Dimensional constants

Dimensional constants are physical quantities that have a fixed dimension and are independent of any system of units. They are used to derive the dimensions of other physical quantities. The gravitational constant is an example of a dimensional constant.

Gravitational constant

The gravitational constant, denoted by G, is a physical constant that appears in the formula for Newton's law of universal gravitation.

Newton's law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The magnitude of the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The formula for Newton's law of universal gravitation is:

F = G * (m1 * m2) / r^2

where F is the gravitational force between two point masses, m1 and m2 are the masses of the point masses, r is the distance between them, and G is the gravitational constant.

The value of G is approximately equal to 6.67430 × 10^-11 m^3 kg^-1 s^-2. Its units are derived from the formula for gravitational force, and are m^3 kg^-1 s^-2.

Since G has a fixed dimension, it is considered a dimensional constant. It is used to derive the dimensions of other physical quantities, such as the mass of the Earth or the radius of a planet's orbit around the Sun.