# 7.1.1 Gravitational Force

According to legend, it was when an apple fell on Isaac Newton’s head that he had this epiphany: every mass attracts every other mass in the universe gravitationally.

$\displaystyle {{F}_{g}}=G\frac{{{{M}_{1}}{{M}_{2}}}}{{{{d}^{2}}}}$

More specifically, Newton’s Law of Gravitational states that the force of attraction Fg between any two point masses M1 and M2 is directly proportional to the product of the masses (M1M2) and inversely proportional to the square of the separation between them (d2).

G, the gravitational constant, has turned out to be a very small number. $G=6.67\times {{10}^{{-11}}}\text{ N k}{{\text{g}}^{{-2}}}\text{ }{{\text{m}}^{2}}$.

Two things to note:

• Non-point masses can often be treated as point masses at their centres of masses. So d is going to be the centre-to-centre distance.
• The mutual force of attraction is an action-reaction pair. As dictated by N3L, two masses must always exert the same magnitude of gravitational pull on each other, even if they are of different masses.

Example

Calculate the gravitational force of attraction between the two bowling balls shown below.

Solution

\displaystyle \begin{aligned}{{F}_{g}}&=G\frac{{{{M}_{1}}{{M}_{2}}}}{{{{d}^{2}}}}\\&=(6.67\times {{10}^{{-11}}})\frac{{3.6\times 7.2}}{{{{{0.22}}^{2}}}}\\&=3.57\times {{10}^{{-8}}}\text{ N}\end{aligned}

Video Explanation

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