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) FF between two objects. Measurements show that formula is correct when distance between objects is at least  200 μm\text{ }200\text{ }\mu\text{m}. Newton's Formula, which is very accuate for large distances in space, is as follows.

F=Gm1×m2d2m1=mass of one objectm2=mass of another objectd=Distance between two objectsG=Gravitaional Constant=6.67×1011m3/(kgs2)\begin{align} F &= G\cdot\frac{m_1 \times m_2}{d^2} \nonumber \\ m_1&=\text{mass of one object} \nonumber \\ m_2&=\text{mass of another object} \nonumber \\ d&=\text{Distance between two objects} \nonumber \\ G&=\text{Gravitaional Constant}=6.67 \times 10^{-11} m^3/(kg \cdot s^2) \nonumber \end{align}
Observations
  • GG is very small quantity in multiplication. This will reduce FF.
  • dd is squared. d2d^2 is in denominator. That means, if distance increases, then FF decreases quite a lot. If you increase dd by 100100, FF will decrease by 1000010000.
  • If you consider two objects of 1 kg\text{1 kg} mass, 1 m\text{1 m} apart, gravitational force will be G Newton\text{G Newton}, which is extremely small number - very negligible.
  • If you consider two humans of 70 kg\text{70 kg} mass, 1 m\text{1 m} apart, gravitational force will be 3.2683×107 Newton3.2683 \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 5.972×1024 kg5.972 \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 103610^{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.

BodyGravitational Force on Human of 70 kg\text{70 kg} massRelative to Earth's gravitational forceNotes
Earth690 Newton690 \text{ Newton}1Reference
Moon2.6991×103 Newton2.6991 \times 10^{-3}\text{ Newton}0.00000391180.0000039118Very negligible compared to earth's
Sun4.1495×101 Newton4.1495 \times 10^{-1}\text{ Newton}0.000601390.00060139Negligible compared to earth's
Sagittarius A*6.2639×1013 Newton6.2639 \times 10^{-13}\text{ Newton}0.00000000000000090780.0000000000000009078Extermely negligible compared to earth's
Data
mhuman=70kg on averagemmoon=7.347×1022 kgmearth=5.972×1024 kgmsun=1.989×1030 kgmSagittarius A*=8.54×1036 kg\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}
dhuman-human=1m on averagedhuman-moon=3.565×108 m (nearest)dhuman-earth=6.357×106 m (nearest)dhuman-sun=1.496×1011m average distancedhuman-Sagittarius A*=2.523×1020 m (typical)\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}