Gravity Acceleration by Altitude

Description

The gravity of Earth, which is denoted by g, refers to the acceleration that the Earth imparts to objects on or near its surface due to gravity. In SI units this acceleration is measured in metres per second squared (in symbols, m/s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1). It has an approximate value of 9.81 m/s2, which means that, ignoring the effects of air resistance, the speed of an object falling freely near the Earth’s surface will increase by about 9.81 metres (32.2 ft) per second every second. This quantity is sometimes referred to informally as little g (in contrast, the gravitational constant G is referred to as big G).

There is a direct relationship between gravitational acceleration and the downwards force (weight) experienced by objects on Earth, given by the equation F = ma (force = mass × acceleration). However, other factors such as the rotation of the Earth also contribute to the net acceleration.

The precise strength of Earth’s gravity varies depending on location. The nominal “average” value at the Earth’s surface, known as standard gravity is, by definition, 9.80665 m/s2 (about 32.1740 ft/s2). This quantity is denoted variously as gn, ge (though this sometimes means the normal equatorial value on Earth, 9.78033 m/s2), g0, gee, or simply g (which is also used for the variable local value).

Gravity decreases with altitude as one rises above the Earth’s surface because greater altitude means greater distance from the Earth’s centre. All other things being equal, an increase in altitude from sea level to 9,000 metres (30,000 ft) causes a weight decrease of about 0.29%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which lessens an object’s buoyancy. This would increase a person’s apparent weight at an altitude of 9,000 metres by about 0.08%)

It is a common misconception that astronauts in orbit are weightless because they have flown high enough to escape the Earth’s gravity. In fact, at an altitude of 400 kilometres (250 mi), equivalent to a typical orbit of the Space Shuttle, gravity is still nearly 90% as strong as at the Earth’s surface. Weightlessness actually occurs because orbiting objects are in free-fall.

The effect of ground elevation depends on the density of the ground (see Slab correction section). A person flying at 30 000 ft above sea level over mountains will feel more gravity than someone at the same elevation but over the sea. However, a person standing on the earth’s surface feels less gravity when the elevation is higher.

The formula shown here approximates the Earth’s gravity variation with altitude.

Related formulas

Variables

ghgravitational acceleration at height h above sea level. (m/s2)
g0Standard gravity
reEarth's mean radius. (km)
haltitude (km)