How long or short is a year?

[Lucius]

A question for the astronomy geeks:

 

 

Assuming an Earthlike planet, i.e. similar in mass and climate with the potential for large oceans that never freeze over completely and don't boil away either - in other words, a prime world to colonize for Humans -

 

how long could the year possibly be, and how short could it be? I'm especially interested in extreme length. I've seen Human or Humanoid occupied planets in fiction with orbits up to 20 or 25 years, and I'm wondering where that fits on the spectrum from "In line with current scientific theory" to "fit for a Saturday morning cartoon, maybe."

 

I'll probably use it regardless, unless someone with more scientific acumen than myself tells me it's flatly impossible.

 

Lucius Alexander

 

Did the palindromedary eat my tagline?

[Outsider]

Re: How long or short is a year?

 

The temperature range of an earth like planet depends on how much energy it gets from its star. A big, energetic star could have planets that get the right amount of energy quite far out.

 

Of course, big energetic stars have a different life cycle than Sol type stars, so even if the energy density is right out at a 25 year orbit, it isnt likely that an earth like bioshpere will have developed there. If our current models of how that happens are near right, anyway.

[torchwolf]

Re: How long or short is a year?

 

There are a lot of figures that have been done on the subject of the biosphere zone of various stars... basically if you have a yellow-white star (F), you get a longer possible year, with a yellow star (G, like Sol) you get around the same year as Earth, an orange one (K) a shorter year, a red one (M) the shortest. This also depends on the density of the atmosphere (longer possible year) and whether the planet is a planet or actually a moon orbiting a gas giant like Jupiter or Saturn. In that case you get some heat from the gas giant, too.

 

In essence, if you want a year that long you might want to place it around a type F (yellow-white), as a satellite world to a large gas giant. Incidentally this will also probably give you the gas giant as an enormous moon in the sky even during the day, probably several other moons visible at night, and a spectrum tilted higher than Earth (toward the UV but quite close to Sol). If you are close to a gas giant you might experience large tide water effects, slightly more with more moons closeby. This will provide for more internal heat as the planet/moon contracts/expands with the tides (speculated to be happening with Saturn's moon Titan which is Earth-like in size).

 

The star itself would probably not be too much larger than Sol.

[AmadanNaBriona]

Re: How long or short is a year?

 

There are a lot of figures that have been done on the subject of the biosphere zone of various stars... basically if you have a yellow-white star (F), you get a longer possible year, with a yellow star (G, like Sol) you get around the same year as Earth, an orange one (K) a shorter year, a red one (M) the shortest. This also depends on the density of the atmosphere (longer possible year) and whether the planet is a planet or actually a moon orbiting a gas giant like Jupiter or Saturn. In that case you get some heat from the gas giant, too.

 

In essence, if you want a year that long you might want to place it around a type F (yellow-white), as a satellite world to a large gas giant. Incidentally this will also probably give you the gas giant as an enormous moon in the sky even during the day, probably several other moons visible at night, and a spectrum tilted higher than Earth (toward the UV but quite close to Sol). If you are close to a gas giant you might experience large tide water effects, slightly more with more moons closeby. This will provide for more internal heat as the planet/moon contracts/expands with the tides (speculated to be happening with Saturn's moon Titan which is Earth-like in size).

 

The star itself would probably not be too much larger than Sol.

As an added bonus, I think this arrangement would mean that any other appropriate moons around the gas giant would also be in the green zone.

[Cancer]

Re: How long or short is a year?

 

So far so good on the responses so far. There's some complicated effects with stellar evolution when you look deeper.

 

For life like us, dwelling on the surface, liquid water oceans, etc., the classical definition of the "Habitable Zone" applies. You can handwave/roll your own estimates here, in this way.

 

It is commonly assumed that planet surface temperature scales in some way with the amount of radiant energy it receives from the star, and two things go into that: stellar luminosity and planetary distance. There is a greenhouse effect term in here which is terribly complex. I'll get back to that. For the moment, take the simplest possible assumption, that planetary temperature scales linearly with received flux.

 

Very approximately, the bolometric luminosity (total power output integrated over all wavelengths) of a star goes as mass to the 4.75 power for stars near one solar mass.

 

The flux of that starlight falls off as distance to the -2 power (that is, the inverse square law).

 

Combine those three and make a simple scaling law. Using M for stellar mass, d for planet's distance from the star, and T for average surface temperature of the planet, you can write

(M/M sun)^4.75 * (d/d Earth)^-2 = (T/T Earth)

where M/M sun i the mass of the star in solar masses, d/d Earth is the planet's distance from the star in AU, and T/T Earth is the ratio of the planet's surface temperature to Earth average, about 280 K.

 

Now, you can combine that with Kepler's 3rd Law:

(M/M sun)(P)^2 = (d/d Earth)^3

Where P is the orbital period in Earth years, and the other terms have the same meaning as above.

 

If you like, you can take those two and go nuts with a spreadsheet. There are hazards to that. To wit, if you insist on keeping T/T Earth fixed at 1, then there's a direct relation between mass and orbit size; mash that into Kepler's 3rd Law, hold your nose and perform algebra with blissful irreverence in the back-of-the-envelope tradition, and you'll get that orbital period goes as M/M sun raised to the 43/16 power. Whee! (For which a 20-year orbital period falls out for a star with 3.05 solar masses, but that's outside the regime where the 4.75 power is valid, so it's mildly bogus.)

 

The question exists, over what range can that work? For the most part, this is asking about the greenhouse stuff we glossed over.

 

One pessimistic estimate (here) is that it might work in between the extremes where the left-hand-side of the first scaling rule above falls between 1.1 and 0.53.

 

More complicated issues involve:

• Stellar evolution effects. As stars age, they inevitably increase in luminosity, so their "habitable zones" move outward with time. More massive stars evolve faster. The Sun has increased in luminosity by about 40% over the last 4.5 Gyr.
  
• Stellar spectrum effects. The emergent spectrum varies with mass on the main sequence (which is what we're talking about here), in the sense that the emergent spectrum is bluer/harder for more massive stars. The more massive the star, the more UV it puts out, which seems bad for biochemistry like ours. However, this might not matter at the end of the day, since I've seen computations that suggest that no matter how much ultraviolet a star puts out (as long as you're below one threshold and above another one) the photodissociation of water into H2 and O2 will end up making enough ozone in the atmosphere to shield the surface from the UV.
  
• Evolution of life effects. Earth's oxygen-rich atmosphere is the result of biology, and our atmosphere wasn't oxygen-rich until about 2 to 2.5 Gyr ago. The indications are that life got started very early on this planet, so there's an argument that you can't get an O2 atmosphere in less than 2 Gyr. If that's right, then there are no habitable planets orbiting stars more massive than about 1.5 solar masses because those stars evolve off the main sequence too fast, swell to become red giants, and engulf all the nice terrestrial planets you're interested in before their cyanobacteria can make the O2 atmosphere you want. If that's the case, then the silly mass-to-the-43/16-power nonsense above says the max orbital period is 3 years.
  
• Other greenhouse assumptions: Loosen the rigid insistence on having the stellar flux be so close to Earth's, and then planetary atmosphere warming might expand the habitable zone limits some, which would increase the spread in tolerable planets and thus their orbital periods.
  

 

Anyway, interesting question that I hadn't considered before, though if my ramblings above are anything like right, then the longest orbital period for a truly Earthlike surface environment is certainly no more than 3 years and maybe less. I'm swamped with grading for the coming week or so, but if I get more ideas I'll post them.

[Outsider]

Re: How long or short is a year?

 

Heck, we'll grade your student's papers for you if you keep doing the math for our Star Hero games...

[Cancer]

Re: How long or short is a year?

 

Naaah, there's issues of how to get them back and forth in a timely way.

[Lucius]

Re: How long or short is a year?

 

Cancer, one more question:

 

What's your opinion of the possibility of a habitable moon associated with a gas giant?

 

Lucius Alexander

 

Associated with a palindromedary

[Kristopher]

Re: How long or short is a year?

 

http://en.wikipedia.org/wiki/Jupiter#Magnetosphere

http://en.wikipedia.org/wiki/Io_(moon)#Interaction_with_Jupiter.27s_magnetosphere

 

IIRC, at least in some cases, there's a serious radiation issue around gas giants.

[Nyrath]

Re: How long or short is a year?

 

For life like us' date=' dwelling on the surface, liquid water oceans, etc., the classical definition of the "Habitable Zone" applies.[/quote']

Then those clowns at the University of Washington try to be party poopers and narrow the definition of a habitable planet.

http://uwnews.org/article.asp?articleID=50350

[Cancer]

Re: How long or short is a year?

 

Cancer, one more question:

 

What's your opinion of the possibility of a habitable moon associated with a gas giant?

 

Lucius Alexander

 

Associated with a palindromedary

Possible but not likely is my guess.

 

Close-in the tides and electromagnetic effects are pretty unpleasant. The Jovian system's example of Io is extreme, but cautionary. Further out you get more or less ice worlds. A large moon with an ice-water mix might be colonizeable... I admit would never make a guess that something like Titan existed if it wasn't already known, though.

 

That's assuming gas giants out where they "should be", 5+ AU away from a 1 solar mass star.

 

If you make a gas giant and its moons (again, out where they "should be"), and have it migrate its way inward through the presystem disk (the way "hot jupiters" are believed to be made), and such migration does not lose the moons that formed with the planet (I haven't seen that question addressed, but I haven't gone looking for it either), and the planetary migration stops around 1 AU for a 1 solar mass star, then those outer ice moons could be turned into ocean worlds ... where the ocean isn't a few kilometers deep, but rather 2/3 of the moon's radius deep. Such a world is not habitable, but it'd be useful and interesting for other reasons.

 

Nyrath's link to the U of Washington guys ... I know some of them reasonably well. Part of the point is that when people think speculatively about existence of earthlike worlds, there's a tendency to latch onto effects that seem to work in favor of making such worlds, and neglect (or not think through) concomitant effects that work oppositely.

[Nyrath]

Re: How long or short is a year?

 

Nyrath's link to the U of Washington guys ... I know some of them reasonably well.

Whups. Sorry.

[Cancer]

Re: How long or short is a year?

 

No problem at all; they're above board, good people. I attend their talks when I can make them!