The Naked Scientists

The Naked Scientists Forum

Author Topic: How would an explosion detonated at a cosmic distance be felt?  (Read 5749 times)

Offline Rapha

  • First timers
  • *
  • Posts: 1
    • View Profile
Raph Colella  asked the Naked Scientists:

Imagine I had a metal rod that could reach from Earth to Point X 100 light years away. If there were some gigantic explosive device at Point X (one whose destructive force was great enough to wipe out the Earth) that I activated with the metal rod, then a) would the action of activating the explosive device be instantaneous from when I twisted the rod from Earth and b) would I feel gradual destruction of the rod (weight etc) as the explosive impact travelled towards earth or would the rod still feel complete until the moment the explosion reached Earth 100 years later?

Cheers,
Raph

What do you think?


 

lyner

  • Guest
The shortest time you could take to set off the explosion would be 100 years (a radio / light link).
Poking a rod would take probably a hundred thousand times longer than that. - speed of sound / pressure through a solid.
There would be a similar delay between seeing the flash and feeling anything on the rod (not to mention the losses on the way due to internal friction in the material of the rod. Whilst the far end of the rod would definitely marmalized, there would be a point where the rod would remain unharmed - a long way from Earth.

The losses of light power due to the inverse square  law would be much less.
 

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • Posts: 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
There are some important concepts relating to the strength and rigidity of solid materials to get over here.   

We are all familiar with large bridges tall buildings and see mountains as rock solid bit it is important to remember that human beings with their structural skills are approaching the limits set by the strengths of materials and the  value of the earth's gravity. 

Beyond this limit all materials are pastic and will easily deform under the stresses and will not form rigid structures.  In space and micro gravity it may be possible to build a structure one hundred miles long but it will be quite flexible and compressible  ie it will not transmit an impulse very quickly or very well(compared with the velocity of light)  the concept of a rod much longer than this just does not exist because well before the rod was the size of our solar system it would collapse into a globe under its own gravity. That is assuming it was made well away from anything else because if it was in the solar system it would be torn apart by differential gravity forces unless it was built curved and in an orbit. 

The concept of a rigid structure 100 light years long is just ridiculous.

Planets are spherical because their self gravity forces them to be that way.

Almost everything in space of any size is gaseous or plasma or plastically deformed solids.  Only the smaller asteroids can be irregularly shaped.
« Last Edit: 31/07/2008 09:13:40 by Soul Surfer »
 

lyner

  • Guest
Quote
well before the rod was the size of our solar system it would collapse into a globe under its own gravity
I just don't believe that statement.
Ignoring the effect of a planet that it might be attached to, there is very little compressive force on the rod.
If its mass per m is k, the total force of attraction of the whole rod, due to one arm of the rod on 1m of central section would be equal to the compressive force and would be:

Integral (0.5 - ∞)(Gk2/x2) dx)
(The Gm1 m2/x2 formula applied to the rod from 0.5m away to infinity)

This gives Gk2(1/2 - 1/∞)
or 2Gk2

Which isn't much force at all ( G is tiny tiny).
My choice of 1m was arbitrary to avoid doing any double integration. It's valid enough though.

Remember, the distant bits of the rod wouldn't really know about each other.
This all assumes that the rod stays straight so it would need to be rigid enough to avoid curling up.

Building the rod from the Earth's surface would be a very different matter - the force on the bottom section would be massive, due to the Weight, caused by the nearby Earth's mass.

The reason that planets tend to form spheres is that their mass is huge, started off relatively concentrated even in the form of a dust cloud with no rigidity. After they had coalesced, the mass was concentrated enough to produce a great enough force to form a sphere. An asteroid doesn't have enough mass to overcome its rigidity. The same applies to our mythical rod.

There are lots of practical reasons for the experiment not to work but I don't think yours is one of them.
« Last Edit: 31/07/2008 15:03:03 by sophiecentaur »
 

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • Posts: 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
I must admit I did'nt do any serious calculations. I realised that the cylindrical geometry would significantly reduce the compressive forces along the length of the rod compared with a spherical condensation but I did not realise that it would integrate out to be a constant and assumed it would increase as long as the length of the rod increased and so would eventually get large enough for the material to collapse.

However I am not sure that you have analysed the geometery properly to get the compression  I think you need to start at one of the open ends of the rod where for simplicity the compressive force if the first meter is the mass of that meter and the gravity of the whole length of the rod in the other direction and the next meter is that plus the weight of the metre and the gravity of the rod less the gravity of the one metere of rod.  I think that would buid up to a much bigger value but still may not be enough to crush the material as long as the rod remained straight.
 

lyner

  • Guest
Nope. There is NO stress at all on the final section of the rod. The maximum stress must be in the centre. No force from the left - there's nothing there so, unless it actually moves, and why would it(?), the force from the right must also be zero.
My cylinder was assumed to be ' infinitely thin' but, after a few million miles, anything you could make would be near as dammit 'infinitely thin'.

If you want to prove me wrong on this, you'll have to do some visible sums. Spherical is very different from cylindrical - if it were a sphere, you'd have a black hole before you could say Schwarzschild .
 

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • Posts: 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
I now agree with your analysis. The way I did it was to consider that the rod was mass m for unit length and consider the attractive force between two rods of length n as n varied. 
The masses of the rods are mxn.
The centre of gravity of the rods are at the middle and the distance between them is therefore n so putting these into the normal gravitational equation G.m1.m2/r^2
you get  G.m.n.m.n/n^2  so the length n just cancels out. 
this avoids doing the integration.
Yet another interesting propery of the inverse square law that I have learned.
 

Offline LeeE

  • Neilep Level Member
  • ******
  • Posts: 3382
    • View Profile
    • Spatial
Ah - as cylinders have come up I thought I'd just mention this link (for fun)

http://en.wikipedia.org/wiki/Tipler_cylinder
 

lyner

  • Guest
I'm surprised that neilp isn't having one of those delivered next Tuesday.
 

Offline Rapha

  • First timers
  • *
  • Posts: 1
    • View Profile
hey guys, thanks for the discussion on this.... however, the rod isnt really what was intriguing me. the rod itself is an unrealistic proposition of course. i merely used it to suggest a scenario in which the physical laws of the universe had me confused (re the speed of light limit). so please assume one end of the rod is in my hand... and the other is already against the toggle of the explosive device. also assume it has enough strength to stay straight and flick the toggle when it is turned from earth.

Sophie... thanks for that first reply. I assumed it wouldn't be instantaneous but I still don't understand why. Obviously there most be something counter-intuitive in this sense of a 'solid' object I have. if I twist it my hand, does that mean this 'solid' rod actually curves/twists?? otherwise it WOULD toggle the switch immediately, right? hmmmm.... sorry if these questions seem inane.

lastly, i guess the answer to the above question would also answer the time it takes for the destruction of the end of the rod to be felt my me on earth.

thanks again for the effort in education a true novice :-)
 

lyner

  • Guest
How would an explosion detonated at a cosmic distance be felt?
« Reply #10 on: 04/08/2008 09:23:15 »
To transmit a force (even through a 'solid') the atoms have to push / pull against their neighbours, all along the chain. Atoms are not infinitely hard / still - they distort and, even more, the bonds between atoms / molecules can flex. All this springiness involves a delay in transmitting the force from your explosion to your hand. That is the same as saying the impulse moves through the rod at the speed of sound. (Much higher than the speed of sound in air, of course.)
« Last Edit: 04/08/2008 09:24:49 by sophiecentaur »
 

Offline syhprum

  • Neilep Level Member
  • ******
  • Posts: 3823
  • Thanked: 19 times
    • View Profile
How would an explosion detonated at a cosmic distance be felt?
« Reply #11 on: 04/08/2008 10:08:56 »
Early railway signals were operated by long metal rods actuating semaphore type signals if you live anywhere near an old line operated by enthusiasts you may well be able to see such a system in operation.
There is quite a noticeable delay between the signalman hauling the lever back and the semaphore signal rising.
 

lyner

  • Guest
How would an explosion detonated at a cosmic distance be felt?
« Reply #12 on: 04/08/2008 12:05:25 »
There would also be a lot of 'slop' in such a system, built-in to allow for expansion and also, unintentional, in each joint. The points were done that way too.
 

Offline LeeE

  • Neilep Level Member
  • ******
  • Posts: 3382
    • View Profile
    • Spatial
How would an explosion detonated at a cosmic distance be felt?
« Reply #13 on: 04/08/2008 18:32:41 »
I have a few friends who were signalmen back in the days of BR and apparently there was a real 'knack' in getting very long rod runs to work properly.  They had to sort of pump them up, getting the timing exactly right between pumps, before finally throwing the lever over.
 

Offline Bored chemist

  • Neilep Level Member
  • ******
  • Posts: 8670
  • Thanked: 42 times
    • View Profile
How would an explosion detonated at a cosmic distance be felt?
« Reply #14 on: 04/08/2008 19:13:10 »
"We are all familiar with large bridges tall buildings and see mountains as rock solid bit it is important to remember that human beings with their structural skills are approaching the limits set by the strengths of materials and the  value of the earth's gravity.  "

Some sort of contradiction there I think.
The tallest building is about 2000 feet, but we could easily make one 10 times taller by copying a mountain- plenty of them are over 20000 feet.
The problem's not the strength of materials but the other constraints we put on buildings like not being vastly wider at the base than the top, having windows etc. One of the major problems in ultra high buildings is how long people are prepared to wait for lifts.
Anyway, if you push one end of a bar suddenly eg by hitting it with a hammer, you send a compression wave running along it. That wave, if it's not absorbed, bounces back and to between the ends of the bar. The frequency with which it retuns to one end is the frequency it rings at. That gives a reasonable way of measuring the speed of sound in metals. It's generally a lot faster than in air, so an organ pipe will have a lower pitch than a glockenspiel bar of the same length.
 

lyner

  • Guest
How would an explosion detonated at a cosmic distance be felt?
« Reply #15 on: 04/08/2008 22:00:13 »
Quote
The frequency with which it retuns to one end is the frequency it rings at.

Our rod would have a pretty low resonant frequency (1/a year)!
 

Offline Bored chemist

  • Neilep Level Member
  • ******
  • Posts: 8670
  • Thanked: 42 times
    • View Profile
How would an explosion detonated at a cosmic distance be felt?
« Reply #16 on: 05/08/2008 18:41:40 »
Care for another guess?
100 light years long would give a resonant frequency of 1/100 years if the speed of the wave were c.
Since sound will be something like 100 000 times slower you are talking about 1/10,000,000 years (if I have kept track of the zero's properly). (As a pointlesss practical matter the Q would be pretty near zero anyway)
 

The Naked Scientists Forum

How would an explosion detonated at a cosmic distance be felt?
« Reply #16 on: 05/08/2008 18:41:40 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums