Why is the gravitational force between two people negligible?

The gravitational force between two people is negligible because their masses are small and they are relatively far apart.

The gravitational force between two objects is given by Newton's law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force is represented by the equation F = G * (m1 * m2) / r^2, where F is the force of attraction between the objects, m1 and m2 are the masses of the objects, r is the distance between the centres of the two objects, and G is the gravitational constant.

In the case of two people, their masses (m1 and m2) are relatively small, especially when compared to massive objects like planets or stars. This means that the product of their masses (m1 * m2) is also small. Additionally, the distance between them (r) is relatively large, especially when compared to the distances between celestial bodies. Since the force of gravity decreases rapidly as the distance increases (due to the r^2 in the denominator of the equation), the gravitational force between two people is extremely small.

For example, consider two people each with a mass of 70 kg standing 1 metre apart. Using the gravitational constant G = 6.674 * 10^-11 N(m/kg)^2, the gravitational force between them would be F = G * (70 kg * 70 kg) / (1 m)^2 = 3.3 * 10^-9 N. This force is so small that it is effectively negligible.

In comparison, the gravitational force that the Earth exerts on one of the people (with a mass of 70 kg) is F = G * (70 kg * 5.972 * 10^24 kg) / (6.371 * 10^6 m)^2 = 686 N. This force is many orders of magnitude larger than the force between the two people, which is why we can feel the Earth's gravity but not the gravity of other people.

In conclusion, the gravitational force between two people is negligible because their masses are small and they are relatively far apart, which results in a very small force according to Newton's law of universal gravitation.