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Lesson 3, Topic 1
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# Gravitational Field between Two Masses

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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.

## Newtonâ€™s Law of Universal Gravitation

Any object is attracted by the earth within the earthâ€™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 Newtonâ€™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

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