Force between two 100 kg spheres

Problem

Two spheres of mass $100\ \text{kg}$ each are $1{,}0\ \text{m}$ apart. Calculate the gravitational force between them. Compare it with the weight of one of them on Earth. Given: $G = 6{,}67\cdot 10^{-11}\ \text{N}\,\text{m}^2/\text{kg}^2$.

Solution

Law of universal gravitation. $F = \frac{G\,m_1 m_2}{d^2} = \frac{6{,}67\cdot 10^{-11}\cdot 100\cdot 100}{(1{,}0)^2} = 6{,}67\cdot 10^{-11}\cdot 10^4$

$\ev{F \approx 6{,}67\cdot 10^{-7}\ \text{N}}$

Comparison with the weight. The weight of one sphere on Earth is $P = m\,g = 100\cdot 9{,}8 \approx 9{,}8\cdot 10^{2}\ \text{N}$

The ratio is $\frac{P}{F} \approx \frac{9{,}8\cdot 10^{2}}{6{,}67\cdot 10^{-7}} \approx 1{,}5\cdot 10^{9}$

The gravitational force between the two objects is about a billion times smaller than their weight: this is why gravity between everyday objects is completely imperceptible, and only shows up when astronomical masses are involved.

Links

Topics: Gravitation Concepts: Law of universal gravitation · Weight force Skills: Symbolic set-up