Spinning an Asteroid to Death

A lot depends on the physical integrity of the asteroid.

A loose aggregation of assorted particles, held by self gravity, might not provide a surface to which torque or other forces can be applied to spin it fast enough to scatter ot or to apply a force vector to change it's destination so it misses the target.

Some seem to be a tight aggregation, others not so much. Loose aggregations migth lend themselve to explosive scattering? A lot more data is needed.

Fair enough, let's take Bennu as an example then....

101955 Bennu has a mean diameter of approximately 492 m (1,614 ft; 0.306 mi)

is a carbonaceous asteroid

There is a well-defined ridge along the equator of Bennu. The presence of this ridge suggests that fine-grained regolith particles have accumulated in this area, possibly because of its low gravity and fast rotation.^[13]Observations by the OSIRIS-Rex spacecraft has shown that Bennu is rotating faster over time.^[21] This change in Bennu's rotation is caused by the Yarkovsky-O'Keefe-Radzievskii-Paddack effect, or the YORP effect.^[21] Due to the uneven emission of thermal radiation from its surface as Bennu rotates in sunlight, the rotation period of Bennu decreases by about one second every 100 years.^[21]

Astrometric observations between 1999 and 2013 have demonstrated that 101955 Bennu is influenced by the Yarkovsky effect, causing the semimajor axis to drift on average by 284±1.5 meters/year. Analysis of the gravitational and thermal effects has given a bulk density of ρ = 1260±70 kg/m³, which is only slightly denser than water. Therefore, the predicted macroporosity is 40±10%, suggesting the interior has a rubble pile structure. The estimated mass is (7.8±0.9)×10¹⁰ kg.^[6]

^{https://en.wikipedia.org/wiki/101955_Bennu}

Well, Bennu is a good candidate for a bomb in a centered hole to scatter it, but not good to 'lassoo' it

Agreed. If its a rubble pile, that's good news. It's much easier to scatter pieces in all directions than to move the entire mass in one direction.

A sphere has gravitational energy:

https://en.wikipedia.org/wiki/Gravitational_binding_energy

For Bennu, R = 246m and M = 7.8 * 10¹⁰ kg,

Plugging in the radius and mass of Bennu the gravitational energy is: 990 MJ

The NASA HAMMER spacecraft with a mass of 8000 Kg and a collision speed of 10 km/sec would have an energy E = .5 mv² = 400000 MJ, far in excess of the amount of energy needed to disperse the rubble pile, even if a small fraction of the kinetic energy is employed for the task.

https://www.extremetech.com/extreme/265350-nasa-designs-hammer-spacecraft-deflect-nuke-dangerous-asteroids

Dispersing the rubble pile would only overcome the very weak gravitational binding energy and the swarm of debris would continue in its solar orbit, but the majority of pieces hopefully would miss the Earth.

The density would seem to be very important, if desired results are to be realized...The density and size of both the projectile and the target....

The energy of the projectile must be completely transferred to the target....So the relationship between the densities and size of each must be included in the formula...I wonder if such a calculator exists...?

This shows how people get misled when they extrapolate what asteroids are by looking at what a meteorite is here on Earth. The very solid and dense material of iron/nickel and chondrite meteorites are what's left after rapid deceleration in our atmosphere and impact with the ground. Certainly, some of the asteroids are individual hunks of dense material. But it has long been conjectured that many asteroids are just locally aggregated groups of various density level pieces of gravel that may or may not have a nucleus of very dense material. The Hubbel telescope has found one of these gravel asteroids. Unless the spinning motion imparts enough kinetic energy onto a part of the group to achieve escape velocity from the rest these separated particles will just slow regroup with the rest.

One of the theoretical mechanism to make a bolide is during the high heat of atmospheric entry the gravel cloud fuses together to make a solid outer skin. The internal pressure behind this skin quickly climbs to an explosive eruption.

..." achieve escape velocity from the rest these separated particles will just slow regroup with the rest."...

I don't think this would happen in a relevant time period, if at all....

https://www.smithsonianmag.com/science-nature/space-garbage-the-dark-cloud-above-80279582/

Which would you wanna be 'hit' by? A large single 45-caliber bullet, or 4,500 individual jagged-edged buck-shot pellets?

Spinning a "rocky-composition' rockpile apart is OK with loosely held rocks, pebbles and sand/dust.

Spinning a "metallic" core body is only gonna impove it's "aiming" point (ala' rifling).

One large object is more likely to reach the ground....the smaller particles, if they're spread out, will likely burn up in the atmosphere...

You would certainly want the apin axis to point somewhere near Earth so that you aren't at risk of higher velocity pieces coming off towards Earth.

It makes me wonder if the right spin could be introduced such that a sizeable asteroid might be made to skip off the atmoaphete instead of dig in and strike the ground.

I'm thinking rifling would not make any difference in the vacuum of outer space. It only serves to keep the orientation of a bullet "pointy end forward" so that drag forces on the bullet are not unbalanced as they would be if the bullet were tumbling.

I agree...an asteroid can actually be steered by the orientation and direction of its axis rotation...

..."Bennu makes one orbit around the Sun every 1.2 years. It makes one full rotation on its axis every 4.3 hours. Bennu makes a close approach to Earth every six years, although its exact distance from Earth during these approaches varies. Its orbital path is tilted about 5 degrees relative to Earth’s.

The asteroid’s equator is tilted by about 175 degrees, such as that its north pole is pointing “down” relative to Earth’s north pole."...

..."Bennu’s average orbital distance from the Sun is about 105 million miles (168 million kilometers), which is only slightly farther than Earth’s average orbital distance of 93 million miles.​"...

Hopefully, we're not depending on radiation pressure (Yarkovsky effect) to steer this thing!

As to your original question, can an asteroid be spun to death, it should be possible if there were a means to spin it up to the critical rotation rate. The critical rate is only proportional to the density and not on the size of the body (rubble pile body) for the following reason.

1. Surface gravity is proportional to radius x density:

The surface gravity F(ρ) ~ m / r² ~ (ρ r³) / r² ~ ρ x r

2. Centrifugal force is proportional to rotation rate times radius. F(ω) = ω x r

So at a critical rotation rate proportional to the density, the surface gravity will equal the centrifugal force, F(ρ) = F(ω), regardless of the radius, r, and the rubble pile should disintegrate. This rate is approximately 1 rotation every 2.2 hours for typical density.

The data supports this:

" Population studies, specifically those that observed brightness variations over time to derive rotation rates (known as “lightcurves”), found a lack of very rapidly rotating bodies (Burns 1975; Pravec et al. 2000,2002). The critical spin limit, which no sizable (larger than ~200m) asteroid exceeded, was ~2.2 hours (see Figure 2). This is similar to the rotation rate at which free particles could leave the surface of a spinning body of density similar to most meteorites. The absence of bodies with rotation rates faster than the observed limits argues that their internal structures do not allow it, but does not mandate it. This useful and highly suggestive dataset, with spin and shape as a combined constraint will be referred to later as a tool to estimate allowable shape and spin configurations relating to granular flow properties of known materials and to constrain their internal structures. "

https://arxiv.org/ftp/arxiv/papers/1810/1810.01815.pdf

So theoretically we could mount a trio of co2 or solid fuel thrusters on either north or south pole of the axis and accelerate the rotation, and cause the destruction, at least in part, of Bennu....

from the looks of it, there is no 'mounting point'

I'm thinking that getting a grip on a rubble pile might be problematic. It would be like trying to push a pile of sand, and once it was spinning faster, it would get looser and looser. The most straightforward way to destroy the asteroid would be to release a lot of energy from inside it, i.e., a buried bomb.

The gravitational energy, U, for a sphere of mass M and radius R is:

For Bennu, R = 246m and M = 7.8 * 10¹⁰ kg,

U = 990386165 kg m² /sec² = 990 MJ, equivalent to about 500 lb of TNT, about the same as non-nuclear bunker buster bombs. Of course, this is the minimum with 100% efficiency, your mileage may vary. You would definitely want some overkill.

Yes I understand it might not be the best way, but it could be done....You could strap the thruster assembly onto the asteroid maybe...or perhaps shoot harpoons into the beast creating mounting points...

Not even Ahab would use a whale harpoon to catch a school of sardines.

236 days at sea.....the White Devil is spotted!

If you can figure out how to get a grip on it, here is the good news. It's already rotating at once every 4.3 hours, which accounts for its weird shape. That's half as fast as it needs to go to start coming apart (once in 2.2 hours).

https://www.asteroidmission.org/wotw-rotation-period-3/

The moment of inertia of a sphere is I = (2/5) m r²

https://en.wikipedia.org/wiki/List_of_moments_of_inertia

For Bennu, r = 246m and m = 7.8 * 10¹⁰ kg,

I = 1888099200000000 kg m²

ω1 = 2π / (4.3 * 3600) = 0.00040589 sec^-1 Current rotation speed

ω2 = 2π / (2.2 * 3600) = 0.00079333 sec^-1 Disintegration rotation speed.

If we mount booster rockets at the equator with a total thrust F for time t, we can calculate the total impulse (Impulse = thrust x time) necessary to accelerate the asteroid spin from ω1 to ω2.

Impulse = ( (ω2 - ω1) x I) / r = 2.97 x 10⁹ newton seconds or 6.685 x 10⁸ pound seconds

To put things into perspective, one of the SRBs for the space shuttle generates about

1300 MN s, almost half of what is needed to spin up the asteroid.

http://www.braeunig.us/space/specs/shuttle.htm

As a practical matter, to minimize the force on each thruster mount, you would want to maximize the number of thrusters and the amount of time thrust is applied.

It's pretty big....

Q: "How Tall is Asteroid Bennu?"

A: Big enough to ruin your day.

Apparently asteroids are alive and some of them are tall and on'ry.

....they do have a striking appearance.

On the subject ...I have no problem trying any reasonable method on asteroids that may strike in 10 or 90 years.

Go after a long shot twice a year or whatever. Set the trajectory in deep space and come what may.

If we don't start practicing various methods on distant objects we will never have the technology or Knowledge to pursue an immediate threat.

The upside is we may be able to prevent future catastrophe and sweep the area for future generations.

I'm certainly not for spending of umpteen millions on so called preparedness that has never been tested in a variety of ways.

The cool factor would be off the charts as well.

TRANSLATION -- Any "anti-Armageddon" devices need to be tested/demonstrated/perfected BEFORE they're needed.

There are some problems with this kind of testing. Getting to an asteroid that's not near Earth will mean a long time to complete a test to change the asteroid path and/or its composition. Getting to a non-impacting near-Earth asteroid can take less time but at the risk of making some or all of the asteroid to impact Earth.

We are also in the early stages of asteroid exploration. We don't know what type of asteroid compositions are typical or even which asteroids we can deflect at all.

Sorry.. I didn't elaborate.

I'm thinking of the repeat offenders. The ones that pass by every so many years and are noted as being potential problems in the future.

Plan to have the equipment intercept during a near miss event and blow the sucker to bits when it's reached and outbound trajectory.

I remember reading a recent scientific analysis using computer simulation performed on "blowing up" an asteroid just like the two movies from 21 years ago. (I cannot find the paper now or I would post a link.) The basics were that unless the explosive provided enough energy for most of the individual fragments to reach the escape velocity (of the whole rubble pile asteroid) that eventually the parts would just coalesce back into a rubble pile asteroid. Since the few known nearby offenders usually can take a decade if not much more to return for a possible intersection the pieces usually have time to reform.

That doesn't seem to be very demanding, I mean what would escape velocity be 5 mph? If the asteroid has weak gravity to begin with, after it's scattered it won't have any at all....I remember Allan Shepard hit a golf ball on the Moon once, and I believe it traveled over 2 miles....The Moon by comparison is nearly 2200 miles in diameter....

Now something like Lutetia at roughly 100 km diameter, might be another story...

Bennu is too small to even show up on this comparison....

Just don't appear to be loose piles of rubble. I suppose looks could be deceiving.

Does anyone have any good data on how many of these are mostly composed of small rubble and how many are mostly composed of a few large solid pieces that individually won't be broken down by moderate spin rates?

Hayabusa2 shoots asteroid Ryugu supposedly creating a nearly 10 meter crater, this should give some data on the debris behavior....

https://gizmodo.com/hayabusa2-spacecraft-blasts-artificial-crater-in-astero-1833825034

Ryugu is about 1km diameter, or about twice the size of Bennu....

Explosive testing for Hayabusa2 crater creator...a small disc of HMX high-explosive...

https://www.npr.org/2019/04/05/710285475/japan-very-carefully-drops-plastic-explosives-onto-an-asteroid

Yeah but having enough energy to accelerate any or even most of the rubble pile to escape velocity in some direction is not the difficulty. Achieving escape velocity in the vector directly away from the original center of mass is the only thing that will prevent the ruble pieces from reforming. I doubt Alan Shepard achieved a velocity of even 2 km/sec in any direction let alone the 3.36 km/sec required for escape velocity with the ball at a perfect 45° angle above the surface of the moon.

So a bomb detonated next to a rubble pile in zero-G will scatter any organization they originally had but eventually, most of them will recollect in a different pattern.

Let us say we analyze the explosive type needed! It must be more or less centrally located and can not be a 'high explosive'. By that I mean an explosive of a high explosion wave front propagation, aka Brisance. https://en.wikipedia.org/wiki/Brisance

We do not want to blow a small hole in the center - we need a sustained central low velocity thrust, which the so called fuel-air or oxygen explosive would provide,. We would use oxygen and fuel https://en.wikipedia.org/wiki/Thermobaric_weapon

Such a blast would provide an outward streaming flow of combustion gasses from a central area, and the size, density etc of the particles would determine how they responded to the explosion - if I can call it that. This explosion would be designed to provide a low thrust of a large volume of combustion gasses expanding towards infinity. You can even insert a ballon, inflate it with the mixture and create a cavity inside the mass - if there are no sharp items to make it leak. Once inflated it can be set off to see what it does. The assembled rubble will act like water in a fluidized bed (quick sand) abd with the correct corrections for reynolds numbers etc, they could probably model one of these explosions in a computer. It may be that a succession of bangs would be better able to deal with such an asteroidal aggregation. In any event, I suspect that we should start on solving this at the theoretical level ASAP, in case we need it soone or later.

Getting to the center of a distant rubble pile in space will be easier said than done.

A little pressure on a taperd long shaft will gradually work in the direction thust as the pieces migrate around it, once at the center a ballon with one gas can be inflated, followed by gas 2, allow diffusion mixing and set it off

Whether the material ejected from the rubble pile will reassemble depends on the direction it is ejected. I wrote a Matlab script to trace the orbit of a piece of the asteroid ejected in different directions and plotted the distance from the asteroid for two year's time. The ejection speed is 1% of the orbital velocity and the four directions plotted are toward and away from the sun and parallel to the orbit, forward and backward.

If it is ejected either directly toward the sun or away from the sun, it will trace a small circle and return close to the same place. If it is ejected either in the forward direction or backward direction, it traces a spiral outward.

The size of the spiral is much larger than the small circle, so almost any direction material is ejected would have a much larger spiral component than a circle component. Most material ejected most likely would not return.

With your simulation having an initial velocity of 670 MPH, what is the escape velocity of the simulation?

The escape velocity from the surface of Bennu is about 0.7 kph or 0.5 mph max. It's not considered significant for the simulation, which was only intended to determine whether ejected pieces were likely to regroup.

https://solarsystem.nasa.gov/asteroids-comets-and-meteors/asteroids/101955-bennu/by-the-numbers/