Surface gravity

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The surface gravity of any celestial body, like a star, a planet, a dwarf planet, or a moon, is actually the acceleration due to gravity of a falling object at or near the surface.

Contents

Terminology

Surface gravity is an acceleration, and is commonly measured in the units of acceleration, which are distance (or length) per square unit of time. The SI units of acceleration are m/s².

But surface gravity has another unit, g. The lowercase g is always italicized in the technical literature, mainly to distinguish it from g for gram, and also from g as a symbol for the quantity called surface gravity as opposed to its value. The quantity g is the standard surface gravity of the earth. By definition this is 9.80665 m/s².

In the discussion below, body refers to a celestial body and object refers to a much smaller object that might rest on a body.

Mass v. Weight

Mass and weight are often confused, especially in the US customary system of units or any other system of ancient or medieval origin. In such systems, mass and weight are regarded as fundamentally the same. But weight can change with altitude or even with latitude.

Weight and mass are related in the following manner:

W = mg\,\!

where g is the surface gravity at any given point on any given body and m is an object's mass.

The concept of weight still has a practical meaning in the planning of missions, crewed or non-crewed, to various celestial bodies. Weight is the force that a spacecraft's engines will need to counteract during liftoff and landing. Moreover the difference in the weight of a man on Earth and on a body to be explored will dictate how much equipment an exploratory crewman can carry on that body.

Calculation of surface gravity

Surface gravity derives directly from the Newtonian law of gravity:

g = \frac{GM}{R^2}

where G is Cavendish's gravitational constant, M is the mass of the body, and R is the radius of the body at any given point on its surface.

See also

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