Vedatom Physics Mechanics / Gravitation
◈ Simulations ▤ Full book
Reading gravity right
One law, everywhere. Every pair of masses pulls along the line joining them with F = GMm/r² — the same rule for a falling apple and a moon.
A sphere acts like a point at its centre. Outside, use r from the centre; inside a uniform sphere only the mass beneath you pulls, so g falls linearly to zero at the core.
Bound orbits keep two things fixed. Angular momentum (equal areas in equal times) and total energy E = −GMm/2a — negative for every closed orbit.
Escape is an energy threshold. Reach E = 0 and the body just barely coasts to infinity: v_esc = √(2GM/R) = √2 × orbital speed.
fly the orbit simulator · §03
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Mechanics · all fourteen modules inked · all lit
§02

Field & potential — inside and out

The field g(r) is the slope of the potential V(r). A thin shell pulls nothing inside it — yet its potential is not zero; it sits flat at the surface value, so no work is done moving around within. A solid sphere pulls linearly toward the centre inside, and its potential dips to −3GM/2R at the core. Slide the probe through both and read the two curves.

{{ fieldLabel }}
surface · r = R probe field g
distance from centre{{ fieldR }} R
field g (÷ GM/R²)
{{ fld.gval }}
potential V (÷ GM/R)
{{ fld.vval }}
field g vs r
R r
potential V vs r · the well
R 0
{{ fld.noteTitle }} {{ fld.note }}