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Variation of g with altitude
Intermediate
g decreases as one moves away from Earth.
g' = g(R/(R+h))²At height h above the surface g' = g(R/(R + h))² ≈ g(1 − 2h/R) for small h. It decreases slowly.
At 400 km (ISS) g' ≈ 8.7 m/s², still 89% of the surface value.
Astronauts are weightless due to free fall, not because gravity vanishes.
In more detail
At height h above the surface, g decreases to g(R/(R+h))², because the distance from Earth's centre increases. For small heights, the decrease is roughly 2h/R.
Real-world uses
- Satellite altitudes change the effective gravity they experience.
- Gravity measurements on mountains are corrected for altitude.
- Pilots and satellite designers account for the slight drop in g with altitude when computing orbital and flight data.
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Frequently asked questions
How much does g fall on a high mountain?
On the top of Everest it is about 0.3% smaller than at sea level.
Why does altitude matter for g?
Because it increases the distance from the centre of the Earth, so the pull is weaker.
Does g drop to zero at high altitude?
It falls but never reaches zero. At the height of the International Space Station, g is still about 90 percent of its surface value.
Related topics in Gravitation & Orbits
Universal law of gravitation · Gravitational constant G · Acceleration due to gravity · Variation of g with depth · Effect of Earth's rotation on g · Gravitational field