If a solid, brittle object were near the 2015 black hole merger would it shatter?

[repoman]

Just a random question I have. Also, how close would it have to be if so? This is assuming the object was in the plane of maximum intensity.

Also a cool article:

https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf

 

[steve_bank]

Not an expert but imagine a long rod being pulled in with a vertical orientation. As it gets pulled in there should be a growing difference or gradient of gravity across the rod.

We expeince it but it is very small.

 

[bilby]

Just a random question I have. Also, how close would it have to be if so? This is assuming the object was in the plane of maximum intensity.

Also a cool article:

https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf

You don't need gravitational waves to achieve that effect. The tides sufficiently close to a sufficiently small black hole would be more than sufficient to shatter a brittle object, such as a rocky planetoid.

 

[repoman]

Just a random question I have. Also, how close would it have to be if so? This is assuming the object was in the plane of maximum intensity.

Also a cool article:

https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf

You don't need gravitational waves to achieve that effect. The tides sufficiently close to a sufficiently small black hole would be more than sufficient to shatter a brittle object, such as a rocky planetoid.

You mean related to the Roche Limit?

Yes, but I mean non Roche related fracturing.

 

[bilby]

Just a random question I have. Also, how close would it have to be if so? This is assuming the object was in the plane of maximum intensity.

Also a cool article:

https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf

You don't need gravitational waves to achieve that effect. The tides sufficiently close to a sufficiently small black hole would be more than sufficient to shatter a brittle object, such as a rocky planetoid.

You mean related to the Roche Limit?

Yes, but I mean non Roche related fracturing.

Well any force that varies with distance will cause tidal effects, so your question becomes 'are these large enough in the case of gravitational waves caused by merging black holes', and the answer is 'possibly, but it depends on the actual strength and shape of the object and on the force gradients it experiences' - there are too many variables to give a more specific answer than 'maybe'.

How long is a piece of string?

If you are writing science fiction and use this as a plot device, you are probably not going to get too much hate mail telling you that it couldn't possibly happen.

 

[steve_bank]

What do you mean by close to a BH? I can not do it off the top of my head. On a 1 meter rod what is the differential force versus r? The force would place the rod in tension, stretching.

It would be dF/dr at a radius of r where F is force in Newtons and r radius in meters. The rod has a mass dm the incremental mass at a point on the rod in kg. Force = m * a where a is the gravitational acieration at a distance r.

When t a dr of 1 meter F > the bonding force or energy of the material's atomic structure the material comes apart.

Learn something new everyday.

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


In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche (pronounced [ʁɔʃ] (French), /rɔːʃ/ rawsh (English)), who was the French astronomer who first calculated this theoretical limit in 1848

 

[bilby]

Learn something new everyday.

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


In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche (pronounced [ʁɔʃ] (French), /rɔːʃ/ rawsh (English)), who was the French astronomer who first calculated this theoretical limit in 1848

Perhaps today's lesson could be 'nobody wants or needs posts that are mostly cut-and-paste from Wikipedia'?

 

[lpetrich]

One can crudely estimate how much force a g-wave makes with some rather hand-waving arguments.

First, it is a sort of tidal force, a force of one object relative to another that increases with increasing distance:

(Force) = (force per unit distance) * (distance)

Since gravitational force is proportional to mass (the equivalence principle), we have

(Force) = (acceleration per unit distance) * (mass) * (distance)

The acceleration per unit distance for G-waves is roughly (space-time distortion) * (angular frequency)^2

where (angular frequency) = 2*pi*(linear frequency)

 First observation of gravitational waves has the details. I'll assume a space-time distortion of around 1. The maximum G-wave frequency was 250 Hz, giving an angular frequency of 1.5 kiloradians/second. So the force on a 1-kg object is about 10^6 newtons/meter. Since a water-density object will have size 1 decimeter, its surface area is 10^(-2) square meters, though the force across it will be 10^5 newtons. That gives a stress of 10^7 newtons/m^2 = 10^7 pascal = 10 megapascals. Consulting  Yield (engineering), that is well below the yield strengths of common metals, but only a bit below the yeild strengths of some common plastics.

Extending to a size of 1 meter, the G-wave pressure increases to 100 MPa, and that is enough to break some common plastics, and it is at the yield strengths of some of the softer metals. Going up to 10 meters, this gives 1000 Mpa, and only some superstrong metals and organic polymers (Kevlar, spider silk, carbon fiber) can resist it.

 

[steve_bank]

Off the top of my head as an approximation to illustrate the problem I looked at it assuming Newtonian gravity. mass object <<< mass BH.

F = m(r) * a(r)

Take the derivative of Force with respect to radius. What would complicate it is as the rod stretches m(r) would not be linear with r. That would take some work to figure out for me, not so much for a materials engineer.

Density is mass/unit volume. For a square bar mass = density * volume = density * l*w*dr.

g = G*[m/(r - h)^2] where G is the gravitational constant and h height above surface.

https://planetcalc.com/1758/

https://en.wikipedia.org/wiki/Black_hole#Physical_properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.[24] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[66] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[67]

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And so endeth todays lesson in developing a first order model from basic principles and Calculus 101. One starts with an expression at a first order that can be managed and understood. Then add other effects. It is called the incremental method.

 

[skepticalbip]

If a solid, brittle object were near the 2015 black hole merger would it shatter?

Is this a concern for your beer bottle breaking while you are getting trying to get close enough for a good look at that BH? I certainly understand that loosing a bottle of bear is a bitch.

 

[repoman]

If a solid, brittle object were near the 2015 black hole merger would it shatter?

Is this a concern for your beer bottle breaking while you are getting trying to get close enough for a good look at that BH? I certainly understand that loosing a bottle of bear is a bitch.

From what lpetrich says, it seems like the spaceship hull will break first.

 

[steve_bank]

There is no known shield for gravity. Ship and occupants experience the same gravity,

I'd say your body gets pulled apart before the ship.