Research paper and sources investigating Earth's moons

[emily-]

TL;DR Summary

Looking for some scientific papers and articles (even simulations) that investigate how many moons earth can have

Hi. I am looking for scientific papers, articles and/or even simulations that investigate how many moons it would be possible for earth to have and maybe modern theories about what these moons can be and look like (i.e what characteristics they have) if they were to exist. I have googled and searched everywhere but the only relevant source I have found was "Moon-packing around an Earth-mass Planet" study by Suman Satyal, Billy Quarles and Marialis Rosario-Franco. I am grateful for any suggestion, thanks beforehand!

 

[fresh_42]

What do you mean by moons? Earth actually has already tens of thousands of moons, i.e. orbiting masses.

 

[emily-]

What do you mean by moons? Earth actually has already tens of thousands of moons, i.e. orbiting masses.

But they don't count as moons? I mean moons in the sense of natural satellites in sizes comparable to other moons of other planets. A moon with a stable orbit around earth and a known orbiting period.

 

[Baluncore]

TL;DR Summary: Looking for some scientific papers and articles (even simulations) that investigate how many moons earth can have

I am grateful for any suggestion, thanks beforehand!

Welcome to PF.

What do you class as a moon?
How stable must it be over time?
If there was somewhere stable, it would have rocks in it, look for articles about them.
This article will probably help classify moons, and has references.
https://en.wikipedia.org/wiki/Claimed_moons_of_Earth

 

[emily-]

What do you class as a moon?
How stable must it be over time?
If there was somewhere stable, it would have rocks in it, look for articles about them.
This article will probably help classify moons, and has references.
https://en.wikipedia.org/wiki/Claimed_moons_of_Earth

I mean moons in the sense of spherical and big-mass bodies (that are detectable and somewhat visible). As for stability time, it should last for at least decades and not be temporary as in some passing asteroids or such. I have already read the article linked but I am wondering if there's some recent research about the subject. It seems as if there are many articles written about how two or more moons would affect earth but barley any that describes how many moons (such as Ceres and Luna) it would be possible for earth to have.

 

[berkeman]

As for stability time, it should last for at least decades

Um, what happens then? Do we all die? This thread is getting depressing...

Can we change the question to Jupiter maybe? Oh wait, it already has lots of moons...

 

[Baluncore]

Two-body systems, without tidal losses, can be stable for a very long time.

Three-body orbital systems evolve by exchange of energy through tidal forces, until at some point when the biggest moon, like a cuckoo, kicks or throws out the smallest moon.

With many-body orbital systems, resonance between orbital periods becomes important to stability, and to the rejection of lesser members by a local gang of thugs, working together with chaos.

So I would say that only two bodies could be stable. But is that the Sun and Earth, or the Earth and the Moon?

We have sufficient moons now. The one we have is gradually moving away. There is nowhere to place another moon, that could increase the stability.

 

[Drakkith]

I mean moons in the sense of spherical and big-mass bodies (that are detectable and somewhat visible). As for stability time, it should last for at least decades and not be temporary as in some passing asteroids or such. I have already read the article linked but I am wondering if there's some recent research about the subject. It seems as if there are many articles written about how two or more moons would affect earth but barley any that describes how many moons (such as Ceres and Luna) it would be possible for earth to have.

The problem is that the maximum number is somewhat arbitrary. A few thousand moons could be temporarily placed into different orbits, but they would quickly get thrown out by gravitational interactions. You'd need to specify the timeframe in which these moons are relatively stable. The longer the time frame, the fewer the number of moons we could have. The number of moons we could have over a timespan of a billion years or so is probably small.

Adding to the difficulty is the lack of a exact solution to multi-body problems like this. That means you can't just write down a series of equations for each body and then plug in a value for time to get their locations. You actually have to do a numerical simulation. These are relatively easy to do for large numbers of objects if you're just looking at a short period of time, but if you want to look decades or centuries into the future you need to reduce the number of objects you're simulating or reduce the accuracy of the simulation. Neither of which is ideal.

If you'd like to do your own amateur 'research', you can always grab something like Universe Sandbox and play around. If that's too much like a game or not to your liking there are probably a few dedicated scientific grade gravitational simulators online.

 

[emily-]

T

The problem is that the maximum number is somewhat arbitrary. A few thousand moons could be temporarily placed into different orbits, but they would quickly get thrown out by gravitational interactions. You'd need to specify the timeframe in which these moons are relatively stable. The longer the time frame, the fewer the number of moons we could have. The number of moons we could have over a timespan of a billion years or so is probably small.

Adding to the difficulty is the lack of a exact solution to multi-body problems like this. That means you can't just write down a series of equations for each body and then plug in a value for time to get their locations. You actually have to do a numerical simulation. These are relatively easy to do for large numbers of objects if you're just looking at a short period of time, but if you want to look decades or centuries into the future you need to reduce the number of objects you're simulating or reduce the accuracy of the simulation. Neither of which is ideal.

If you'd like to do your own amateur 'research', you can always grab something like Universe Sandbox and play around. If that's too much like a game or not to your liking there are probably a few dedicated scientific grade gravitational simulators online.

Thank you for your answer. Maybe I didn't formulate myself clearly but that is quite what I am searching for. I understand that the number of possible moons can vary depending on the time frame and mass but I wonder if some researches such as the one I have mentioned in my post have been made whether they involve the usage of numerical simulation or not.

 

[emily-]

Two-body systems, without tidal losses, can be stable for a very long time.

Three-body orbital systems evolve by exchange of energy through tidal forces, until at some point when the biggest moon, like a cuckoo, kicks or throws out the smallest moon.

With many-body orbital systems, resonance between orbital periods becomes important to stability, and to the rejection of lesser members by a local gang of thugs, working together with chaos.

So I would say that only two bodies could be stable. But is that the Sun and Earth, or the Earth and the Moon?

We have sufficient moons now. The one we have is gradually moving away. There is nowhere to place another moon, that could increase the stability.

As for the three-body system, when thinking about the collision/ejection of the smaller moon, would it be possible to have that happen after decades or thousands of years or does these events tend to happen quickly and within short time period. Isn't it possible to have some kind of a stable three-body configuration that lasts intact thousands of years before any of the aforementioned events take place?

 

[Baluncore]

Isn't it possible to have some kind of a stable three-body configuration that lasts intact thousands of years before any of the aforementioned events take place?

Almost anything is possible, given time. One thousand years is but an instant. A system that lasts for 100 million years might be called stable, but I think not one that lasted only 10 million years.
The Hijri Calendar is not yet 1500 years old. It relies on the Moon to keep doing its thing. There have been other lunar calendars before. How would things change if we lost our Moon?

A heavy natural object would probably orbit for a very long time, as it gradually crept to a point where it could play a part in catastrophically ejecting some smaller moon. The longer game would then be changed for the surviving bodies, with a period of unpredictable confusion until things settled down again.

Does "punctuated equilibrium" count as stability?
https://en.wikipedia.org/wiki/Punctuated_equilibrium

Some possible stable and unstable systems are described and simulated here.
https://en.wikipedia.org/wiki/Three-body_problem

 

[fresh_42]

Our moon is especially big. It would probably be easier to pack more typical moons at a time when it is farther out. And a small planet like Pluto has 5 moons! So ...

The problem is that the maximum number is somewhat arbitrary.

 

[Vanadium 50]

I don't think you will find much.

Spherical means big. Like a few percent of the mass of the moon. So where is it? It's not in orbit and it's not in the Trojans. So where did it go?

People tend not to write papers that don't solve any problems but cause others.

 

[emily-]

Almost anything is possible, given time. One thousand years is but an instant. A system that lasts for 100 million years might be called stable, but I think not one that lasted only 10 million years.
The Hijri Calendar is not yet 1500 years old. It relies on the Moon to keep doing its thing. There have been other lunar calendars before. How would things change if we lost our Moon?

A heavy natural object would probably orbit for a very long time, as it gradually crept to a point where it could play a part in catastrophically ejecting some smaller moon. The longer game would then be changed for the surviving bodies, with a period of unpredictable confusion until things settled down again.

Does "punctuated equilibrium" count as stability?
https://en.wikipedia.org/wiki/Punctuated_equilibrium

Some possible stable and unstable systems are described and simulated here.
https://en.wikipedia.org/wiki/Three-body_problem

Thanks for your answer!

 

[Klystron]

While NOT a peer-reviewed science paper, one might glean references to relevant papers from geologist Erik Asphaug's interesting book "When the Earth Had Two Moons".

There are several other related popular astronomy books I have enjoyed on this topic including "The Big Splat, Or How Our Moon Came to Be" by science author Dana Mackenzie, but here we digress even farther from peer-reviewed science.

 

[Ken G]

Another place you might find some useful references is in the area called "exoplanets." We have discovered a lot of "super-Earths" orbiting other stars, and a natural question to ask is, how many of those planets have large moons, and how many large moons do they have? The idea here is, one way to imagine a hypothetical Earth that is different from ours is to actually look at exoplanets, which are not hypothetical at all. The way one could see a large moon is when the exoplanet first starts to cross in front of the star (for exoplanets detected by "transits"), or when it first starts to exit from being in front of the star. If it has a large moon, those periods of time will look a little different, producing a telltale signature. There are already plans to look for evidence of atmospheres this way-- if you can see an atmosphere, it would be way easier to see a moon! Here's a general article about the status of that search:
https://www.scienceabc.com/nature/universe/can-exoplanets-have-their-own-moons.html#:~:text=Minute changes in the transit time of the,tests suitable candidates against planet-only and planet-with-moon models.

Apparently, it is still pretty hard to detect exomoons, but it seems likely that our capabilities will improve in the near future, so your question is timely in that context as well. It should also be noted that your question relates to the issue of life elsewhere, because it is thought that having a single large moon has been beneficial for life on Earth (it stabilizes Earth's rotation axis and therefore seasons, it induces tidal pools that provide for various types of life, etc.). So we'd like to know more about how often a planet gets a single large moon, and the planets in our solar system don't have nearly enough members to address that statistically!