Gravitational force, abbreviated as \(F_g\), also called g-force, is the natural force of attraction that exists between any two objects in the universe that have mass. The strength of the gravitational force depends on the masses of the objects and the distance between them. The greater the masses of the objects and the closer they are to each other, the stronger the gravitational force. Gravitational force was first described mathematically by Newton in his law of universal gravitation.
Gravitational Force Formula |
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\( F_g \;=\; G \cdot \dfrac{ m_1 \cdot m_2 }{ r^2 } \) (Gravitational Force) \( m_1 \;=\; \dfrac{ F_g \cdot r^2 }{ G \cdot m_2 }\) \( m_2 \;=\; \dfrac{ F_g \cdot r^2 }{ G \cdot m_1 }\) \( r \;=\; \sqrt{ \dfrac{ G }{ F_g } \cdot m_1 \cdot m_2 } \) |
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| Symbol | English | Metric |
| \( F_g \) = Gravitational Force | \(lbm\) | \(kg\) |
| \( G \) = Universal Gravitational Constant | \(lbf-ft^2 \;/\; lbm^2\) | \(N - m^2 \;/\; kg^2\) |
| \( m_1 \) = Mass of Object 1 | \( lbm \) | \( kg \) |
| \( m_2 \) = Mass of Object 2 | \( lbm \) | \( kg \) |
| \( r \) = Distance Between the Centers of Masses | \( ft \) | \( m \) |
According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Gravitational force is responsible for many of the phenomena we observe in the universe, including the motion of the planets in our solar system, the formation and evolution of galaxies, and the behavior of black holes.
Gravitational Force Examples
- An object falling from a height toward Earth because Earth’s gravity pulls it downward.
- A person standing on the ground, where Earth’s gravitational force pulls the person toward Earth’s center and gives the person weight.
- Earth orbiting the Sun because the Sun’s gravitational force attracts Earth and provides the centripetal force needed for its orbit.
- Ocean tides caused primarily by the gravitational attraction of the Moon, with additional effects from the Sun.
- Artificial satellites orbiting Earth because Earth’s gravitational force keeps them in orbit.
- A pendulum swinging, where gravity acts as the restoring force that pulls the pendulum toward its equilibrium position.
- Binary star systems, where two stars orbit a common center of mass due to their mutual gravitational attraction.
- Comets traveling in elliptical orbits around the Sun under the influence of solar gravity.
- Material collapsing to form stars and planets within interstellar gas and dust clouds, driven by gravitational attraction.
