Final answer:
Astronauts experience apparent weightlessness in an aircraft because they and the aircraft are in free fall, not feeling the gravitational force due to their accelerated frame of reference. In space, the continuous state of weightlessness is due to the spacecraft's orbital motion, creating a condition of microgravity. However, the sensations are simulated in the aircraft for shorter durations compared to the continuous state in orbit.
Step-by-step explanation:
Astronauts appear to be weightless when in an aircraft accelerating downward at g because they are falling at the same acceleration as gravity's pull. This creates an accelerated frame of reference where the normal force that is usually felt as weight from the ground or a scale is not present because both they and the scale are in free fall. In orbit, astronauts experience microgravity conditions which simulate this weightlessness not because gravity is absent, but because they are in a continuous state of free-fall towards Earth, effectively cancelling the force we perceive as weight.
When astronauts train in a cargo aircraft for the sensation of weightlessness, it is a simulation of the actual conditions in orbit. The same principle applies to the cargo aircraft as with an elevator with a broken cable or an airplane in free fall: they are not opposed by a stronger force such as a solid surface or a floor, thus they do not 'feel' their weight. In essence, the astronauts and the aircraft are falling at the same rate.
While the conditions of apparent weightlessness in the aircraft are a simulation of those in orbit, there is a distinction to be made. In the cargo aircraft, brief periods of weightlessness can be achieved, usually lasting for about 20-30 seconds, by performing parabolic flights. In contrast, weightlessness in orbit is a continuous state because of the spacecraft's constant orbital motion around Earth.