Another Earth-like system near us

[momo666]

I was just curious if it would be possible for another Earth and Moon to exist in our solar system neighborhood. What I mean by that is for it to exist as close as possible to our planet so that it can have the same sort of atmospheric temperature and by extent, similar living conditions, this is where I am getting at. I am pretty sure that to those who are educated on this subject, this is problematic because I suspect this other planet would affect ours in negative ways ?

Anyhow, I hope I conveyed my message clear enough. What about just another Earth-like planet without a natural satellite ? Would it change the said planet so much that it would be drastically different compared to our Earth ?

 

[Bandersnatch]

I don't think there's another stable orbital zone in the inner solar system.
This paper: https://www.nature.com/nature/journal/v399/n6731/full/399041a0.html finds an unoccupied stable zone at around 1.08 - 1.28 AU. That's close enough to maintain the same energy balance as Earth's, providing there's a sufficiently robust greenhouse effect in place - i.e. atmospheric composition would have to differ.
However, the numerical calculations they ran assumed a body of negligible mass (asteroids) orbiting there. Another Earth-like planet would likely end up perturbing Earth's and Mars' orbits, and vice versa. In the end, one or more of these planets would end up ejected from the solar system, or at the very least migrating to its nether parts.

What I'm saying, is that there's just no room for another Earth-like planet in the habitable zone of our star.
Maybe it'd be achievable with some special orbital resonances, but your guess is as good as mine here.

But, perhaps there's a solution - what if that second Earth were to replace the Moon? That'd ensure identical conditions. This paper: https://arxiv.org/abs/astro-ph/0508670 finds that doubling the Earth's mass (which is equivalent to this situation) would not destabilise the system.
Of course, then you'd have both planets not be able to have any other moons - in the sense of having Luna-like satellites, and apart from being each other's moon.

 

[momo666]

Take the second scenario, the one where you replace the Moon with another Earth. Wouldn't that affect our planet negatively ? As in, earthquakes and bigger tides and so on. I am curious just how different would our planet be in that scenario.

Also, in the case of the first scenario, where another Earth perturbs our planet's orbit and causes one or more planets to be ejected from the Solar System, just what is the time scale of that ? Roughly speaking, of course.

Thanks for the very informing response by the way.

 

[Bandersnatch]

Take the second scenario, the one where you replace the Moon with another Earth. Wouldn't that affect our planet negatively ? As in, earthquakes and bigger tides and so on. I am curious just how different would our planet be in the scenario.

Not necessarily. Tidal effects scale with third power of distance, and with first power of mass. So all that you need to do for the tides from an Earth-like planet 83 times as massive as the Moon to be exactly like what we get from the Moon, is to put the other planet $\sqrt[3]{83}=4.38$ times farther.
Now, this comes out to a bit over 1.5 million km, which is too far to keep the system of the two planets stable - they'd be as likely to start orbiting the Sun as individual planets, as they'd be as a pair. However, putting them e.g. 1 million km apart is a stable situation, and tides would be approx. 3 times as strong, which seems reasonably non-apocalyptic.

Or, you can place it at lunar orbit, or even closer than that, and just make the two planets tidally-locked (like e.g. Pluto and Charon are), where each planet orbits at the same rate as it revolves. There will be no visible tidal effects from the planet(s), but there'll still be tides from the Sun (solar tides are approx 1/2 as big as lunar).
Days would be long, though (as long as it takes the planets to orbit one another, which depends on how far apart you place them).

Also, in the case of the first scenario, where another Earth perturbs our planet's orbit and causes one or more planets to be ejected from the Solar System, just what is the time scale of that ? Roughly speaking, of course.

Depends on the particulars of the setup, but up to a few millions of years is a good ballpark. For example, in the second paper linked above, they found out that increasing Earth's mass by a factor of 4-6 ejects Mars after 10 Myrs.

 

[momo666]

The phrase "reasonably non-apocalyptic" made me giggle. Thanks for the amount of information in that post, a lot to look up.

What about another scenario ? Say we put the other Earth on the same orbit as the Earth, only at a different point. I suppose that means they would collide at some point in the future right ? Do we have any guesses of a timeline if that is the case ?
I was also thinking that we could put it as close as we could to the Earth's orbit. Something like the same orbit as Earth + some distance (so they have the same orbit but they cannot collide) but I suspect that still brings the same problems of future ejection and destabilization of other planets.

 

[Bandersnatch]

Say we put the other Earth on the same orbit as the Earth, only at a different point.

This is a well-analysed case, and it is universally unstable - unless the body you're placing in co-orbit is of negligible mass (again, like a few asteroids). The concept to look up here is called 'Lagrangian points'. The Wikipedia article will explain it much better than I could do here, and with nice visualisations to boot.
Anyway, no it won't work.

 

[mfb]

However, putting them e.g. 1 million km apart is a stable situation

I don't think it would be long term stable.
Technically the Hill-sphere is for the case of a strict mass hierarchy (like Sun >> Earth >> Moon), but the situation shouldn't change too much for a binary planet. The Hill sphere is the outermost range where an orbit is possible at all - but orbits out there are not stable over time. 1 million km is less than half the radius of the Hill sphere, which means the orbit changes a lot over time.

There is another option: Make both tidally locked in an orbit that just needs one day. The planets deform a bit to reach an equilibrium, and then you don't have any tides.
You also get spectacular views of one side of the other planet from half of the surface.

 

[snorkack]

This is a well-analysed case, and it is universally unstable - unless the body you're placing in co-orbit is of negligible mass (again, like a few asteroids). The concept to look up here is called 'Lagrangian points'. The Wikipedia article will explain it much better than I could do here, and with nice visualisations to boot.

The analysis of Gascheau suggests otherwise. For example, from:
http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=8093&context=etd_theses
page 75. Suggesting that another Earth-like planet in a Lagrange point should be stable.

 

[Bandersnatch]

The analysis of Gascheau suggests otherwise. For example, from:
http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=8093&context=etd_theses
page 75. Suggesting that another Earth-like planet in a Lagrange point should be stable.

Huh. That's a first. I'll take a read later.

 

[snorkack]

Another point:
Moon would not be stable on a geostationary orbit. However, if Moon were about 1,5 time more massive (by my estimate), it would be stable.

 

[mfb]

Another point:
Moon would not be stable on a geostationary orbit. However, if Moon were about 1,5 time more massive (by my estimate), it would be stable.

Why would it be stable with a larger mass?

It would be stable with a double bound rotation.

 

[snorkack]

Why would it be stable with a larger mass?

It would be stable with a double bound rotation.

Precisely.
Deimos and Phobos are unstable because of their small mass.
Deimos orbits near areostationary orbit - its orbital period is slightly longer than Mars´ rotation period.
What happens due to tidal friction?
Deimos, like Moon, has a slower angular speed of orbit than the rotation of the planet. Therefore, the effect of tides is to accelerate the satellite.
Tidal acceleration causes the satellite to climb to a higher orbit.
Which, by Kepler´s laws, causes the angular velocity of the satellite to decrease.
Tidal acceleration does also cause the rotation of the planet to decrease. But the size of that effect depends on the mass of the satellite. If the mass of satellite is small, as is the case with Deimos, then an appreciable increase in orbital period of satellite would cause a small increase in rotational period of planet.

If a satellite is massive enough, then an increase in orbital period of satellite would cause a large increase of the rotational period of planet, so a small difference of angular speeds would decrease till the bodies reach a double lock.
But by my estimate, Moon is not massive enough for a stable double lock on geostationary orbit.

 

[Bandersnatch]

Deimos and Phobos are unstable because of their small mass.
Deimos orbits near areostationary orbit - its orbital period is slightly longer than Mars´ rotation period.
What happens due to tidal friction?
Deimos, like Moon, has a slower angular speed of orbit than the rotation of the planet. Therefore, the effect of tides is to accelerate the satellite.
Tidal acceleration causes the satellite to climb to a higher orbit.
Which, by Kepler´s laws, causes the angular velocity of the satellite to decrease.
Tidal acceleration does also cause the rotation of the planet to decrease. But the size of that effect depends on the mass of the satellite. If the mass of satellite is small, as is the case with Deimos, then an appreciable increase in orbital period of satellite would cause a small increase in rotational period of planet.

If a satellite is massive enough, then an increase in orbital period of satellite would cause a large increase of the rotational period of planet, so a small difference of angular speeds would decrease till the bodies reach a double lock.

But what does it have to do with anything? It was never a question whether the Moon can synchronise the Earth's rotation. The scenario proposed was to magically put the Moon (or another planet) in a 1:1 synchronous orbit. There is no more tidal development between the two bodies in this situation.

Sure, if we did that, then solar tides would still kick the Moon out of this geostationary orbit and crash it into Earth, but the timescales for that are very long, and it is not unstable in the sense of ejecting one of the bodies.

The analysis of Gascheau suggests otherwise. For example, from:
http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=8093&context=etd_theses
page 75. Suggesting that another Earth-like planet in a Lagrange point should be stable.

If I'm reading it right, a 10 Jupiter mass body in Earth-Sun L4 or L5 would be stable? That doesn't seem intuitively right. Likely I'm missing something, or my intuition is just no good. Any comments?

 

[mfb]

If I'm reading it right, a 10 Jupiter mass body in Earth-Sun L4 or L5 would be stable? That doesn't seem intuitively right. Likely I'm missing something, or my intuition is just no good. Any comments?

Earth would be the Trojan in this scenario. You need a big mass ratio, but you can have Earth-sized moons around the massive planet.

 

[snorkack]

But what does it have to do with anything? It was never a question whether the Moon can synchronise the Earth's rotation. The scenario proposed was to magically put the Moon (or another planet) in a 1:1 synchronous orbit. There is no more tidal development between the two bodies in this situation.

My point is, Moon like Deimos would be unstable. A small violation of tidal lock would increase, due to tidal evolution.

Sure, if we did that, then solar tides would still kick the Moon out of this geostationary orbit and crash it into Earth, but the timescales for that are very long,

Only if the tidal lock is stable.

and it is not unstable in the sense of ejecting one of the bodies.

Might well be. Though this would require a closer in orbit.

 

[Lowedown]

Try "adding" another child (say a two-year-old) to a family with a newborn, a one-year-old and a three-year-old who already have staked out their places in the family dynamics. The tension and desire for attention from the parents creates turmoil. You are making an assumption that a stable solar system is static. It is dynamic and the equilibrium comes from a stability of all the planets as their orbits have been established by multiple factors of gravity over long periods of time.

 

[Dr_Zinj]

Trying to remember where I read it, but wouldn't placing duplicates of the Earth-Moon system every 60 degrees around the Sun be a stable configuration? Each pair would have an equal mass in front and following in the L4 and L5 positions.

 

[snorkack]

Trying to remember where I read it, but wouldn't placing duplicates of the Earth-Moon system every 60 degrees around the Sun be a stable configuration? Each pair would have an equal mass in front and following in the L4 and L5 positions.

I´m not sure about that!
To begin with placing just 3 equal masses at 60 degrees from each other: while nr. 2 is at 60 degrees from nr. 1 and nr. 3 each, nr. 1 and nr. 3 are 120 degrees from each others, so they are perturbing each other. Is perturbation from the mass at 120 degrees liable to exceed the stabilization from the mass at 60 degrees?

 

[Dr_Zinj]

I´m not sure about that!
To begin with placing just 3 equal masses at 60 degrees from each other: while nr. 2 is at 60 degrees from nr. 1 and nr. 3 each, nr. 1 and nr. 3 are 120 degrees from each others, so they are perturbing each other. Is perturbation from the mass at 120 degrees liable to exceed the stabilization from the mass at 60 degrees?

Total number of pairs added would be 6, not 3, equally spaced (every 60 degrees) around the Sun in the Earth-Moon orbit. Or are you referring to the Sun, E-M1, E-M2 as a three body problem?

 

[Sue Rich]

Just an out-there question. Is it possible another Earth could be in our own orbit in such a position that we never see it?

 

[mfb]

Trying to remember where I read it, but wouldn't placing duplicates of the Earth-Moon system every 60 degrees around the Sun be a stable configuration? Each pair would have an equal mass in front and following in the L4 and L5 positions.

It would be unstable.

Just an out-there question. Is it possible another Earth could be in our own orbit in such a position that we never see it?

The orbital perturbations caused by it would be obvious (something like "this value disagrees from predictions at 10000 times the measurement uncertainty"), and various space probes would have seen it directly. There is also no stable orbit where anything could hide permanently out of view.