Formula
The gravitational force between two objects is given by Newton's Law of Universal Gravitation:
```
F = G * (m1 * m2) / r^2
```
Where:
* F is the force of gravity (in Newtons)
* G is the gravitational constant (approximately 6.674 × 10^-11 N m²/kg²)
* m1 is the mass of the Earth (approximately 5.972 × 10^24 kg)
* m2 is the mass of the ball (in kilograms)
* r is the distance between the center of the Earth and the center of the ball (approximately the radius of the Earth plus the height h from which the ball is dropped)
Important Notes:
* Earth's Gravity as an Approximation: In most cases, when dealing with objects near the Earth's surface, we use the simplified formula `F = m * g` where 'g' is the acceleration due to gravity (approximately 9.81 m/s²). This formula is a good approximation because the distance from the Earth's surface to the ball is much smaller than the Earth's radius.
* The ball also exerts a gravitational force on the Earth: Newton's Law of Universal Gravitation works in both directions. The ball exerts a force on the Earth, but since the Earth's mass is vastly larger, this force is negligible.
Example
Let's say you drop a 0.5 kg ball from a height of 10 meters:
1. Find r: The radius of the Earth is about 6,371,000 meters. So, r = 6,371,000 m + 10 m ≈ 6,371,010 m.
2. Calculate F:
F = (6.674 × 10^-11 N m²/kg²) * (5.972 × 10^24 kg) * (0.5 kg) / (6,371,010 m)²
F ≈ 4.9 N
This example shows that the force of gravity on the ball is almost exactly the same as you would get using the simplified formula `F = m * g` (F = 0.5 kg * 9.81 m/s² = 4.9 N).
In conclusion:
While the gravitational force between the Earth and the ball is technically calculated using Newton's Law of Universal Gravitation, the simplified formula `F = m * g` is a good approximation for most scenarios involving objects near the Earth's surface.
