◄ WORLD V · SONNY 5DART 561 · a helldive down the well

THE GRAVITATIONAL BINDING ENERGY the cost to pull a world apart

How much energy would it take to disassemble a planet, hauling every piece out to infinity against its own gravity? For a uniform sphere, U = −3GM²/5R — negative, because the assembled world sits in a well it dug itself. It is why big things are round, why stars fight collapse, and (in reverse) the energy a supernova must beat to blow a star apart.

THE TECHNIQUE U = −3GM² / 5R

The demo computes the coefficient and sign of U = −3GM²/5R (unit values): live demo







  
HISTORY & CREDIT uniform-sphere integral

  
“Binding energy is positive energy stored inside.” — it is negative: you must ADD |U| to unbind the body; the assembled state is lower. cited

  
the shells · integrate the work to bring each spherical shell from infinity.
the result · U = −3GM²/5R for uniform density.
why round · a body minimizes U by becoming a sphere — hydrostatic equilibrium.

  
The debt a world owes its own gravity. physics






  
RECOMMEND FOR I-13 the sign, on the compiler

  
On i-13 (unit G, M=6, R=2), U = −10.8, negative — energy must be added to unbind:

  
$ i13 run gw_binding.i13   # U = -3GM^2/(5R)
RUN OK · 28 step(s)
coeff = 3/5
U = -10.8   -- for G=1, M=6, R=2
is_negative = 1

  
Recommend as a NULL — a theorem (B39). The 3/5 coefficient is an exact integral over a uniform sphere; U is a pinned function of M and R. NULL — the cost to pull a world apart.