Asteroid hits moon → moon hits Earth possible?

Blue_Jaunte

I had a vivid nightmare the other night where I went outside in broad daylight and saw that the moon was not only visible but also enormous. I saw people running around in a state of panic and asked one of them what was going on. He told me a large asteroid had struck the moon on the side opposite the one we see and now the moon was going to crash into Earth. I could hear a distant radio well enough to make out an announcer say "...it's a matter of hours now, not days". Understandably, I was a bit shaken when I woke up.

So is such a scenario even possible? Could an asteroid collision with the moon send it out of orbit and careening into us? Would such a collision be a global-killer?

Thanks

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D H

Staff Emeritus
An asteroid hitting the moon opposite the Earth will add energy to the Moon's orbit. Such an asteroid would make the Moon's orbit a bit more eccentric and would make the Moon's average distance from the Earth increase. To make the Moon plummet toward the Earth, the asteroid will have to hit the Moon so that it exactly cancels the Moon's orbital velocity. Such a collision would be visible on the limb of the Moon. It would still take days for the Moon to plummet to the Earth.

You can rest easy as the asteroid would have to have momentum equal to that of the Moon's orbital momentum. Since the Moon is many orders of magnitude more massive than the largest near-Earth object, the asteroid would have to have a relative velocity many orders of magnitude larger than the Moon's orbital velocity. Such an asteroid would escape the solar system.

So what about some maurauder from outside the solar system? We would see it coming. If it were big enough we would not be able to do a thing about it. Such is the stuff of multiple science fiction stories ...

Chris Hillman

Of course, if an asteroid or meteor strikes the Moon, it might well happen that a small piece of the Moon might be ejected and eventually happen to strike the Earth. Similarly for Mars (indeed, certain rare meteorites are thought to have originated in just this fashion.)

But if you want to have more realistic nightmares, dream about something like the next global pandemic. Or dying of thirst. Or the economy crashing. Or a combination. That chances of a major asteroid strike occuring in your lifetime are extremely remote.

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Astronuc

Staff Emeritus
Geez - I saw "Asteroid hits moon " and thought - wow what an event. Then when the thread opened, I saw that it was a hypothetical.

D H said:
It would still take days for the Moon to plummet to the Earth.
That would make an interesting calculation. Take the moon and Earth released from rest at their nominal distance and determine how long it would take for them to come together. Acceleration is not constant.

The consequences of an asteroid/Moon collision of course depend on the size of the asteroid. It would certainly make a crater, which is how the craters got made way back when. The would be some ejecta coming out of the impact area.

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tony873004

Gold Member
That would make an interesting calculation. Take the moon and Earth released from rest at their nominal distance and determine how long it would take for them to come together. Acceleration is not constant.
5 days 6 hours 6 minutes from apogee
4 days 19 hours 19 minutes from the Moon's average distance
4 days 7 hours 44 minutes from perigee

This assumes an initial velocity of 0. Of course, the asteroid could knock the Moon towards or away as well yielding an initial radial velocity other than 0.

D H

Staff Emeritus
That would make an interesting calculation. Take the moon and Earth released from rest at their nominal distance and determine how long it would take for them to come together. Acceleration is not constant.
I wrote a simple velocity verlet integrator in Excel. Nothing much of interest happens for the first day. After one day, the Earth-Moon separation drops by a mere 2.6% and the relative velocity reaches 0.24 km/sec. It takes 3.3 days for the velocity to climb to 1 km/sec, at which time the Earth-Moon separation has dropped by nearly a third. Things get interesting on the final day. After 4.8 days or so, the Earth and Moon finally collide with an impact velocity of about 9 kilometers per second.

cpalms

The force it would take an asteroid to do something like that is mind boggling.Bordering on impossible.Plus the affect the moon coming closer to the earth would have would be devastating without it crashing into it.The immense gravity change would probably cause flooding throughout the planet.You would think right?

Michael Mozina

No known or identified asteroid could do that. As DH pointed out, any asteroid traveling at that kind of speed would be moving too fast to be trapped by the gravitational influence of our sun. It would have to come from outside of the solar system, and it would have to be traveling at many orders of magnitude faster than anything inside our solar system.

Michael Mozina

I wrote a simple velocity verlet integrator in Excel. Nothing much of interest happens for the first day. After one day, the Earth-Moon separation drops by a mere 2.6% and the relative velocity reaches 0.24 km/sec. It takes 3.3 days for the velocity to climb to 1 km/sec, at which time the Earth-Moon separation has dropped by nearly a third. Things get interesting on the final day. After 4.8 days or so, the Earth and Moon finally collide with an impact velocity of about 9 kilometers per second.
Just out of curiosity, how did you calculate the time it would take to impact?

D H

Staff Emeritus
Just out of curiosity, how did you calculate the time it would take to impact?
I used numerical integration techniques, specifically a velocity Verlet integrator.

Herein I place an upper bound on the time. For simplicity, assume the initial lunar orbit is circular with an orbital radius of $a$ and period $T$. Now suppose the Earth and Moon are point masses rather than solid masses. I don't have to worry about the actual collision with this assumption. If all but a tiny fraction of the Moon's initial tangential velocity is canceled at some point in its original circular orbit, the point mass Moon and Earth will now orbit each other in a highly elliptical orbit with some semi-major axis $a_e$. By Kepler's third law, the period of this new orbit will be $T_e = T\;(a_e/a)^{3/2}$. The time from apogee to perigee is half the orbital period. If a collision between the real Earth and real Moon occurs, it will be sometime before this half period interval: $T_c < T_e/2 = 1/2\;(a_e/a)^{3/2}\;T$.

In the limit that the tangential velocity becomes zero, the semi-major axis of this new orbit is simply half the semi-major axis of the original orbit. Thus

$$T_c < \left(\frac1 2\right)^{5/2} T$$

Since the moon's orbital period is 27.32 days, the collision will occur in less than 4.83 days. Note that this agrees with the result obtained by numerical integration. The upper bound is very close to the collision time as the Moon's velocity is awfully high at the time of collision and would grow even higher if only the Moon and Earth were point masses.

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BrainTeaser48

Consider changing the direction of a rolling bowling ball. In order to change its direction significantly you would need to match its momentum with an object of similar momentum. A BB would need to travel well above the speed of a bullet to have an effect, but another bowling ball needs only be in its way. The Moon would need a massive body to change its orbit significantly enough to approach the Earth. Such an event would destroy the moon. Any planetary body has the consistancy of a creampuff with respect to such colisions. Also, the trajectory is the only change that would occur unless the moon is slowed down in its orbit since the angular momentum would continue to carry most debris of such an event in its original orbit.

Michael Mozina

I used numerical integration techniques, specifically a velocity Verlet integrator.
Thanks for that explanation. I appreciate it.

cesiumfrog

Another way to approach this nightmare: Such an asteroid would have to not only have great momentum, but would need to strike at a very specific angle.

But if the same asteroid hit the earth, it would wipe us out no matter what the angle was. And the earth is a much bigger target. And even a comparatively much smaller (and slower) asteroid would still be enough to do this.

So rest assured that it is far more likely that civilisation will end due to a direct impact (with little warning at all since, realistically, it just isn't easy to spot an asteroids at long distances) rather than by some improbable trick-shot that gives you the luxury of watching the moon grow for some number of minutes.

andrewj

collision

Of course, if an asteroid or meteor strikes the Moon, it might well happen that a small piece of the Moon might be ejected and eventually happen to strike the Earth. Similarly for Mars (indeed, certain rare meteorites are thought to have originated in just this fashion.)

But if you want to have more realistic nightmares, dream about something like the next global pandemic. Or dying of thirst. Or the economy crashing. Or a combination. That chances of a major asteroid strike occuring in your lifetime are extremely remote.
yes dying of thirst is bad news but it was just a thought a possible aesteroid moon collision

Count Iblis

The Moon could also make a spontaneous quantum jump to a lower orbit.

DaveC426913

Gold Member
Man, what would the energy of that released photon be?

pervect

Staff Emeritus
I'm a bit dubious about the possibility of such a thing happening. It corresponds to a forbidden quantum transition. It definitely couldn't happen with a single photon if you want to conserve energy and angular momentum, but some sort of multi-photon process might make it possible - I'm not really positive it's possible even so, but I'm not positive it's impossible, either.

Count Iblis

Many gravitons, not photons, must be emitted. Classically, a system of two rotating bodies will emit continuous gravitational radiation. If you look at it more precisely (i.e. quantum mechanically), you see that the system makes jumps to lower energy states emitting gravitons. Selection rules apply to matrix elements <a|H|b> where H is the effective Hamiltonian of the gravitatonal field in second quantization. But to higher order in peturbation theory the amplitude for the transition probability contains terms

<a|H|b1><b1|H|b2>...<bk|H|b>

corresponding to emission of many gravitons....

JustVisiting

Has anyone examined the concept of diverting a near-Earth asteroid towards the Moon? Would such an effort alter the orbital path of the Moon? It would seem to be easier to do, since the gravitational pull from the Moon would assist at some point.

russ_watters

Mentor
Welcome to PF.
Has anyone examined the concept of diverting a near-Earth asteroid towards the Moon?
Except as you just did, with a speculative hypothetical, no.
Would such an effort alter the orbital path of the Moon?
Certainly. But how much? Answer: not enough to matter. Consider that all those craters we see on the moon were caused by near-earth asteroids hitting it. And since the far side isn't shielded by earth, it looks even worse!

Researcher X

I wonder how fast Ceres would have to go to do it (being the largest asteroid/planetoid available), not that it would ever do so (mad scientist?)...

I looked this up, and amusingly, the momentum of ceres even at a blistering nonsensical speed of Mach 1000 (about the speed of solar wind) is less than the moon's orbital angular momentum by a factor of 10 billion, despite having 3.4 times the kinetic energy needed to scatter the moon permanently (approx 4.053e29 joules).

So, really, even if the conditions were right, it looks like the moon would be destroyed by an impact long before it was harsh enough to perturb its orbit significantly. Doesn't make sense to me.

Chronos

Gold Member
That would be a whopper of an asteroid, much larger than any known asteroid in our solar system. A smaller asteroid would need to travel very fast to knock the moon out of orbit. So fast that it would blast chunks out of the moon, which would pretty much spoil the whole effect.

Staff Emeritus
I looked this up, and amusingly, the momentum of ceres even at a blistering nonsensical speed of Mach 1000 (about the speed of solar wind) is less than the moon's orbital angular momentum by a factor of 10 billion, despite having 3.4 times the kinetic energy needed to scatter the moon permanently (approx 4.053e29 joules).
You can't compare linear and angular momentum. They have different units.

Ceres weighs about 1.2% of what the moon does. It will be difficult to make a comparison where there is a factor 10 billion difference between them.

D H

Staff Emeritus
In fact, Ceres hitting the Moon head-on at 80 km/s (Mach 230) (Earth-relative velocity) will do the trick. What would give Ceres a velocity of 80 km/s is of course a different trick.

Count Iblis

In fact, Ceres hitting the Moon head-on at 80 km/s (Mach 230) (Earth-relative velocity) will do the trick. What would give Ceres a velocity of 80 km/s is of course a different trick.
There can be a Ceres sized asteroid kicked out from another solar system that would enter our solar system. It could have the required velocity, because an object arriving from rest at infinity can already have a maximum relative velocity w.r.t. Earth of 72 km/s.

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