In sci.physics, mike3
<mike4ty4@yahoo.com>
wrote
on 8 Oct 2005 14:01:56 -0700
<1128805316.061727.79550@g47g2000cwa.googlegroups.com>:

Hi.

A question: I've heard that it takes over a week's worth of the Sun's
entire power output worth of heat to explode a planet like the Earth,
because you have to overcome the gravity holding it together.

Now, exactly how hot would the planet get, if you could get this much
energy and cram it in?

Assume some rabid loony al Qaeda member has planted a
nice big bomb in the center of the Earth. (Never mind
the technical issues, this is a thought experiment. :-))

Or, if one prefers, assume that Darth Vader's Death Star
is sitting in orbit near Earth and wants to blow us up
for some unfathomable reason (Galactic rebellion? *What*
rebellion?). Or maybe the Klingons or ... well, never mind.

How much energy at a minimum would be required to blow
each and every particle of the Earth into escape velocity,
assuming a nice, symmetrical explosion and ignoring the
usual things such as air density and rotational effects?

As an extremely crude first approximation, we could
Mcelwainize [*] the Earth, pushing all of the mass into a
hollow shell where all of the mass is uniformly distributed
on the surface. One then picks a dA and flings it into
orbit; because we're assuming a uniform Earth, and since
the requisite velocity to do so is v = sqrt(2gr) with r =
6.378*10^6m and g = 9.805 N/kg, one gets E = 1/2 m (2gr),
where m = 5.976*10^24 kg, and therefore E = 3.737*10^32 J.

The Sun's power output is 3.94 * 10^26 W. Ergo, the amount of
energy required would be 948520 seconds' worth, or about 11 days,
at a minimum.

A better approximation might be had by explicitly lifting
the bit to the surface, then flinging it into orbit.
Assuming a homogenous Earth, the force on something within
its interior is directly proportional to the distance from
its interior (as opposed to inversly proportional to the
square of the distance, in massless space). This might
increase the required energy by a factor of 2 at most, but
I'll leave the details to the interested reader.

(Note that the rocks from such an explosion will be flying a
few km/sec towards, say, the Millennium Falcon. I hope
Han Solo and Chewie know how to duck. :-) )

As for temperature...an interesting question, that. If one
assumes 800 J/(Kg K) for rock, one gets a temperature difference
of 78,000 K -- which introduces some major thermodynamic issues
if one directly uses the Sun as a power source, since the Sun is
only about 5800K.

[*] A legendary net.kook. The idea of a hollow Earth, however, did
not originate with him, but I'd have to look at this point.

--
#191,

mike3 wrote:

Hi.

A question: I've heard that it takes over a week's worth of the Sun's
entire power output worth of heat to explode a planet like the Earth,
because you have to overcome the gravity holding it together.

Now, exactly how hot would the planet get, if you could get this much
energy and cram it in?

It would not change temp at all. It would disaggregate to infinity.
If it warmed it would stay gravitationally bound.

If you pull something strange out of your ***** for public discussion,
at least exercise the minimum competence to provide a citation. That
allows onlookers to determine if you are stupid, or your source is
stupid, or both are stupid, or if you have something interesting to
share.

Uncle Al always gotta lift the heavy end,

<http://www.aeiveos.com/~bradbury/MatrioshkaBrains/PlntDssmbly.html>

The value for Earth is too small because it assumes a homogeneous mass
distribution. Earth has an iron core the size of Mars. Given that,
the proposed number should be 12% larger. Note the tablulated numbers
are for for solar cell effciency, not the solar constant.