Fact check: Planetary collisions

[Noisy Rhysling]

Just watched a Youtube of a TV show about "weird planets". They show early on a collision between two planets, proportioned about the same as the Earth and the Moon. The interesting thing is that they show part of the "Earth" being pulled up to meet the "Moon."

Could this happen? Could it happen on an Earth-like planet in collision with an Moon-like body? Could the pull of the Moon's gravity "levitate" part of the Earth's crust. Could an old hack write that scene well enough for the reader to picture?

"WEIRDEST PLANETS discovered by NASA Kepler Satellite Documentary!"

 

[CrackerMcGinger]

Well, to start you off I'm going to ask you something. How does the moon effect the earth?

 

[Noisy Rhysling]

Well, to start you off I'm going to ask you something. How does the moon effect the earth?

[I am a historian] It pulls on the Earth.

 

[Grinkle]

I think he means to use the imagery of Earth's moon creating a bulge to set the scene for the more dramatic crust-busting event.

 

[Noisy Rhysling]

I think he means to use the imagery of Earth's moon creating a bulge to set the scene for the more dramatic crust-busting event.

The video showed that, but it was very quickly ruptured as big chunks flew toward the impactor. That was the part that had me scratching the place my hair used to be.

 

[CrackerMcGinger]

The moon is 238,900 miles (384,400 km) away from Earth, and it pulls on the Earth causing tides. Now close the distance to two meters. As the moon gets closer to Earth the Earth pulls on the moon more. Every action has an equal and opposite reaction. As the moon is pulling earth, the Earth is pulling the moon. This can cause parts of our crust to reach towards the moon.

 

[Noisy Rhysling]

The moon is 238,900 miles (384,400 km) away from Earth, and it pulls on the Earth causing tides. Now close the distance to two meters. As the moon gets closer to Earth the Earth pulls on the moon more. Every action has an equal and opposite reaction. As the moon is pulling earth, the Earth is pulling the moon. This can cause parts of our crust to reach towards the moon.

I know that. But is the pull strong enough to overcome Earth's gravity and yank pieces off old Terra?

 

[CrackerMcGinger]

The Earth reaches for the moon as the moon reaches for the Earth. This can result in the crust being pulled apart due to tidal forces. To be precise, the moons surface should start to be pulled apart before the Earths crust is, but the result should be that the Earths crust starts to be ripped apart by tidal forces a few moments before impact. Now it would probably be a lot less dramatic than what the episode showed you, but it can happen.

 

[Noisy Rhysling]

The Earth reaches for the moon as the moon reaches for the Earth. This can result in the crust being pulled apart due to tidal forces. To be precise, the moons surface should start to be pulled apart before the Earths crust is, but the result should be that the Earths crust starts to be ripped apart by tidal forces a few moments before impact. Now it would probably be a lot less dramatic than what the episode showed you, but it can happen.

Any problem with me using a SWAG number, like five minutes before actual impact? I also have to figure if the lunar ejecta would impact Earth before the vice was versa'd.

And all this will be about one page of text, I think. I don't want to beat the reader to death with the dynamics of the process, just let them picture a cataclysm.

 

[Jonathan Scott]

The case where a smaller body is pulled apart by a larger one is well known, and occurs when the body passes within the "Roche Limit" (Google that for more information). For a body with great tensile strength, it is theoretically possible for the smaller body to pull bits off the larger one as well, but what is most likely to happen is that the smaller body will be ripped apart first and dispersed by the tidal forces.

The basic principles are quite straightforward. A spherical body has the same gravitational effect outside its surface as an equal point mass, so the acceleration field is $GM_2/d^2$ where $M_2$ is the mass of the other body and $d$ is the distance between the centres of the bodies. When the bodies are in free fall near each other, the average relative acceleration of each body towards the other is determined by the field at their centres. For the surface nearest the other body, the effective acceleration due to the field of the other body is increased because it is closer. If the radius of the body is $r_1$, the field at that location increased to $GM_2/(d-r_1)^2$. If the difference between these two accelerations caused by the other body (at the centre and the surface) is greater than the acceleration downwards caused by the body's own field $GM_1/r_1^2$ then surface material will be lifted up with an acceleration initially equal to that difference. For more details, see the Wikipedia entry on Roche Limit, where the initial derivation uses the same simplified model, then it goes into more detail, allowing for more factors.

 

[Noisy Rhysling]

Thanks. Now to find somebody who speaks Maths.

 

[Grinkle]

If you are concerned about being realistic, I speculate that the most dramatic and first effects would be atmospheric. The Earth's atmosphere would be torn away / ejected / ignited. Any bodies of water would be sloshed around a lot sooner than solid land masses. The combination of these gas / liquid disturbances would probably sterilize the planet before any of the crust moved.

What would plausibly and easily explicably (to me) cause the crust to rise would be its decreased weight vs the pressure underneath it. As the moon approached, it would in some sense weigh less because the moon is pulling up on it. For pieces of crust that are at this time held in place by their own weight on top of molten material that is pushing up on the crust, they would be blown out / away by the underneath pressure.

If you can't follow the math about the gravity, perhaps that pressure imagery can work and be easier for you to articulate.

 

[Noisy Rhysling]

Interesting. Would there be some kind of super tidal effect, on the side nearest the intruder and on the opposite side of the planet?

I can picture the seas "boiling" because of low air pressure.

And I have a friend at Purdue who is a steely-eyed missile man, I'll get him to do the math. If he doesn't I'll tell his wife about Olongapo.

 

[Grinkle]

Something the size of the moon tearing into our atmosphere would transfer enough energy to the atmosphere via heating from friction to cause all manner of disturbance. I wasn't thinking about gravity when I wrote that, just the kinetic energy of such a huge moving mass entering the atmosphere. The tidal effects would come some seconds later, I think, and might be hard to distinguish from the effects of the atmospheric heating, as that will seem like a tremendous planet-wide explosion. At least for a time there might not be any atmosphere to speak of left after the moon passed on, until outgassing and perhaps steam replaced some of the blown away atmosphere.

 

[Noisy Rhysling]

Our Hero and Fair Damsel will be escaping from the far side of the planet, ala "Rescue Party". One of their group has a super computer where his left lung used to be, and figured out there was a problem nobody had noticed. They'll get away and go on the vengeance trail.

 

[BillTre]

If your moon were a neutron star, you might get the kind of effects you mentioned as it gets closer to the earth, however, it could have other effects making life on the planet untenable.

Another thought is that I visualize such an impact as occurring rather rapidly (a few seconds in the atmosphere). Not much time to detach things from the planet and get them moving before the moon crushes them back down or knocks them sideways.

 

[Noisy Rhysling]

If your moon were a neutron star, you might get the kind of effects you mentioned as it gets closer to the earth, however, it could have other effects making life on the planet untenable.

Another thought is that I visualize such an impact as occurring rather rapidly (a few seconds in the atmosphere). Not much time to detach things from the planet and get them moving before the moon crushes them back down or knocks them sideways.

That was the impression I had. The video wasn't required to be faithful to the laws of physics, but I answer to grumpy critics who tend to say "You can do better!"