On 12/06/2023 15:40, Vir Campestris wrote:
> On 10/06/2023 18:52, Java Jive wrote:
>>
>>      Asteroid's momentum before collision:  Mab
>>      Impacter's momentum before collision:  Mib
>>      Asteroid's momentum after collision:   Maa
>>      Impacter's momentum after collision:   Mia
>>      Change in asteroid's momentum:         Delta(Ma) = Maa - Mab
>
> You have omitted the momentum of the debris.

You're way behind events here, and you've also omitted most of the
important context of the above quote ...

1) I wasn't really trying to define beta exactly at that point, more I
was pointing out problems with the definition as it was described
verbally in the paragraph that I'd previously quoted but you snipped.

2) It turned that the verbal description was inaccurate anyway, and
couldn't be used in algebra to define beta correctly. The correct
algebraic definition was given in another link, in reply I think, by Robin.

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On 12/06/2023 03:08, Java Jive wrote:
> On 11/06/2023 16:34, Robin wrote:
>>
>> On 11/06/2023 16:20, Java Jive wrote:
>>>
>>> On 11/06/2023 15:56, Robin wrote:
>>>>
>>>> You often asking for citations.  Can you please cite a published
>>>> reference to these energy-releasing explosive surface properties?
>>>
>>> It's one *you* gave:
>>>
>>> https://www.nasa.gov/feature/predicting-the-unpredictable-the-dynamics-of-dart-s-dive-into-an-asteroid
>>> "Dawn Graninger, an APL physicist, ran many simulations of DART
>>> crashing into rubble-pile asteroids with tens to hundreds of “rocks”
>>> beneath their surfaces. Whether in 2D or 3D, the collision caused
>>> those subsurface rocks to explode, erupting in a cloud of debris that
>>> burst into space."
>>>
>>> Seems a clear enough description to me, and also it fits their
>>> mathematical treatment in the other link that you gave.
>>
>> The use of "explode" there is entirely consistent with the dictionary
>> definition I gave and you snipped.  It implies nothing about
>> energy-releasing action.
>
> They use an active word 'explode', not a passive word such as
> 'disentigrate' or 'shatter'.  Perhaps you'd like to do some maths
> showing whence in your view the energy comes to obtain a beta = 5, as in
> their best case scenarios, starting with just the kinetic energy of the
> impact?
>

The masses of the Asteroid, impactor and ejecta are 1000, 1 and 20
respectively.

the impactor's speed is 10

the impactor sticks and the 20 ejecta have speed of -2.202517013
(minus 'cos it's back in the direction the impact came from

the rest of the asteroid plus impactor moves off at speed 0.055097187

total momentum before impact was
10 x 1 = 10

total momentum after impact is
0.055097187 x (1000 +1 -20) - 2.202517013 x 20 = 10

total kinetic energy before impact was
1/2 x 1 x 10x10 = 50

total kinetic energy after impact is
1/2 x (1000 +1 -20) x 0.055097187 x 0.055097187 + 1/2 x 20 x
2.202517013 x2.202517013 = 50 (to 5 sig figs)

So we have conservation of both momentum and kinetic energy.

We also have the asteroid moving off with momentum of
0.055097187 x (1000 +1 -20) = 54

So beta = 5.4

On 12/06/2023 23:33, Robin wrote:
>
> On 12/06/2023 03:08, Java Jive wrote:
>>
>> They use an active word 'explode', not a passive word such as
>> 'disentigrate' or 'shatter'.  Perhaps you'd like to do some maths
>> showing whence in your view the energy comes to obtain a beta = 5, as
>> in their best case scenarios, starting with just the kinetic energy of
>> the impact?
>
> The masses of the Asteroid, impactor and ejecta are 1000, 1 and 20
> respectively.
>
> the impactor's speed is 10
>
> the impactor sticks and the 20 ejecta have speed of -2.202517013
> (minus 'cos it's back in the direction the impact came from
>
> the rest of the asteroid plus impactor moves off at speed 0.055097187
>
> total momentum before impact was
> 10 x 1 = 10
>
> total momentum after impact is
> 0.055097187 x (1000 +1 -20) - 2.202517013 x 20 = 10
>
> total kinetic energy before impact was
> 1/2 x 1 x 10x10 = 50
>
> total kinetic energy after impact is
> 1/2  x (1000 +1 -20) x 0.055097187 x 0.055097187 + 1/2 x 20 x
> 2.202517013 x2.202517013 = 50 (to 5 sig figs)
>
> So we have conservation of both momentum and kinetic energy.
>
> We also have the asteroid moving off with momentum of
> 0.055097187 x (1000 +1 -20) = 54
>
> So beta = 5.4

Tx, but I'm not going to bother to check it, because since inviting you
to do the work above, I've noticed the animation about 3/4 down the
webpage that you linked, which unambiguously shows exploding surface
material!

--

Fake news kills!

I may be contacted via the contact address given on my website:
www.macfh.co.uk