Gravity is weak force of nature

4 minutes

astronomylaws

physicsgravity

Intermediate

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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.

**$G$ 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.

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 |
---|---|---|

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

Moon | $2.6991 \times 10^{-3}\text{ Newton}$ | $0.0000039118$ |

Sun | $4.1495 \times 10^{-1}\text{ Newton}$ | $0.00060139$ |

Sagittarius A* | $6.2639 \times 10^{-13}\text{ Newton}$ | $0.0000000000000009078$ |

It is clear from above table that relative to Earth's gravitational force, other forces are negligible.

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

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