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Writing: Input Wanted The role of cosmology on a world...

  1. Oct 30, 2016 #1
    I apologize if I'm vague in how I present this discussion.

    As I am actively developing, I do want to try and keep certain specifics more private. At the same time, I want to encourage a vibrant discussion with a free range of ideas. You have an open ability to interpret what I'm asking, so feel free to utilize it.

    We've seen lots of stories in which a world might have multiple suns or moons, where the passage of time is different due to different orbits. From a speculative scientific perspective, what would be different about a habitable world in a system different than our own?

    For example: What if the star was much larger than our sun, but the world was still in the hospitable temperature range. Would that world's sun appear larger in their sky? How would the planet's orbit around that "sun" reflect in how the passage of time was marked.
     
  2. jcsd
  3. Oct 30, 2016 #2

    jedishrfu

    Staff: Mentor

    I think you know the answer to your questions:

    The day might be longer or shorter, the seasons might be longer or shorter and the year might be longer or shorter all affected by how the planet rotates its star and what axial tilt it has. This would affect the rhythms of life if present.

    The suns light affects how things grow and evolve on the Earth so it's safe to say that if life developed on this planet the suns light would be different and affect evolution a bit different.

    Next the planets tectonic activity and composition would affect the terrain and oceans if any which in turn would affect how life developed and evolved.

    And then there's the weather affected by all of these external factors which redistributes material again affecting life.
     
  4. Oct 31, 2016 #3
    I know some of the answer, but not completely. For example, I don't know how far away the habitable zone for a larger "sun" would be, and whether or not that distance would make it appear more like our sun, or if it would still dominate the sky.
     
  5. Oct 31, 2016 #4

    jedishrfu

    Staff: Mentor

  6. Oct 31, 2016 #5

    Bandersnatch

    User Avatar
    Science Advisor
    Gold Member

    Here, I've made a quick spreadsheet that you can use as a reference for your worldbuilding:
    https://docs.google.com/spreadsheets/d/18dC2D_xyW3tFvWT47kb7Om6hW4YaHpwtUIYtEjvPEEM/edit?usp=sharing

    It should be treated only as first approximation - there are some assumptions and rough calculations used there, that wouldn't fly under more rigorous scrutiny, but it will give you a general idea of ballpark figures quite sufficient for non-professional uses.

    You can drag down the whole shebang to include heavier stars, but you shouldn't do it for over 10 solar masses (or for less than 1, for that matter - the values would need adjusting). Besides, even with the range as it is, you should see that the lifetime of heavier stars become so short, that a life-bearing planetary system becomes a stretch.

    Oh, and it works only for main sequence stars.

    If you want, I can write a short explanation about what's going on in there and why, but then again, if you just need the size of the stellar disc - it's there for a range of stellar masses.
    Ok, I've got some time to burn, so I'll explain it anyway:
    All values in the table have their units given, and they're either in multiplies of respective solar values (e.g. a '2' in the luminosity column means twice as luminous as the Sun) or of Earth values (orbital parameters and received solar flux)

    The basic imput is the stellar mass.

    The spreadsheet uses some basic relationships that the main-sequence stars obey:
    - The mass-radius relationship and mass-luminosity relationship (see here). These are determined empirically and can be reduced to simple exponential dependence on mass. In general terms, as a star gets more massive, it grows in size more slowly than linearly (because you're adding 'volume' to a sphere, and looking at the growth of radius, plus the added gravity compresses the gas into a more dense package), and it gets much more luminous than a linear relationship would suggest (the exponent is close to 4 for 1-10 solar mass stars; this can be understood as the extra mass needing more energy to support, so the fusion reactions must progress more rapidly).
    - The mass-lifetime relationship. Here, the lifetime simply calculated as mass/luminosity, normalized to our Sun's lifetime. The reasoning is that you get more fuel (mass) than the Sun has, that is then consumed with rapidity proportional to luminosity. Since the latter grows as ~M^4, the lifetimes get quickly and progressively shorter as you go up with mass. A bit more on that here.

    These give you information about physical characteristics of the star. They're not terribly rigorous, and omit e.g. the influence of metallicity or age on the fusion processes (stars get brighter as they age).

    The luminosity of a star determines its habitable zone. The reasoning for the calculations used is as follows: take the habitable zone of the Sun, as calculated in this paper. And scale it with increasing luminosity of the star using the inverse square law. This is simplistic, but for most part seems to roughly track the habitable zones the paper's accompanying calculator outputs.

    Having calculated the habitable zone range, it's then just a matter of applying the small-angle approximation to ascertain angular size (disc width) of the star as visible from the inner and outer edges of the habitable zone. This simply means that a width of the stellar disc grows proportionally to the radius of the star, and decreases proportionally to the distance. Since distances to the habitable zone grow faster than the radius of the star (again, because of rapidly increasing luminosity), you get smaller and smaller disc as you sit in the HZ of more and more massive stars.
    Note, that the amount of stellar flux (irradiation) received by the hypothetical planet remains the same, which means that the smaller discs must be brighter (e.g. a disc half the size has 1/4th of the area, so it must be 4 times brighter). This gives the same brightness of a 'day', but with much more intensely concentrated light source - if you were to look at it directly.

    Orbital periods use Kepler's 3rd law in a straightforward way, outputting periods in Earth-years.

    The bit with flux ranges to the right comes from the paper cited earlier, as the range of irradiation that may produce Earth-like climate (temperature-wise) depending on the strength of the greenhouse effect. It's mostly there to be used in calculations.

    Stars over 10 solar masses and less than 1 solar masses have a bit different internal physics, so the slopes of some relationships differ.

    Bottom line, larger stars look smaller from the vantage point of their habitable zones. Smaller, but more intensely bright discs.
     
    Last edited: Oct 31, 2016
  7. Nov 1, 2016 #6
    Assumptions are fine. When we get into the realm of fiction, we have to be able to suspend disbelief, but we can only do that if it's at least plausible. Thanks for the resources, both of you. :)
     
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