The concept of the expanding universe is intrinsically linked to the idea of the 'observable universe'. The observable universe refers to the part of the universe that we can see or detect from Earth, limited by the speed of light. Since the universe has a finite age (around 13.8 billion years), light from objects more than 13.8 billion light-years away hasn't had enough time to reach us. As the universe expands, distant objects recede from us, causing their light to take increasingly longer to reach us. This expansion affects our observation, as objects that were once observable may move beyond our observation horizon. Conversely, as time passes, light from more distant objects may eventually reach us, making them observable. Therefore, the expanding universe directly influences the size and contents of the observable universe, a dynamic boundary shaped by the age of the universe and the speed of light.

Redshift is a key concept in understanding the universe's expansion. It refers to the phenomenon where light from distant galaxies is shifted towards the red end of the spectrum. This shift occurs because as the universe expands, the space between us and distant galaxies also expands, stretching the light waves and increasing their wavelength. Measuring redshift involves observing the spectral lines of elements in a galaxy's light. These lines are characteristic of specific elements and have known wavelengths. By comparing the observed wavelengths with the known wavelengths, astronomers can determine how much the light has been redshifted. The extent of the redshift provides information about the galaxy's velocity relative to us, underpinning Hubble's Law. High redshift values indicate galaxies moving away faster and being farther away, supporting the theory of an expanding universe.

While the Hubble constant is essential for estimating the age of the universe, there are several limitations to this approach. Firstly, the value of the Hubble constant is not precisely known; different methods of measurement have yielded slightly different values. These variations can significantly impact the calculated age of the universe. Secondly, the assumption that the Hubble constant has remained constant over time is an oversimplification. The expansion rate of the universe may have changed due to factors like dark energy. Lastly, the method assumes a universe that has been expanding at a constant rate since its inception, which may not account for complex early universe dynamics. Therefore, while the Hubble constant provides a useful estimate, it is subject to uncertainties and simplifications that limit its accuracy.

Dark matter and dark energy are crucial concepts in understanding the expanding universe and Hubble's Law. Dark matter, which does not emit or absorb light, is believed to constitute about 27% of the universe's mass-energy content. It plays a vital role in the formation and clustering of galaxies, influencing the universe's large-scale structure. Dark energy, on the other hand, is a mysterious form of energy that makes up about 68% of the universe and is believed to be responsible for the acceleration of the universe's expansion. Hubble's Law, which describes the expansion of the universe, is influenced by dark energy, as this energy affects the rate at which galaxies are moving away from each other. The discovery of the universe's accelerating expansion, which deviates from the predictions made by Hubble's Law under the assumption of only gravitational forces, suggests the presence of dark energy as a dominant force in the universe's dynamics.

Hubble's Law is not applicable to objects within our galaxy due to the law's reliance on the large-scale structure of the universe. Hubble's Law states that the velocity at which a galaxy moves away from us is proportional to its distance, a relationship that holds true for distant galaxies. However, within our galaxy, the gravitational interactions between objects dominate over the effects of the universe's expansion. The motion of stars and other objects within the Milky Way is influenced more by the galaxy's gravitational field than by the expansion of space. Therefore, the velocities and positions of these objects cannot be accurately described using Hubble's Law, which is designed to explain the behaviour of objects on a much larger, intergalactic scale.