◄ WORLD V · SONNY 5DART 551 · a helldive down the well

THE ORBITAL VELOCITY falling forever, missing the ground

An orbit is a fall that keeps missing. For a circle, gravity GM/r² exactly supplies the centripetal need v²/r, giving v = √(GM/r). In low Earth orbit that is 7,673 m/s — and it is exactly 1/√2 of escape velocity: an orbit is halfway out of the well.

THE TECHNIQUE v = √(GM/r)

The demo computes √(μ/r) at a 400 km altitude (the ISS): live demo







  
HISTORY & CREDIT Newton · the cannonball

  
“Astronauts float because there is no gravity up there.” — gravity in LEO is ~90% of surface; they float because they are in free fall, orbiting. cited

  
the balance · gravity GM/r² = centripetal v²/r.
the speed · v = √(GM/r) = escape / √2.
Newton · the cannonball fired fast enough to fall around the world (A Treatise of the System of the World).

  
An orbit is a permanent near-miss. physics






  
RECOMMEND FOR I-13 the ISS speed, on the compiler

  
On i-13, circular orbital velocity at 400 km altitude is 7,673 m/s:

  
$ i13 run gw_orbital.i13   # v = sqrt(mu/r)
RUN OK · 790 step(s) · call depth 42
v2    = 58868704.8
v_orb = 7672.59   -- m/s (ISS ~7.66 km/s)

  
Recommend as a NULL — a theorem (B39) + resource (B40). Circular orbital speed is pinned by M and r; the sqrt is a Newton workaround. NULL — falling forever, missing the ground.