### Gravity is weak force of nature

4 minutes

astronomylaws

physicsgravity

**Intermediate**

anybody

Gravity is not a force according to *General Relativity* published in 1915 by *Albert Einstein*.
Gravity is inherent natural curvature of 4-dimensional spacetime.
Amazingly, *Issac Newton*, in 1687, published simple formula for calculating gravitational force (equivalent to spacetime curvature) $F$ between two objects.
Measurements show that formula is correct when distance between objects is *at least* $\text{ }200\text{ }\mu\text{m}$.
Newton's Formula, which is very accuate for large distances in space, is as follows.

##### Observations

**$G$ is very small**quantity in multiplication. This will reduce $F$.- $d$ is squared. $d^2$ is in
*denominator*. That means, if distance increases, then**$F$ decreases quite a lot**. If you increase $d$ by $100$, $F$ will decrease by $10000$. - If you consider two objects of $\text{1 kg}$ mass, $\text{1 m}$ apart, gravitational force will be $\text{G Newton}$, which is extremely small number - very
**negligible**. - If you consider two humans of $\text{70 kg}$ mass, $\text{1 m}$ apart, gravitational force will be $3.2683 \times 10^{-7}\text{ Newton}$, which is
**extremely small**- very negligible. - Even a child with quite weak muscles
**can jump away from Earth**. Looking at size of earth, gravity of earth can be considered weak as even child can jump away from it, albeit momentarily. If earth was a magnet, same child would not be able to pick small iron piece from surface of earth. - We can easily a pick a book and hold the book away from earth
**against gravity**of earth whose mass is $5.972 \times 10^{24} \text{ kg}$, and book is near to earth ! - Repulsion (due to electromagnetism) between stable atomic structure in your shoes and floor's stable atomic structure
**keeps you from falling**through floor, even though there's a gravitational attraction between you and Earth. - Gravity is
**weakest among four**of fundamental forces. Smaller the scale, gravity become even more weak. At a small scale, other forces control environment. For example, electromagnetic force between two electrons is approximately $10^{36}$ times stronger than the gravitational force between them. - If you combine gravitational forces of Sun, Moon and Sagittarius A*, even then that
**combined force is negligible**compared to earth's. See calculations below. Human is essentialy affected by earth's gravity and rest is negligible.

##### Gravitational force calculations

Here is table showing gravitational force, as calculated with Newton's formula, on human by individual celestial bodies.

Body | Gravitational Force on Human of $\text{70 kg}$ mass | Relative to Earth's gravitational force | Notes |
---|---|---|---|

Earth | $690 \text{ Newton}$ | 1 | Reference |

Moon | $2.6991 \times 10^{-3}\text{ Newton}$ | $0.0000039118$ | Very negligible compared to earth's |

Sun | $4.1495 \times 10^{-1}\text{ Newton}$ | $0.00060139$ | Negligible compared to earth's |

Sagittarius A* | $6.2639 \times 10^{-13}\text{ Newton}$ | $0.0000000000000009078$ | Extermely negligible compared to earth's |

##### Data

$\begin{align}
m_{\text{human}} &= 70 \text{kg on average} \nonumber \\
m_{\text{moon}} &= 7.347 \times 10^{22} \text{ kg} \nonumber \\
m_{\text{earth}} &= 5.972 \times 10^{24} \text{ kg} \nonumber \\
m_{\text{sun}} &= 1.989 \times 10^{30} \text{ kg} \nonumber \\
m_{\text{Sagittarius A*}} &= 8.54 \times 10^{36} \text{ kg} \nonumber \\
\end{align}$

$\begin{align}
d_{\text{human-human}} &= 1 \text{m on average} \nonumber \\
d_{\text{human-moon}} &= 3.565 \times 10^8 \text{ m (nearest)} \nonumber \\
d_{\text{human-earth}} &= 6.357 \times 10^6 \text{ m (nearest)} \nonumber \\
d_{\text{human-sun}} &= 1.496 \times 10^{11} \text{m average distance} \nonumber \\
d_{\text{human-Sagittarius A*}} &= 2.523 \times 10^{20} \text{ m (typical)} \nonumber
\end{align}$