Zompist Bboard Again

Posted: **Tue Apr 27, 2021 11:23 am**

what would earth look like if instead of our moon we instead had two moons, but they were each about half the size (that is, half the mass) of the real moon? how would it affect the tides? the earth's rotation? seasons? would they get locked into an "opposite" orbit — both the same distance from earth but on opposite sides of the planet — or would one fall into a lower or higher orbit than the other?

Posted: **Tue Apr 27, 2021 1:10 pm**

Most likely these would need to be captured objects, and they could have a lot of their original momentum. But over time the most likely stable situation is for the two objects to be in harmonic equilibrium with one another.

As for tides, it would mostly just dampen them. When the moons are aligned, the tides are similar to our own. When they are on opposite sides, they will mostly cancel out.

Posted: **Tue Apr 27, 2021 1:47 pm**

Artifexian probably has a YT video on this.

Posted: **Tue Apr 27, 2021 3:02 pm**

Much would depend on how that system would form and that, I'm afraid, is hard to model. We really need a lot more Earthlike planets to look at!

Assuming you have your two moons with all else being equal, though.

You can't have one 'opposite' the other. That configuration is unstable, I believe.
What seems a plausible alternative is to have both moons in orbital resonance. . I mean, hey, it works for Jupiter's moons!
The idea is that if you have your two moons in 2:1 orbital resonance, one takes a month to orbit the Earth, and the other takes two. Or alternatively, one takes 14 days, and the other a (lunar) month.

We'll look at both cases. For the rest of your questions, we need to look at tidal forces. I'll do this using gross assumptions and shoddy back of the envelope calculations.

Case 1:
Selenes's period is 14 days, give or take, and Luna's is about a month. Luna has the same orbit as our moon.

Tidal force is 2G*m*(2r/d³) (with G the gravitational constant, m the moon mass, r Earth radius and d the distance.

Luna has the same distance as our moon, but is only half as massive, so tidal force is 2G*0.5 moon masses*2*Earth radius/(Moon distance cubed)³. So only half as strong.

Now, Selene's distance is approximately and on average d= cubic root (0.5²) * EM distance = 0.62 * Earth-Moon distance. (Assuming and neglecting much detail, of course.)
Using the formula for tidal force, we see that Selene's tidal forces on Earth is twice the Moon's.
When both moons are aligned you get 2 1/2 the tidal force we're used to; when they're on opposite side you get 1 1/2 the tidal force.

So you'd expect a more stable axis tilt (so a more stable climate overall). Day length started IIRC at something like a few hours and gradually slowed down due to tidal effect. All else being equal, with stronger tides, you'd get a much longer day.

Case 2:
Luna still has the same orbit as our moon, but this time Selene is further out, witha period of two months.
This time, d = 1.58 Earth-Moon distance, and tidal forces are 1/8th those of our Moon.

In this case, when both moons are aligned you get a measly 0.625 times the Moon's. When they're on opposite sides, you get 0.375.
So all in all, we'd get a less stable axial tilt (more ice ages!) and a noticeably shorter day.

Posted: **Tue Apr 27, 2021 7:41 pm**

I had a similar question regarding my planet having three moons, a small one that rotates every 6 days, a medium one that rotates 12 days, and a large one one that rotated every 36 days. Opted against it because the data in various gravity simulators always resulted in the moons getting knocked out of orbit within like 20 years, no matter what mass or distance apart they were.

Two moons seems to be really stable for having more than one moon, so now it has a six-day moon and a 36-day moon.

Posted: **Thu Apr 29, 2021 2:19 am**

Ares Land wrote: ↑Tue Apr 27, 2021 3:02 pm Much would depend on how that system would form and that, I'm afraid, is hard to model. We really need a lot more Earthlike planets to look at!

Assuming you have your two moons with all else being equal, though.

You can't have one 'opposite' the other. That configuration is unstable, I believe.
What seems a plausible alternative is to have both moons in orbital resonance. . I mean, hey, it works for Jupiter's moons!
The idea is that if you have your two moons in 2:1 orbital resonance, one takes a month to orbit the Earth, and the other takes two. Or alternatively, one takes 14 days, and the other a (lunar) month.

We'll look at both cases. For the rest of your questions, we need to look at tidal forces. I'll do this using gross assumptions and shoddy back of the envelope calculations.

Case 1:
Selenes's period is 14 days, give or take, and Luna's is about a month. Luna has the same orbit as our moon.

Tidal force is 2G*m*(2r/d³) (with G the gravitational constant, m the moon mass, r Earth radius and d the distance.

Luna has the same distance as our moon, but is only half as massive, so tidal force is 2G*0.5 moon masses*2*Earth radius/(Moon distance cubed)³. So only half as strong.

Now, Selene's distance is approximately and on average d= cubic root (0.5²) * EM distance = 0.62 * Earth-Moon distance. (Assuming and neglecting much detail, of course.)
Using the formula for tidal force, we see that Selene's tidal forces on Earth is twice the Moon's.
When both moons are aligned you get 2 1/2 the tidal force we're used to; when they're on opposite side you get 1 1/2 the tidal force.

So you'd expect a more stable axis tilt (so a more stable climate overall). Day length started IIRC at something like a few hours and gradually slowed down due to tidal effect. All else being equal, with stronger tides, you'd get a much longer day.

Case 2:
Luna still has the same orbit as our moon, but this time Selene is further out, witha period of two months.
This time, d = 1.58 Earth-Moon distance, and tidal forces are 1/8th those of our Moon.

In this case, when both moons are aligned you get a measly 0.625 times the Moon's. When they're on opposite sides, you get 0.375.
So all in all, we'd get a less stable axial tilt (more ice ages!) and a noticeably shorter day.

this is all very helpful, thank you!

when you say that (in case 1, which seems more like what i'm looking for for my conworld) "you'd expect a more stable axis tilt" and "a more stable climate overall", do you mean that the axial tilt would be a smaller degree than a one-moon earth, or just that variations in axial tilt would be lessened?

what effect would these tidal forces have on the oceans themselves? would it mean stronger waves? or just greater difference between high tide and low tide?

Posted: **Thu Apr 29, 2021 2:32 am**

GreenBowtie wrote: ↑Thu Apr 29, 2021 2:19 am when you say that (in case 1, which seems more like what i'm looking for for my conworld) "you'd expect a more stable axis tilt" and "a more stable climate overall", do you mean that the axial tilt would be a smaller degree than a one-moon earth, or just that variations in axial tilt would be lessened?

No problem. The axial tilt would be the same (or anything you like, really) but with overall less variations. For instance, Mars, with its tiny moons has about the same axial tilt as Earth now, but it is possible it could have varied between 0° and 60°.

what effect would these tidal forces have on the oceans themselves? would it mean stronger waves? or just greater difference between high tide and low tide?

I'm not very confident here, because ocean tides are awfully complex and I really don't have much understanding of the subject.

What I gather is that the elevation would be higher. Which would result in stronger waves in appropriate places, depending on local geography. (But for instance, an equivalent to the Mediterranean would still have tiny tides.)

Posted: **Thu May 13, 2021 3:33 pm**

would the moons still always have one side facing earth like the real one does, or would we see them rotate as they orbited?

Posted: **Thu May 13, 2021 4:23 pm**

Emily wrote: ↑Thu May 13, 2021 3:33 pm would the moons still always have one side facing earth like the real one does, or would we see them rotate as they orbited?

The moons would have the same side facing Earth. There's no way they wouldn't be tidally locked.

Posted: **Fri May 14, 2021 11:29 pm**

Ares Land wrote: ↑Thu May 13, 2021 4:23 pm
Emily wrote: ↑Thu May 13, 2021 3:33 pm would the moons still always have one side facing earth like the real one does, or would we see them rotate as they orbited?
The moons would have the same side facing Earth. There's no way they wouldn't be tidally locked.

why wouldn't at least one of them be non-tidally locked?

Posted: **Sat May 15, 2021 1:54 am**

keenir wrote: ↑Fri May 14, 2021 11:29 pm
Ares Land wrote: ↑Thu May 13, 2021 4:23 pm
Emily wrote: ↑Thu May 13, 2021 3:33 pm would the moons still always have one side facing earth like the real one does, or would we see them rotate as they orbited?
The moons would have the same side facing Earth. There's no way they wouldn't be tidally locked.
why wouldn't at least one of them be non-tidally locked?

The tidal forces are strong enough to eventually lock the moon --and affect the Earth's rotation as well.

To have a non-tidally locked moon, you would need either a very recent capture/formation or a very distant moon.

A recent capture is possible for a tiny moon, but I don't see that happening in a mature solar system with a larger body.
(I wouldn't rule out that possibility entirely. Your planet would be a volcanic and climatic hellhole at the very least, so ideal from a grimdark fantasy saga if you can contrive some life surviving at all.)

A very distant moon is possible... But it would appear really tiny in the sky. Pity.

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