# What if the Moon was 100x more massive: Binary planets?

I was reading a couple of Earth-Moon related questions (Mars just collided with Earth! A question of eccentricity, Could the earth have another moon?) and they got me thinking about planet-moon systems in general.

Binary star systems are pretty common. The types of the two stars in the binary can vary pretty widely (main sequence, puslar/neutron star, black hole, white dwarf, giant phases, etc, etc), but some are formed of a pair of roughly equal mass (within a factor of <10).

I can't say I've ever heard of a binary planet system, though. Of course a planet with a moon is sort of a binary, but I've never heard of an equal mass binary planet. I think the closest thing in the solar system would be the Pluto-Charon system, with a mass ratio of about 10:1.

Is there any reason a binary planet would be unstable? Obviously this is a three-body system, which has some inherent instability, but Earth-Moon-Sun seems pretty stable. Would increasing the mass of the Moon to match that of Earth make the system unstable?

How about gas-giants? I think a Jupiter-Jupiter binary close to a star would be short lived because of three-body interactions, but what about further out? Would, for instance, a double-Jupiter or double-Saturn be stable in our solar system? Or is there some tidal effect that would cause the orbit to decay and the binary planet to merge?

As an aside, it seems that binary asteroids aren't terribly difficult to find... perhaps we just haven't seen any binary planets yet because they're only stable relatively far away from their star, making them difficult to detect outside our own solar system?

• Somewhat tangentially, I remember reading an Isaac Asimov essay many, many years ago related to this. I'll see if I can find it but, in it, he argued that the Earth - Moon system is a double planet system in some sense as opposed to a planet-moon system. Update: Thanks Wiki! en.wikipedia.org/wiki/Double_planet#Tug-of-war_definition – Alfred Centauri Jun 18 '13 at 22:49

They are sometimes also called double planets and they're more widespread in fiction than in observations. I don't think that there is any new instability that would appear for the system of double planets orbiting a star and that wouldn't be present for other, more asymmetric pairs of planets. Obviously, the tidal forces would be really large if the planets were close enough to each other. But because the tidal forces go like $1/r^3$, it's enough to choose the distance that is 5 times larger than the Earth-Moon distance and the tidal forces from the other Earth would be weakened 125 times and would already be as weak as they are actually from the Moon now (with a lower frequency).

One must realize that the systems with two or several planets are rather rare and the condition that the mass of the leading two planets is comparable is even more constraining.

Imagine that each of the two planets has a mass that is uniformly distributed between 1/20 of Earth's mass (like Mercury) and 300 Earth masses (like Jupiter) on the log scale. The interval goes from the minimum to the maximum that is 6,000 times heavier. That's more than 12 doublings, $2^{12}=4,096$. So if you pick the first planet to be at a random place on that interval of masses (uniformly at the log scale), the probability that the second planet's mass (which is independent) differs by less than the factor of $\sqrt{2}$ from the first mass is about $1/12$.

Only $1/12$ of systems that look like a pair of planets will be this symmetric. And the number of pairs of planets - even asymmetric ones – is rather low, indeed. The reason is really that during the violent eras when Solar-like systems were created, rocks had large enough velocities and they flew in pretty random directions so they were unbound at the end. It's just unlikely to find two large rocks in the same small volume of space: compare this statement with some high-temperature, high-entropy configurations of molecules in statistical physics.

It's also rather unlikely that a collision with another object creates two objects that will orbit one another. After all, the two-body orbits are periodic so if the two parts were in contact during the collision, they will collide again after one period (or earlier). Equivalently, the eccentricity of the orbit is likely to be too extreme which will lead to a fast reunification of the two new planets. Moreover, even if something would place the two newly created planets from a "divorce" on a near-circular orbit, perhaps a collision with a second external object (good luck), it's very unlikely that such an orbit will have the right radius, like the 1 million km I was suggesting in the case of the hypothetical double Earth above. If the two objects are too close, the tidal forces will be huge and (at least for some signs of the internal angular momentum) they will gradually make the planets collapse into one object again. And if the energy with which the planets are ejected from one another is too high, no bound state will be created at all. So the initial kinetic energy of the newborn 2 planets would have to be almost exactly tuned to their gravitational potential energy (without the minus sign) and that's generally unlikely, too.

• If you actually simulate the condition, the possible results are : 1. Slingshot, one of the bodies leave the systen 2. Collision 3. Stable Orbit in decreasing order of probability, and the probability for No. 3 is extremely lower than the others. – Cheeku Jul 11 '13 at 23:02

The Moon is so large compared to the Earth that many consider it to be a double planet system (Pluto-Charon being the other). The key is that the Moon's orbit around the Sun is never concave (away from the Sun, which I interpret as "never moving backwards relative to the Earth"). The Moon is also large enough to stabilize the Earth's axial tilt despite gravitational perturbations from Jupiter and Saturn. Without that, life might not have gotten very far.

I bought program, that simulates 3D universe. You can create own simulations, but you can also use created assets. One of them, is "earth & moon".

According to what I understand you ask. I change weight of moon that was orbiting earth from "1.00 moons" to "100.00 moons" , program automatically changed it to "1.23 earths".

Although they behave like binary stars. It looks, like earth isn't able to stabilize it's orbit around moon. Program has estimated, that earth is orbiting moon. But moon isn't orbiting anything. As I already said, earth cannot stabilize it's orbit around moon. Program calculated (future) trajectory (marked with blue line) of earth. It looks like whirl.

You may find this strange: but they look like they would like to hug, but there is spring between them. The more closer they got, the further they're thrown from each other.

If you want footage of it. Write in comments below.

• Is this program possibly called "Universe Sandbox"? If so, it is not a reliable program. For instance, it lets objects accelerate to above the speed of light. – Jim Feb 3 '14 at 20:49
• As if. It remains reliable as long as you aren't typing impossible things in it. If you put VY Canis Majoris in place of Sun and change gravity to 1000, you can surely expect totally random and strange things would happen. But as long as you create things that could appear in reality. I think it's quite reliable. For instance. Planet with mass "1" and another planet with mass "1.23" seems pretty possible to me in our gigantic universe. At the end, why accelerating object above speed of light would be possible? Haven't you yet seen article announcing that speed of light is not greatest speed? – Rik Telner Feb 4 '14 at 15:12
• Universe Sandbox is a video game. It is meant to provide a functionally basic simulator for playing around with astrophysics. It is not meant to be used for serious simulations intended to represent reality. Furthermore, the speed of light is a limiting speed. There exists no credible, peer-reviewed article that claims to show some tidbit of information is able to arrive at a destination before a simultaneously transmitted beam of light along the the same path. – Jim Feb 4 '14 at 15:19
• On another hand. Look, I don't know almost nothing about universe. I am very low beyond average of people around here. At the actual end. Offcourse it's not perfect. But for this simulation only things program uses is gravity, density, weight and speed. I super highly doubt that there are glitches with that. – Rik Telner Feb 4 '14 at 15:20
• en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly – Jim Feb 4 '14 at 15:24