Gravitational Field between Two Masses

It is a common experience that when an object is thrown upward it falls down to the earth as a result of gravitational pull or force, and this force is known as force of gravity. This force of gravity attracts every object towards the earth.

Newton’s Law of Universal Gravitation

Any object is attracted by the earth within the earth’s gravitational field. Any two objects also attract each other with a force that is equal and opposite. After a series of investigation about the interactive forces acting on two object or mass, Newton was able to come up with the following discoveries laws:

• Two masses experience a force in gravitation which is directly proportional to the product of their masses

f = m₁ m₂ _________________ (1)

• Force is inversely proportional to the square of the distance between the masses \( \scriptsize f \propto \normalsize \frac{1}{r^2} \) (2)

Combining equation (1) and (2)

\( \scriptsize f \propto \normalsize \frac{m_1 m_2}{r^2} \)

Which is Newton’s law of universal gravitation and it is stated as 

Every two particles or objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

\( \scriptsize F =\normalsize \frac{GMM}{r^2} \)

F = force between two masses m and m

G = universal gravitation constant and it has a value of 6.67 x 10 ¹¹NM²/Kg²

r =distance between the masses

Example

An electron of mass 9.10 x 10 ^-31 kg revolves round a hydrogen nucleus with a proton of mass 1.67 x 10 ^-27 kg. If the radius of the orbit is 5.90 x 10 ^-11 m. calculate the gravitational force of attraction between the proton and the neutron. (6.67 x 10 ¹¹NM²/Kg²).

Solution

\( \scriptsize F = \normalsize \frac{GMM}{r^2} \)

=\( \frac{6.67 \times 10^{-11} \; \times \;1.67 \times 10^{-27}\; \times \; 9.1 \times 10^{-31}}{(5.9 \times 10^{-11})^2} \)

F =2 .9 N x 10 ^-47