible with life.

    Send me a message if you want to talk more. This is actually a pretty nice planet idea.
  5. Jan 19, 2017 #4
    Isn't it a little simpler than this? Because an hour can be considered an arbitrary definition unless you path it out all the way to an SI source like oscillations of a predictable atom. When our clock system was first devised, they just...made the call. Who's to say an hour has to be 60 Earth minutes? For the hours-in-a-day part, you can change this almost at will.

    Rkolter's definition is really quite nice, and I would like to add to something that was alluded to: the phrase "for a Sunlike star" is important -- if you move about in the star spectrum, you can have an Earthlike planet at a farther orbit without needing to change the chemistry (much) by having it orbit a hotter star. The hab zone of a star is dependent upon its size and output, meaning that there's a lot of flexibility inherent in where a habitable planet (well, by our standards) can be in relation to its parent star.
  6. Jan 22, 2017 #5
    I calculated using earth hours because hours are an Earth concept and the OP mentioned hours.

    It sounded in my mind like the OP was having humans visit or live there - and humans would say it had "36 hours in a day" regardless of what the locals had defined for braking up a day into time slices.
  7. Jan 28, 2017 #6
    Well if you want to get into the nitty gritty of things I subject watching some of Atrifexian's videos https://www.youtube.com/user/Artifexian although there is math involved to find them, if you fallow the videos you can find what you want and more
  8. Jan 30, 2017 #7


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    It depends. Do want your planet to receive about the same illumination/heating from its star as the Earth gets from the Sun? If so, you are going to need to use a star more Luminous/ massive than our Sun.
    At the size range of the Sun, this works out to being a star ~1.5 times the mass of our Sun. This should give you an orbit with the proper length
    As already noted, if you are orbiting a sun-like star, yo are going to get a lot less warming from your star; about 1/4 as much.
    You could compensate by orbiting a more luminous star, but that also means a more massive star, which means that in order to maintain the same orbital period, you have to orbit even further out. Luckily luminosity grows at a faster rate than the mass, so this doesn't pose an unsolvable problem.

    Thus, if your star had a mass of ~1.5 times that of our Sun, and you orbited at ~2.27 AU, you would get just about the same amount of radiation from the star as we get from the Sun and still have your required orbital period.
    Assuming your month is based on the synodic(full moon to full moon) period of the planet's Moon, and the planet was of equal mass to that of the Earth, then it would orbit at ~734,000 km.
    You can work this out the following way in case you decide to change your values
    Orbital period of planet: 676 days
    Synodic period of moon: 52 days

    Then the sidereal (fixed star to fixed star) period of the Moon can be found by

    [tex]T= \frac{1}{\frac{1}{52}+\frac{1}{676}} = 48.29[/tex] days

    Convert this answer to seconds using a 36 hour day

    and plug it into

    [tex]R =\sqrt[3]{ \frac{T^2GM}{4 \pi^2}}[/tex]

    Where M is the mass of the planet

    There is one thing about this solution however. A star of 1.5 solar masses falls in the A spectral class (like Sirius). A class stars radiate more intensely in the ultraviolet range, so, for Earth-like conditions, you are going to need more atmospheric protection.

    An alternate solution would be to go with a star somewhat less massive, in the F spectral class, and then, as suggested by rkolter, compensate with Greenhouse effect. This way you don't need as much greenhouse effect nor a star that produces as much in the ultraviolet. You might be able to just get away with increasing the atmosphere thickness somewhat.
    Again, this all revolves around how Earth-like you need your planet to be. ( For example, if the air needs to be breathed by humans, then if you increase the atmospheric pressure significantly, you have to decrease the oxygen percentage, in order to maintain a safe partial pressure for the oxygen, as too high a partial pressure cab result in oxygen poisoning.)
    Last edited: Jan 30, 2017
  9. Jan 30, 2017 #8
    "Hour" and "Month" aren't based on anything astronomical, so assuming those are consistent with Earth's usage is the best way to start. ("Month" was historically about the moon, but isn't in modern usage.) . So I agree with Rkolter's approach. Similarly, the speed a planet rotates doesn't have anything to do with how long it takes to orbit its star.

    A slower rotation would mean bigger drops in temperature from day to night. If you go with more greenhouse effect, that might reduce this, but if you use a brighter star, expect lots of icy dew in the mornings.
  10. Jan 30, 2017 #9


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    It's hard to say without more information as to the intended planet. Is it a totally alien culture, or is it an Earth colony?

    If an alien culture, we need to assume that they had something to base the length of their month on. 13 seems an pretty impracticable choice to divide the year up by if it was just an arbitrary decision. Something made them decide on that length and number of months. It could be cultural( maybe they worship 13 deities), but again without more information, we can only guess. Maybe their month isn't based on the full moon cycle at all. Maybe they have two moons and the month is a measure of time between conjunctions.

    If an Earth colony, 13 still seems a bit of an odd choice especially if we are not tying the month length to any astronomical event. I could see keeping months of ~30 days and adding more months to make up the difference, or keeping twelve months and extending their length, But why extend the length of the month and add an extra month?

    So I added a way of calculating a moon distance based on synodic month, in case this was the OP's intention.
  11. Jan 30, 2017 #10
    It could be that the numbers just add up nicely for that planet. 676 = 13x13x2x2. So you can have an equal progression of months there.
  12. Feb 2, 2017 #11
    We're not actually being asked to explain why the locals or colonists chose a system of 13 months each with 52 days, each day 36 hours long. We're just being asked to help the OP describe/figure out how to describe the planet. Based on an orbital period of 24,336 hours (13 months * 52 days * 36 hours) and the assumption that the planet is habitable to a human without wearing a spacesuit, here's what we have:

    For a 0.5 Solar mass star, the planet orbits at 1.56 AU (about 145 million miles).
    ** This is why the sun can't really be smaller than our star - the orbital period requires the planet orbit at a distance way outside the habitable zone - you would need something unique and special to keep it habitable.

    For a Sun-like Star, the planet orbits at 1.97 AU (about 183 million miles).
    ** Outside the habitable zone but with greenhouse gases, you might keep this planet habitable.

    For a 1.5 Solar mass star, that's 2.26 AU (about 210 million miles).
    ** As Janus noted, this star would radiate heavier in the ultraviolet. The planet would be in the habitable zone.

    For a 2 Solar mass star, that's 2.48 AU (about 231 million miles).
    ** This one is still in the habitable zone too, but keep in mind that higher mass stars TEND to be more volatile. Habitable, but prone to large flares that regularly wipe all but the most hardened electronics and play havoc with data and power transmission? Regular viewing of auroras?

    Calculator site: http://www.1728.org/kepler3a.htm

    Regardless of size, because you have a 36 hour day, the surface will get the same amount of light. The smaller the planet, the slower the rotation. The smaller the planet, the colder the nighttime temperatures, and the larger the temperature difference when the sun rises. You could reduce the nighttime chill by having a warm ocean with fast, regular currents. Planets much smaller than the Earth would start to fall out of the definition of "Habitable". This limits your planet's size to roughly earth size. Humans could handle a little more gravity, or a little less. But too much gravity would impair us, and too small a planet would have a hard time avoiding freezing or holding an atmosphere of sufficient density.

    Tell us more, OP. This is an interesting world.
  13. Feb 2, 2017 #12
    I don't follow this. Why is angular speed relevant? Wouldn't a smaller planet more easily conduct heat to the far side, thus having smaller differences from one side to the other?
  14. Feb 6, 2017 #13
    The rotation has to do with mixing the atmosphere. Rotation has a large impact on a planet's weather. A planet with a slower rotation will have more sedate weather than a quickly rotating planet. Since we know whatever planet is chosen, will have a 36 hour day, we know the smaller the planet we model, the slower its rotation must be. That means a slower rotating planet will tend to have more difficulty equalizing the temperature between it's daylight side and nighttime side.

    Again assuming all things are otherwise equal. Maybe the small planet has a very strange geometry that funnels air through tight channels, making it have extreme and volatile winds? If it was a water world, it would hold in more heat, and would have another route to transfer heat to the night side.
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