Weightlessness on the ISS

Problem

Weightlessness on the ISS. Astronauts on the ISS appear “weightless”. Is gravity really zero at that altitude? What are they actually experiencing?

Solution

Gravity is NOT zero. The ISS orbits at about $h = 400$ km altitude. The orbital radius is $r = R_T + h = 6{,}37\cdot 10^6 + 4\cdot 10^5 = 6{,}77\cdot 10^6$ m. Gravity there is $g(r) = \frac{GM_T}{r^2} = \frac{6{,}67\cdot 10^{-11}\cdot 6{,}0\cdot 10^{24}}{(6{,}77\cdot 10^6)^2} \approx 8{,}7\ \text{m/s}^2$ that is about $90\%$ of the surface value ($9{,}8$ m/s$^2$). Gravity is almost full strength.

What they actually experience. The astronauts are in continuous free fall. The station, and everything inside it, accelerates towards the Earth with the same $g(r)$: it is precisely this acceleration that curves the trajectory into an orbit, instead of falling in a straight line. Astronaut, floor and station fall together with the same acceleration.

In the (non-inertial) reference frame of the ISS, the gravitational acceleration and the acceleration of the falling frame cancel out: there is no reaction from the floor, hence no sensation of weight. It is exactly the effect of a falling lift: a scale under your feet would read zero, even though gravity is present.

The correct term is not “absence of gravity” but microgravity or apparent weightlessness.

$\ev{g(400\ \text{km}) \approx 8{,}7\ \text{m/s}^2 \approx 90\%\,g_0;\ \text{the astronauts are in free fall, not without gravity}}$

Links

Topics: Gravitation Concepts: Weight force · Orbits Skills: Analysis of limiting cases and speculative physics Objects: Satellite