Why an astronot in orbiting satellite has a feeling of weightlessness?

the net force on bodies in stable orbit is nil, the force of gravitational attraction , is balanced by the centripetal force of velocity in a circle.

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example, any orbit radius ( if orbit time not important)

choose your orbit radius, calculate force of gravity, tailor velocity to produce balancing centripital force

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f=((G*m1*m2)/d^2) force of gravity

f = m2 *( v^2/d ) centripetal force

G = newtons constant

m1 = earth mass

m2 = satellite mass

d = orbital distance