1. Newton's Law of Universal Gravitation:
This law states that every particle in the universe attracts every other particle with a force that is:
* Proportional to the product of their masses: The larger the masses, the stronger the force.
* Inversely proportional to the square of the distance between their centers: The farther apart the objects, the weaker the force.
Mathematically, this is represented as:
```
F = G * (m1 * m2) / r^2
```
Where:
* F is the gravitational force
* G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2)
* m1 and m2 are the masses of the two objects
* r is the distance between their centers
2. Deriving 'g' from Newton's Law:
For an object near the Earth's surface, the gravitational force acting on it is its weight (W). We can set the gravitational force (F) equal to the weight (W) and simplify:
```
W = F = G * (m1 * m2) / r^2
```
Where:
* m1 is the mass of the object
* m2 is the mass of the Earth
* r is the radius of the Earth
Since W = m1 * g, we can substitute to get:
```
m1 * g = G * (m1 * m2) / r^2
```
Simplifying, we get the formula for acceleration due to gravity:
```
g = G * m2 / r^2
```
3. Calculating 'g':
Using the values for the gravitational constant (G), the mass of the Earth (m2), and the radius of the Earth (r), we can calculate 'g' to be approximately 9.81 m/s².
Important Notes:
* The value of 'g' varies slightly depending on altitude and latitude due to changes in Earth's density and rotation.
* The formula above assumes a point mass for the Earth, which is not entirely accurate. However, it provides a good approximation for most practical purposes.
Let me know if you'd like more details or have any other questions!
