ISS astronaut and weightlessness

Problem

Why is an astronaut aboard the International Space Station (ISS) “weightless” if the Earth’s gravitational field at that altitude is still about $89\%$ of its surface value? Explain the difference between weight and the sensation of weight.

Solution

The true weight still exists. At an altitude of about $400\ \text{km}$ the gravitational field is still about $89\%$ of its surface value: the astronaut therefore experiences a weight force $P = mg$ almost identical to what they would feel on the ground. It is not true that “there is no gravity in orbit” — quite the opposite, it is precisely that gravity that curves the orbit.

What the sensation of weight is. What we perceive as “weight” is not the gravitational force itself, but the normal force that a surface (floor, chair) exerts on us, pushing us upwards. It is this constraint reaction that compresses the body and activates the receptors: the “sensation of weight”.

Why it disappears in orbit. The astronaut and the ISS are in free fall: gravity is the only force acting, and it gives both the same acceleration $g$. They fall together, with the same acceleration, along the same trajectory (the orbit is a “continuous fall” that keeps missing the Earth). Since there is no surface pushing against the astronaut with a normal force, the sensation of weight is absent.

$\ev{\text{true weight } P=mg \text{ present; normal force} = 0 \;\Rightarrow\; \text{absence of the } \textit{sensation}\text{ of weight}}$

It is the same effect felt for an instant in a lift that starts to descend, or on a roller coaster: microgravity = free fall, not absence of gravity.

Links

Topics: Gravitation Concepts: Weight force · Centripetal acceleration · Orbits Objects: Satellite