Gravitational acceleration is the acceleration a body would experience if it were in free fall on a celestial body such as the Earth or Moon.
Different bodies are attracted to the Earth's surface, as there is a force of attraction between them and the Earth - the gravitational force. This force produces a gravitational acceleration that draws objects towards the Earth or, more precisely, towards the Earth's center.
The gravitational accelerations for the Earth and Moon are..:
|g_{T} = 9.8 \: \text {m/s}^2 = 9.8 \: \text {N/kg}|
|g_{L} = 1.6 \: \text {m/s}^2 = 1.6 \: \text {N/kg}|
Here are the gravitational acceleration values for the other stars in our solar system.
|g_{\small \text {Mercure}} = 3,7 \: \text {m/s}^2 = 3,7 \: \text {N/kg}|
|g_{\small \text {Vénus}} = 8,9 \: \text {m/s}^2 = 8,9 \: \text {N/kg}|
|g_{\small \text {Mars}} = 3,8 \: \text {m/s}^2 = 3,8 \: \text {N/kg}|
|g_{\small \text {Jupiter}} = 24,8 \: \text {m/s}^2 = 24,8 \: \text {N/kg}|
|g_{\small \text {Saturne}} = 10,5 \: \text {m/s}^2 = 10,5 \: \text {N/kg}|
|g_{\small \text {Uranus}} = 8,8 \: \text {m/s}^2 = 8,8 \: \text {N/kg}|
|g_{\small \text {Neptune}} = 11,2 \: \text {m/s}^2 = 11,2 \: \text {N/kg}|
|g_{\small \text {Soleil}} = 273,9 \: \text {m/s}^2 = 273,9 \: \text {N/kg}|
The units representing gravitational acceleration are expressed in |\: \text {N/kg}| in the previous formula. However, these units are equivalent to |\: \text {m/s}^2| that were used in the kinematics.
A planet's gravitational field represents the zone within which a star attracts every object on its surface.
As we move away from the star, the gravitational attraction it exerts on objects diminishes. As mentioned above, the Earth's gravitational pull on an object is approximately |\small 9,8 \: \text {N/kg}|, while the Moon's gravitational pull is around |\small 1,6 \: \text {N/kg}|. This means that a person on Earth is attracted six times more by the Earth than if they were on the Moon. This is why astronauts “float” on the Moon: they are so unattracted by the Moon that they can move around very easily.
|\displaystyle g = \frac{G \cdot m}{r^{2}}|
where
|g| represents the gravitational field (or gravitational acceleration) |\small (\text {N/kg})|
|G| represents the universal gravitational constant |\small \left( 6,67 \times 10^{-11} \displaystyle \frac {\text {N} \cdot \text {m}^{2}}{\text {kg}^{2}} \right)|
|m| represents the mass of the star |\small (\text {kg})|
|r| represents the star's radius |\small (\text {m})|
What is the Moon's gravitational field?
For the Moon, the following information is known.
||\begin{align}G &= 6,67 \times 10^{-11} \displaystyle \frac {\text{N} \cdot {\text{m}}^{2}}{\text{kg}^{2}} &m &= \: 7,35 \times 10^{22} \: \text{kg}\\
r&= 1,74 \times 10^{6} \: \text{m} \\ \end{align}||
Simply use the formula to find the intensity of the gravitational field.
||\begin{align} \displaystyle g = \frac{G \cdot m}{r^{2}} \quad \Rightarrow \quad
g &= \frac{6,67 \times 10^{-11} \displaystyle \frac {\text{N} \cdot \text{m}^{2}}{\text{kg}^{2}} \cdot 7,35 \times 10^{22} \: \text{kg}}{(1,74 \times 10^{6} \: \text{m})^{2}}\\
&= 1,62 \: \text{N/kg} \end{align}||
The answer obtained means that every kilogram on the Moon's surface is attracted with a force of |1,62 \: \text {N}|.
Gravitational force is the force created by the attraction between two bodies. This force depends on gravitational acceleration.