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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.
== Terminology ==
Surface gravity is an acceleration, and is commonly measured in the units of acceleration, which are mass per square unit of time. The [[International System of Units|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:
<math>W = mg\,\!</math>
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:
<math>g = \frac{GM}{R^2}</math>
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 ==
* [[Escape speed]]
[[Category:Astronomy]]
== Terminology ==
Surface gravity is an acceleration, and is commonly measured in the units of acceleration, which are mass per square unit of time. The [[International System of Units|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:
<math>W = mg\,\!</math>
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:
<math>g = \frac{GM}{R^2}</math>
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 ==
* [[Escape speed]]
[[Category:Astronomy]]