The formula is E = -GMm/r where the negative sign shows that energy must be added to escape to infinity where E = 0. Gravitational potential V = -GM/r is the energy per kilogram at that point, independent of the test mass. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.
An orbit is just falling — the object accelerates toward the mass forever but keeps missing because it's moving sideways fast enough. Kepler's laws aren't three facts to memorise; they're what falling-forever forces on any orbit: the geometry, the sweeping, and the fixed link between period and radius.
Gravitational potential energy is negative because work must be done against gravity to separate masses to infinity where potential energy is defined as zero, with the system naturally moving toward lower (more negative) energy states.
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