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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. 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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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. 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. 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

Grant Hutchison

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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. No, it's much less complicated.

T2(yrs) = 0.673/0.75

So T = 0.633 years.

Grant Hutchison

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Originally Posted by grant hutchison
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.

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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. Originally Posted by TurkeySloth
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.

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

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Originally Posted by Hornblower
That depends on the masses of the planets
In the end, of density of planet, and:
Originally Posted by Hornblower
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. Wewease the Andwomedan!

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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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I've calculated that four galactic standard years (GSY) will be equal to five Earth years (EY). I'm working on racial ages of maturity for the setting with a friend. He says a race maturing at 11 GSY would be 44 EY (11 x 4), while I say that same race would be 55 EY (11 x 5). Who's correct? If neither, it's because 11 doesn't divide evenly by 4. In that case, what's the real Earth-equivalent age of maturity. Mind you, the last potion is void if one of us is correct.

16. If 4 GSY = 5 EY, then 1 GSY = 5/4 EY. So 11 GSY = 11*5/4 EY, right?

17. Originally Posted by TurkeySloth
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?
This gets into orbital resonance issues, which can be either destructive or give orbital stability. I think, in general, you want their orbital periods to have integer ratios that allow them to never be aligned together while at their periapsis (closest to the host planet). A 2:3 ratio works well for Neptune and Pluto, for example, because even when Pluto crosses over inside of Neptune's orbit, they won't both in alignment with the white Sun.

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Originally Posted by George
If 4 GSY = 5 EY, then 1 GSY = 5/4 EY. So 11 GSY = 11*5/4 EY, right?
Correct.

19. Good luck with your roleplaying setting.

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