Gravitational Force

on . Posted in Classical Mechanics

Tags: Acceleration Gravity

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

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 formula

\(\large{ F_g = G\; \frac{ m_1 \;m_2 }{ r^2 } }\)     (Gravitational Force)

\(\large{ G =  \frac{ F_g \; r^2 }{ m_1 \;m_2 } }\)

\(\large{ m_1 =  \frac{ F_g \; r^2 }{ G \; m_2 } }\)

\(\large{ m_2 =  \frac{ F_g \; r^2 }{ G \; m_1 } }\)

\(\large{ r =  \sqrt{  \frac{ G \; m_1 \;m_2 }{ F_g }  }  }\)

Symbol English Metric
\(\large{ F_g }\) = gravitational force \(\large{lbm}\) \(\large{kg}\)
\(\large{ G }\) = universal gravitational constant \(\large{\frac{lbf-ft^2}{lbm^2}}\) \(\large{\frac{N - m^2}{kg^2}}\)
\(\large{ m_1 }\) = mass of object 1 \(\large{ lbm }\) \(\large{ kg }\)
\(\large{ m_2 }\) = mass of object 2 \(\large{ lbm }\) \(\large{ kg }\)
\(\large{ r }\) = distance between the centers of two bodies \(\large{ ft }\) \(\large{ m }\)


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Tags: Acceleration Gravity