The gravitational attraction between two humans is an extremely small, almost imperceptible force, typically on the order of hundreds of nanoNewtons. While it is not zero, its magnitude is so tiny that it has no noticeable effect on daily interactions.
Understanding Gravitational Attraction
According to Newton's Law of Universal Gravitation, every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This fundamental law is expressed by the formula:
F = G (m₁ m₂) / r²
Where:
- F is the gravitational force between the two objects.
- G is the gravitational constant, approximately 6.674 × 10⁻¹¹ N⋅m²/kg².
- m₁ and m₂ are the masses of the two objects.
- r is the distance between the centers of the two objects.
Calculating the Gravitational Force
To provide an exact answer, let's calculate a typical value for the gravitational force between two humans using reasonable assumptions for their masses and the distance between them.
Assumptions:
- Mass of Human 1 (m₁): 70 kg (approximate average adult mass)
- Mass of Human 2 (m₂): 70 kg (approximate average adult mass)
- Distance (r): 1 meter (a typical close proximity, standing next to each other)
- Gravitational Constant (G): 6.674 × 10⁻¹¹ N⋅m²/kg² Source: HyperPhysics
Let's plug these values into the formula:
F = (6.674 × 10⁻¹¹ N⋅m²/kg²) (70 kg 70 kg) / (1 m)²
F = (6.674 × 10⁻¹¹ N⋅m²/kg²) * (4900 kg²) / 1 m²
F = 3.27 × 10⁻⁷ N
| Parameter | Value | Unit |
|---|---|---|
| Human 1 Mass | 70 | kg |
| Human 2 Mass | 70 | kg |
| Distance Apart | 1 | m |
| Gravitational Constant (G) | 6.674 x 10⁻¹¹ | N⋅m²/kg² |
| Calculated Force (F) | 3.27 x 10⁻⁷ | Newtons |
This means the gravitational force between two 70 kg humans standing one meter apart is approximately 0.000000327 Newtons, or 327 nanoNewtons.
Why This Force is Negligible
The gravitational force between two people is negligible because their masses are small, and even when relatively close, they are far apart compared to astronomical scales. This results in a very small force according to Newton's law of universal gravitation.
To put this into perspective:
- The force required to lift a single grain of sand is vastly greater than this gravitational attraction.
- The force of a small insect landing on your arm would exert a much larger force than the gravitational pull from another human.
- The slight movement of air or a gentle breeze exerts a significantly stronger force than this inter-human gravitational pull.
Our bodies are constantly under the much stronger gravitational influence of the Earth (which has an enormous mass), which is why we remain grounded.
Practical Implications
- No Observable Effect: The gravitational pull between two humans is far too weak to cause any observable movement, attraction, or influence on their daily lives. You will not "feel" yourself being pulled towards another person due to gravity.
- Dominated by Other Forces: Other forces, such as friction, air resistance, electromagnetic forces (like the repulsion between charged particles in our shoes and the ground), and even the slight movements of air currents, are many orders of magnitude stronger and thus completely mask any inter-human gravitational effects.
- Fundamental, But Insignificant for Small Masses: While gravity is one of the four fundamental forces of nature, its effects only become significant when dealing with celestial bodies that have immense masses, such as planets, stars, and galaxies. For everyday objects like humans, the gravitational force they exert on each other is practically non-existent.
