Astronomers discovered that distant galaxies move away from the Earth more rapidly than do nearby ones. To see why, make a model of the problem by drawing three equally spaced dots along a cut rubber band. The dot at one end represents the Earth, and the other two dots represent galaxies. Stretch the rubber band to twice its length. This stretching represents Universe expansion. Pretend that it took 1 second to stretch the line (so Time \(=1\) second). Calculate the velocities of the two galaxies, using the equation: Velocity \(=\) Distance \(\div\) Time. (C)

When we consider the movement of galaxies in the cosmos, we're delving into the remarkable observation that galaxies are not stationary within the universe; rather, they are drifting apart from one another. The motion of galaxies can be visualized using a simple model: imagine the universe as the rubber band in the exercise, with the galaxies represented by dots. As the rubber band stretches, mimicking the expansion of the universe, we observe that the distance between the dots increases.

This increase in distance over time is what astronomers define as the velocity of a galaxy. It is calculated using the fundamental formula: Velocity = Distance ÷ Time. In the exercise example, after the rubber band is stretched, Galaxy 1 has moved a distance 'x' in one second, and Galaxy 2 has moved a distance '2x' in the same time. Therefore, their velocities are 'x' per second and '2x' per second, respectively. This demonstrates that the velocity at which a galaxy is moving away from us is directly proportional to its distance from us—the further away it is, the faster it seems to move away.

The simple yet powerful rubber band model also highlights that as the distance increases, not only does the velocity increase but this occurs at a uniform rate, which is the basic premise behind a much larger principle in cosmology, known as Hubble's Law.

Hubble’s Law, named after astronomer Edwin Hubble, who made the groundbreaking discovery in the 1920s, illustrates a fundamental property of our universe: galaxies appear to recede from each other at speeds proportional to their distances. This concept can be expressed mathematically as: \( v = H_0 \times d \), where \( v \) is the velocity at which a galaxy moves away from an observer, \( H_0 \) (Hubble’s constant) is the proportionality constant, and \( d \) denotes the distance of the galaxy from the observer.

In the context of the classroom exercise, Hubble’s Law can explain why Galaxy 2, which is double the distance of Galaxy 1 from the 'Earth,' moves away at double the velocity. This direct proportionality between velocity and distance underpins the observation that the universe is expanding uniformly. Astronomers utilize Hubble's Law not only to infer the motion of galaxies but also to estimate the scale and age of the universe. This law is monumental in the field of cosmology and is a key piece in understanding how galaxies are distributed in the universe and how they move within the cosmic fabric.

Cosmology is the scientific study of the origins, evolution, and eventual fate of the universe. It encompasses not only the large-scale structures and dynamics of the cosmos but also the laws of physics that govern them. The field relies on theories of physics and astronomical observations to build comprehensive models of the universe’s history and its various components, such as dark matter, dark energy, and black holes.

One of the central themes in cosmology is the expansion of the universe, which has been supported by observational evidence, such as the redshift of light from distant galaxies and the cosmic microwave background radiation. As touched on in the lesson on Hubble's Law, the motion of galaxies allows cosmologists to peek into the very fabric of space-time and deduce that the universe is not static, but rather expanding.

Understanding how the universe expands and the rate at which it does (Hubble’s constant) presents profound implications for our knowledge about its contents and its ultimate destiny. Whether the universe will continue to expand indefinitely, halt, or reverse into a collapse (the 'Big Crunch') is a pivotal question in cosmology. These insights into the behavior of galaxies and the laws that govern them are crucial in comprehending how our universe works as a whole and our place within it.