At the same radius the escape speed-square is twice the circular speed-square, because escape needs exactly the kinetic energy that zeroes out the potential well. The factor of two is exact only for the stated gravity parameter and radius in the ideal circular two-body model. Real orbits add eccentricity, atmosphere/drag, perturbations, central-mass uncertainty, finite-body effects, and measurement uncertainty.

Escape speed-square is checked against the circular source. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The circular source speed-square is four

The circular speed-square source is 4.

vc2=4v_c^{2}=4
Circular source for escapeThe escape check cites this circular speed-square.circular square sourceescape square sourcedouble square relation

Escape speed-square is twice circular speed-square

Twice 4 gives escape speed-square 8.

2⋅4=82\cdot 4=8
Escape is twice circular speed-squareThe factor of two is checked from the same source.circular square sourceescape square sourcedouble square relation