When you stand on Earth, the distance between you and Earth is zero. So why isn't the gravitational force infinite?

The cornerstone of classical physics, Newton's Law of Universal Gravitation, posits that every mass exerts an attractive force on every other mass. This is the intuitive force we feel as gravity. The law's formula is expressed as:
\[ F = G \cdot \frac{{m_1 \cdot m_2}}{{r^2}} \]
Where,

• \(F \) is the gravitational force between two objects,
• \( G \) is the gravitational constant,
• \( m_1 \) and \( m_2 \) are the masses of the objects, and
• \( r \) is the distance between the centers of the two masses.

This relationship shows that the force decreases as the distance squared increases, explaining why celestial bodies can have a profound gravitational effect across vast distances. Gravitational force is the invisible 'string' that holds the planets in orbit around the sun and keeps us grounded on Earth.

The gravitational constant, symbolized by \( G \) and sometimes called the universal gravitational constant, is a key quantity in Newton's law of gravitation. The value of \( G \) is determined experimentally, and it is remarkably consistent across the universe. Its value is approximately \[ 6.674 \times 10^{-11} \, \text{{Nm}}^2/\text{{kg}}^2 \].
The consistency of \( G \) ensures that the gravitational force can be calculated for any two masses, provided their masses and the distance between their centers are known. It's this consistency that allows scientists to predict the gravitational interaction between celestial objects and engineer spacecraft trajectories.

Mass and gravity are intrinsically linked in the cosmos. Mass is a measure of the amount of matter in an object, typically measured in kilograms. The more mass an object has, the more gravitational pull it exerts. If an object is more massive, it will have a stronger force of attraction. Conversely, if an object is less massive, the gravitational force it exerts will be weaker.
This is why, despite Earth being much smaller than the sun, it still has enough gravity to hold us down; it has enough mass within a relatively small volume. Gravitational force increases with increasing mass but is also inversely proportional to the square of the distance between the masses, which is why weightlessness is possible at sufficient altitude, even within Earth's gravitational pull.

The concept of the curvature of space-time comes from Einstein's General Theory of Relativity, where gravity is not merely a force but the result of the bending of space and time by mass and energy. Massive objects like planets and stars create dips in space-time, akin to a heavy ball placed on a stretched sheet. These dips guide the motion of other objects, which follow the curves.
In this framework, objects are not pulling on each other through some unseen force, as the Newtonian picture would suggest, but are simply following the straightest possible paths in a curved space-time. Thus, even if two masses were to overlap — hypothetically 'zero distance' — the force wouldn't be infinite because they warp the fabric of space-time to its extent, not beyond.