Final answer:
An alien astronaut would experience weightlessness due to being in a state of freefall within a circular orbit around their home planet.
Their orbital path is essentially a continuous fall towards the planet, offset by their forward motion, which is governed by Newton's laws and Einstein's equivalence principle.
Step-by-step explanation:
If an alien astronaut has a weight of W_surface at the surface of their home planet, upon reaching a space station in circular orbit where the orbital radius is four times the planet’s radius, the astronaut will not be 'weightless' in the sense of being far from a gravitational source.
Instead, they would experience weightlessness due to being in a state of freefall, where the space station and the astronaut inside it are accelerating towards the center of the planet at the same rate. This is a result of Newton's laws of motion and the concept of an inertial frame of reference, as described by Einstein's equivalence principle.
The International Space Station and experiments conducted with astronauts in orbit provide real-world examples of this phenomenon. Astronauts appear to be weightless and must use special methods to measure mass changes.
A rotating space station can simulate gravity through centripetal acceleration, adhering to principles of classical mechanics. Understanding the effects of gravity in multiple-body systems, such as in the case of planetary orbits, can extend to theoretical scenarios involving aliens or interplanetary travel.