Nuclear explosion size required to create a Shattered Horzion scenario

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SUMMARY

The discussion centers on the hypothetical scenario of a nuclear explosion required to create a Shattered Horizon-like event, where a significant portion of the Moon is fractured and sent into orbit around Earth. It is estimated that an underground nuclear explosion would need to displace approximately 5% of the Moon's mass, roughly 1021 kg, at an escape velocity of 2.4 km/s. This translates to a kinetic energy release of about 1027 Joules, equating to approximately 1012 megatons of TNT. The calculation's accuracy is acknowledged to have a potential error of several orders of magnitude.

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Cifyra
I'm not sure if any of you have heard about the game, Shattered Horizon. It's story takes place in 2047 when the Moon Mining Corporation accidentally fractured a large chunk of the moon and sent fragments and debris in orbit around Earth. International Space Agency workers and MMC miners are now stranded in space, as they fight over scarce resources to survive. How big of an underground nuclear explosion is require to "break" the moon as illustrated in the following video?

 
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Suppose 5% of the moons mass is now moving away from the moon at its escape velocity (2.4km/s according to wikipedia). That 5% has a mass of, very roughly, 10^21 kg. So the kinetic energy of that mass is of order 10^27 Joules. That is, very roughly, 10^12 megatons. The error on this calculation is probably plus/minus several orders of magnitude.
 

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