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Thread: Orbital Periods

  1. #1
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    Orbital Periods

    This is for a roleplay setting I'm working on, but I don't think most people in world building fora (yes, that's the historically correct plural) would have a clue about this subject. While this probably isn't the best place either, you folks will have more of a clue or, at least, know where to point me, if you don't. The Andwomedan Empire (r came to be both spelled and pronounced w) is based on, at least, two planets around the K-type star Doa. According to Wikipedia, Doa's habitable zone could stretch anywhere from 0.3 to 1.3 AU from it, depending on various factors. What are the orbital periods of planets at 0.67 AU, 1 AU, and 1.25 AU from that star?

  2. #2
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    Welcome to CQ, TurkeySloth.
    If you know how know how heavy the star is, then you can just use Kepler's law to get the period.
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  3. #3
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    Just to make sure I'm reading the relevant equation correctly, as G isn't explained: square of orbital period (T2) = (4(3.142))/(semi-major axis (G)(solar masses (M))) = cube of distance (a3)

  4. #4
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    That site will link you to more details about G, the universal gravitational constant.

    http://hyperphysics.phy-astr.gsu.edu...grav.html#grav

    And from Wikipedia:

    The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"[2]), denoted by the letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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  5. #5
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    You can forget about G and the constants of proportionality if you use "Earth units". Then it reduces to:
    P2 = a3/M

    Where:
    P = orbital period in years
    a = orbital radius in AU
    M = star mass in solar masses

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  6. #6
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    Okay. Would the equation for the shorter distance be T2 = (2.68(3.142))/(6.67-10(0.75)) = a3 as the proposed planet's 0.67 AU from Doa, which is 0.75 solar masses?

  7. #7
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    No, it's much less complicated.

    T2(yrs) = 0.673/0.75

    So T = 0.633 years.

    Grant Hutchison
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  8. #8
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    Quote Originally Posted by grant hutchison View Post
    No, it's much less complicated.

    T2(yrs) = 0.673/0.75

    So T = 0.633 years.

    Grant Hutchison
    Thanks, Grant. My post was a reply to schlaugh. However, it didn't show up until after your equation, which I've been using since, because I copied, pasted, and edited the text from my post about the equation on the site with Kepler's Laws.
    Last edited by TurkeySloth; 2018-Nov-21 at 06:59 PM.

  9. #9
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    I've worked out orbital periods of eight, ten, and fourteen months after reducing Lan's size to 0.7 solar masses. Could moons have stable orbits around those planets since the planets are 0.65 Earth radii, 1.4 Earth radii, and 0.92 Earth radii in size, in that order?

  10. #10
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    Quote Originally Posted by TurkeySloth View Post
    I've worked out orbital periods of eight, ten, and fourteen months after reducing Lan's size to 0.7 solar masses. Could moons have stable orbits around those planets since the planets are 0.65 Earth radii, 1.4 Earth radii, and 0.92 Earth radii in size, in that order?
    That depends on the masses of the planets and on how large or small the lunar orbits are.

  11. #11
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    Okay. Is a rocky planet's size tied directly to its density? "Rocky planet" because of Saturn.

  12. #12
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    Quote Originally Posted by Hornblower View Post
    That depends on the masses of the planets
    In the end, of density of planet, and:
    Quote Originally Posted by Hornblower View Post
    and on how large or small the lunar orbits are.
    The question is, are there some stable orbits for moons? And for all likely densities of the planet, the answer is yes.

  13. #13
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    Wewease the Andwomedan!

    (had to be said)

  14. #14
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    I'm thinking the days will be twelve (inner-most), sixteen (middle), and twenty-eight (outer-most) hours long. While I'm fairly sure the third planet's moon will be fine, will the moons orbiting the first two planets be fine?

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