Definition:
In mathematics and physics, G and g are used to represent different concepts. G (capital G) typically refers to the gravitational constant, while g (small g) usually represents the acceleration due to gravity.

G (Gravitational Constant):
The gravitational constant, denoted by G, is a fundamental constant in physics that appears in Newton's law of universal gravitation. It is the proportionality constant that determines the strength of the gravitational force between two objects. The value of G is approximately 6.67430 x 10^-11 N(m/kg)^2.

g (Acceleration due to Gravity):
The acceleration due to gravity, denoted by g, is the acceleration experienced by an object in a gravitational field. It is the rate at which the velocity of an object changes under the influence of gravity alone. Near the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s^2.

Difference between G and g:
1. Concept:
- G: Gravitational constant.
- g: Acceleration due to gravity.

2. Representation:
- G: Capital letter G is used to represent the gravitational constant.
- g: Small letter g is used to represent the acceleration due to gravity.

3. Units:
- G: The unit of G is N(m/kg)^2, which stands for newton multiplied by square meters divided by kilograms squared.
- g: The unit of g is m/s^2, which stands for meters per second squared.

4. Magnitude:
- G: The value of G is a very small constant, approximately equal to 6.67430 x 10^-11 N(m/kg)^2.
- g: The value of g is approximately 9.8 m/s^2, which is significantly larger than G.

5. Application:
- G: The gravitational constant is used in the calculation of gravitational forces between celestial bodies, such as planets, stars, and galaxies.
- g: The acceleration due to gravity is used in various calculations involving free fall, projectile motion, and weight.

6. Dependence:
- G: The value of G is a universal constant and does not depend on the mass or location of the objects involved.
- g: The value of g varies depending on the mass and radius of the celestial body. It is stronger on larger objects with greater mass and smaller radii.

Conclusion:
In summary, G represents the gravitational constant, which determines the strength of the gravitational force, while g represents the acceleration due to gravity, which is the acceleration experienced by an object in a gravitational field. G is a small constant used for celestial calculations, while g is the acceleration experienced near the surface of the Earth.