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The gravitational constant, denoted by the symbol G, is a fundamental quantity in physics that plays a crucial role in the law of universal gravitation. Its value is approximately \(6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2\) and it appears prominently in Newton's equation for gravitational force, which is \(F = G \frac{ M \times m}{ r^2} \), where F is the gravitational force, M and m are the masses, and r is the distance between their centers.

Understanding the gravitational constant is essential because it is the proportionality factor that allows us to calculate the gravitational attraction between any two masses. For a shrinking star, even though its mass remains constant, the gravitational field intensity on its surface changes due to alterations in radius. This is because the gravitational constant serves as the 'multiplier' that, paired with the mass and inverse square of the radius, defines the strength of the gravitational field at a point in space.

Celestial mechanics is the branch of astronomy that deals with the motions and gravity-induced interactions of celestial bodies. It relies heavily on Newton's law of universal gravitation and the laws of motion to predict the orbits of planets, moons, and artificial satellites.

The principles of celestial mechanics can be applied to understand the changes in the gravitational field intensity of a star as it shrinks. As the star's radius decreases, celestial mechanics predicts that objects on or near the star's surface will experience a stronger gravitational pull. This is intertwined with the concept of orbits; for example, if a planet were orbiting the shrinking star, the change in gravitational field intensity could potentially alter its orbit. Overall, celestial mechanics helps us map out the cosmic dance guided by gravity and understand the mechanical consequences of changes in celestial objects.

Stellar evolution encompasses the changes a star undergoes during its lifecycle, from its formation to the ultimate fate that awaits it. This process can take billions of years and is driven by a balance between the gravitational forces and the outward pressure from nuclear fusion occurring at the star's core.

When a star is referred to as 'shrinking', this suggests a phase in its evolution, possibly when it transitions into a white dwarf or after it has exhausted the fuel for nuclear fusion. The increased gravitational field intensity on its surface reflects the physical changes during this phase. Throughout the evolutionary process, the star's structure, chemistry, and dynamics alter dramatically, all of which are intricately linked to gravitational interactions. By examining the stages of stellar evolution, we gain insights not only into the life stories of stars but also into the fundamental forces at play, such as gravity, that sculpt the universe's architecture.