Gravitational Acceleration at Altitude

Gravitational acceleration decreases with altitude above Earth’s surface:

g(h) = g₀ × (R_E / (R_E + h))²

Where:

• g(h) = Gravitational acceleration at altitude h (m/s²)
• g₀ = Standard surface gravity = 9.80665 m/s²
• R_E = Earth’s mean radius = 6,371 km
• h = Altitude above the surface (km or m)

Weight at altitude: W(h) = m × g(h)

Key altitudes:

Why are astronauts “weightless” on the ISS? The ISS orbits at ~400 km, where g is still 8.68 m/s², nearly 89% of surface gravity. Astronauts feel weightless not because gravity has run out, but because they are in free fall.
Both the station and everyone inside it fall toward Earth at the same rate, so nothing presses against anything.
What keeps the station from arriving is its sideways speed: it falls continuously and keeps missing.

Where does gravity actually halve? At 2,639 km up, which is more than six times the ISS altitude and still under a seventh of the way to a GPS satellite. Gravity thins out far more slowly than most people picture, which is the real reason “space starts at 100 km” and “weightlessness” have nothing to do with each other.

Atmospheric pressure note: The “vacuum” of space begins gradually above 80–100 km (the Kármán line). Gravity itself extends infinitely, just growing weaker with distance.