# Could Earth and the Moon be the same size?

Many questions on this site hypothesize about two planets in close orbit of each other, each developing their own civilizations. How feasible is that?

Some 4.5 billion years ago Theia, a planetary object of uncertain size, collided with the young Earth and ejected a significant quantity of the two bodies crusts into space, forming a new object, the moon (if you don't believe this theory, then assume it is true for this question). Is it possible that the same collision, if it had happened at a different speed or impact angle, could have created two planets of approximately equal size orbiting the sun together?

Constraints on the final system:

• Given that the combined mass of the Earth and the Moon is about $6\times10^{24}$ kg, each of the two objects should be about $3\times10^{24}$ kg

• The planets must orbit the sun as a single system, orbiting each other.

• The planets must stay in an orbit approximately the same distance from the sun as Earth is now.

• The planets must maintain the same characteristics that allowed life to arise on Earth: nitrogen atmosphere, plenty of water for oceans, active magnetic field and plate tectonics, etc.

• Is habitability of just one planet an option? I can't imagine an impact being able to scoop out enough core for a working magnetosphere without scattering it all over the solar system. – John Dvorak Dec 30 '17 at 1:21
• @JohnDvorak That is the heart of the question. If you can prove (or strongly intimate) that you can't get two magnetospheres, please post. And thanks, fixed. – kingledion Dec 30 '17 at 1:26
• This is literally the first question tagged hard-science that I actually thought deserved it. Mazel'tov. I'm looking forward to reading the answers. – JBH Dec 30 '17 at 2:33
• Is there any constraint on the original planetoids from before the collision? Especially, must they be from the same proto-planetary disk, or can one (preferably Theia) or both be rogue planets from outside the forming solar system? What about their original compositions, etc.? – Dalila Jan 4 '19 at 19:19

Possible, yes. Likely? No.

I am going to present a short version of the science behind binary planets. For the whole thing you can refer to this article from the California Institute of Technology. Some scientists there made some simulations and published a paper on it.

So, what you want is known as a binary planet. It is different from a system like Pluto-Charon (because Pluto is way more massive than Charon), but similar to 90 Antiope.

The reason why I say it's unlikely is that for a binary planet system to evolve, a shock between to formerly solitary planets must go through a "kissing collision". They must "graze" or "scrape" each other in their impact. The tidal forces involved will cause large tides, which dissipate momentum and causes the system to become bound (i.e.: neither planet will reach the system's escape velocity).

This arrangement is not perfectly stable, and as the article mentions, it may only last a few billion years. The less ideal the collision is, the sooner the system will decouple or collapse. Needless to say this would be catastrophic to any life that has developed on the binary planet. It is possible that one of the resulting planets ends up falling on the star. It is also possible that one of them will be ejected from the star system. It is possible that the parts will collide again, which would merge them into a single planet. This would very likely melt the crust during the merger.

Regardless of whether you plan to give your binary planet denizens such a demise or not, here are the requirements for a binary planet to realistically form and stabilize around a star of spectral class G, such as our sun:

• Must stabilize its orbit around the parent star at least half an AU away from it;
• The surfaces of each part of the binary should stay one planetary radius apart from each other.

Also notice that the parts of the binary planet will necessarily be tidally locked.

So far I have only said what the article says. But from that we can infer some interesting properties of such a system.

For starters, it could reasonably be located withing the goldilocks zone around a G2V star. And since the arrangement can last for billions of years, with the original colliding planets having the same chemical makeup of proto-Earth and Theia, life as we know could develop on such a binary planet.

The orbital period of each around the barycenter would be quite short, in the order of hours. A geosynchronous orbit around Earth - that is, an orbit with a period of one day - requires a satellite to be six Earth radii above Earth's surface. Compare with the figure of a one planetary radius between the components of the binary (lower orbit = shorter period). This would cause daily eclipses (remember that the eclipsing body is way larger and closer to the eclipsed body than the Moon is to us). The region eclipsed on each component is always the same, due to tidal lock. It will get less sunlight everyday, effectively going through a permanent winter - which may be cumulative with the axial tilt related winter during parts of the year.

Just to be clear: insanely short orbital period + tidal lock = a sol that is much shorter than Earth's (I estimate 12-14 hours).

Gravity would be noticeably stronger on the side of each planet that is away from the other. Standing on the "outer" side of the binary, you get the whole pull from two planets. But in the eclipsing region, you get two strong pulls in opposite directions (though the planet you are standing on will have the larger pull). A similar tug-of-war exists between Earth and the Moon, but the Moon's pull is too little to be noticeable at all. Back to the binary, if some species ever makes it to the space age, they will find that at the barycenter the gravity pull is close to zero.

I don't know how to calculate the average gravity for each system component, but I do know that each one's mass is still around five martian masses. So I think average gravity would be much closer to Earth's than to Mars's.

If the binary has no moons, there will be no tides. If there is a moon orbiting the binary, it will have tides, though on a much smaller scale than those on Earth.

Finally, for a non-scientifical thing. It is my favorite part though. There is nothing to tell us how the beliefs of people from such a system would develop - but they have a nice setting to create awesome mythologies.

• I'm not trying to be too mean, but this question ignores the assumptions in the question, doesn't answer the question, and isn't really hard science. I'm not asking about binary planets evolving together, I'm asking about the kinetics of a collision. I'm not talking about a random G2V star, I'm talking about Sol. Why do you pad this answer with comic books images and paragraphs saying what you don't know? – kingledion Dec 30 '17 at 6:50
• "It is possible that one of the resulting planets ends up falling on the star." [citation needed.] Any KSP player knows that colliding with the Sun from Earth's (or Kerbin's) orbit takes ridiculous amounts of delta-v, and I have a hard time imagining how anything like that could be achieved by a collision between two planetoids. (Unless one of them started out in a retorgrade orbit, but that wouldn't be the case if they formed in the same protoplanetary disk.) – Nathaniel Dec 30 '17 at 6:51
• My above comment is especially true given that the article says the planets have to have a very low relative velocity (comparatively speaking) in order for this to happen. – Nathaniel Dec 30 '17 at 7:00

I don't think that anyone can answer this question without doing detailed modelling of protoplanetary collisions -- I'm not aware of any that have been done, but I would not be surprised to find out it has been.

Put aside for the moment the really hard question of whether a collision could result in two Earth-massed bodies in orbit around each other. (I'll come back to it.)

Would the system once formed be stable? Sure. There's nothing special about a true binary planet and as long as they were close enough to stay bound -- 250,000 miles would be just fine -- they'll be about as stable as the existing Earth-Moon system.

Would they be tide-locked? Probably. It depends on how close together they form and how fast they are rotating then. If they form relatively close and are not rotating super-fast, then there's a good chance that the tidal forces that drive them apart will drive them to tidal lock. As long as they are not really fast rotators, there's not so much angular momentum in the system they couldn't tide-lock. (But this is all basically physical intuition. We'd need to do modelling to say for sure.)

Could they be in the life zone. Sure. There's nothing special about that region and the large number of super-Earths we're seeing among the exoplanets tells us that there's likely to be sufficient mass in the habitable zone.

Geochemistry compatible with life? Again, as far as we can tell both of the resulting planets could be Earthlike. The Moon is rather non-Earthlike because it's small and lost all its volatiles, but if it were as massive as the Earth it would have held most of them. There's no guarantee that the twin planets would be just like Earth, but probably they'd be close enough.

The biggest issue is whether a planet with days that are 10-20 Earth-days long (due to tidal lock) would have weather/climate limiting life. My guess is not, because life is really good at evolving to fit any niche, and the oceans, anyway, would be fine.

But the elephant in the room is whether it's likely that more than a very, very rare collision would produce roughly equal-sized planets. My physical intuition says that it's possible, but not very likely, but this is something that really needs proper numerical modelling of collisions with tested codes.

As to how to achieve a stable 2-body system as a product of a collision between bodies A and B, the options are: 1 - propel enough mass to L1 or L2 to form the second planet. Luna formed at half this distance (although again has only 1.2% of Earth mass). To have pushed the material that made Luna twice as far (inverse square law) would have required 4x as much force. This is problematic since you would either need to double the mass of both objects (which is not the desired answer) or double the impact velocity.

My hot take on the collision looks like this: Earth's mean velocity: 30 km/s +/- 300 meters / second owing to the eccentricity of its orbit.

Theia's theoretical velocity: must be similar to Earth's 30 km/s. Mars' speed is 24 km/s and Venus' is 35 km/s. If Theia's speed was off by 5-10 km/s from Earth it wouldn't be co-orbital. But its velocity at impact was likely not its mean velocity.

Earth's current orbit has an eccentricty of .0167086 and an inclination of 7 degrees to Sol's equator. This must be the product of the bodies orbits merging. Theoretically let's say Theia had a higher eccentricity (0.25) and Earth had a lower one (0.05 or less). At various points along the eccentric orbit the velocity changes significantly. Here's some conjectural scenarios:

worst: Earth: 29.8 km/s Theia: 30.6 km/s relative speed of impact: 800 m/s Force = mass * acceleration (Newton's 2nd) each body is subject to 800 * 3x10^24 or 2,400 Septillion Newton-meters of force. The equivalent of 573 quadrillion tons of TNT

best: Earth: 30.2 km/s Theia: 30.3 km/s relative speed at impact: 100 m/s or less each body is subject to 100 * 3*10^24 or 300 Septillion Newtons-meters of force. The equivalent of 71 quadrillion tons of TNT

Another thread established a method to estimate how many tons of TNT or any other energy equivalent would be required to destroy the moon. To overcome the gravitational binding energy of a body with a mass of 3x10^24 kg you would need 6.006456e+33 Joules or 1.43 septillion tons of TNT. We can see both cases have significantly more energy than what it would take to liquify both planets. The impact velocity was probably much less (or I certainly may have misplaced a few zeroes in the conversions) but it still serves to illustrate the gross forces at work.

A simpler solution is to wonder what would have happened if bodies A and B never collide in the first place, with Theia maintaining a stable position at Earth's L4 or L5 Trojan.

A co-orbital body could theoretically remain in a stable position in Earth's plane if it were either in the L4 or L5 Lagrange point, which are 60 degrees prograde and retrograde to Earth's position within its orbital plane around Sol. In one year Earth travels approximately 940 MKM, so L4 and L5 would each be about 156MKM distant. This is a natural phenomena observed often in the Jupiter system. Earth even has a trojan in the L5 Lagrange position, TK7. One cavaet to this mechanic seems to be that the trojan object must have a mass ratio 1/20th or so that of its co-orbital object, and if primordial Earth and Theia had roughly equal mass then I don't believe they would be able to stay in stable trojan orbits, at least not indefinitely.

Objects occupying the L1 and L2 Lagrange points (each about 1 million KM away from Earth which would be closer to the situation to the Earth-Luna system (Luna's mean distance is 385,000 km). However the mass ratio of Luna to Earth works out like this:

Luna: 7.342 x 10^22 kg

Earth: 5.972 x 10^24 kg

Luna's mass ratio to Earth: ~ 1.2 : 100

Whereas one of the assumptions here is that we have two objects of mass 3 x 10^24 kg, the ratio is 1:1. So short answer: if it's possible then the co-orbital body must be inhabiting either its sister's L4 or L5 point and has very few perturbing forces. From that distance the sister planet would be visible with the naked eye but it might be mistaken for a star.

• my math might be off, if you spot an error please let me know cheers