# Gravitational Acceleration

on . Posted in Classical Mechanics

Gravitational acceleration, abbreviated as g, also called acceleration of gravity or acceleration due to gravity, is the force on an object caused only by gravity.  It represents the rate at which an object's velocity changes when it falls freely near the surface of a celestial body, such as Earth.

On Earth, the gravitational acceleration is a constant:

g = 9.80665 $$\large{\frac{rad}{sec^2}}$$ (Metric)

g = 32.1740 $$\large{\frac{ft}{sec^2)}}$$ (English)

Various formulas that include the constant for the acceleration of gravity, on Earth are below.  Note, these are all arranged to solve for the constant but can also be rearranged to solve for any of the other variables, if they are unknown.

It is important to note that gravitational acceleration is not constant across the surface of a celestial body.  It can vary slightly due to factors such as the body's shape, altitude, and local gravitational anomalies caused by variations in the distribution of mass.  However, for practical purposes, a uniform value is commonly used in most calculations involving everyday scenarios.

## Gravitational acceleration formula

$$\large{ g = \frac{G \; m}{r^2} }$$

### Gravitational Acceleration - Solve for g

$$\large{ g = \frac{G \; m}{r^2} }$$

 universal gravitational constant, G mass, m radius, r

### Gravitational Acceleration - Solve for G

$$\large{ G = \frac{g \; r^2}{m} }$$

 gravitational acceleration, g radius, r mass,m

### Gravitational Acceleration - Solve for m

$$\large{ m = \frac{g \; r^2}{G} }$$

 gravitational acceleration, g radius, r universal gravitational acceleration, G

### Gravitational Acceleration - Solve for r

$$\large{ r = \sqrt{ \frac{G \; m}{g} } }$$

 universal gravitational acceleration, G mass, m gravitational acceleration, g

Symbol English Metric
$$\large{ g }$$ = gravitational acceleration  $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$
$$\large{ G }$$ = universal gravitational constant $$\large{\frac{lbf-ft^2}{lbm^2}}$$  $$\large{\frac{N -m^2}{kg^2}}$$
$$\large{ m }$$ = mass $$\large{ lbm }$$ $$\large{ kg }$$
$$\large{ r }$$ = radius $$\large{ ft }$$ $$\large{ m }$$