Question

Astronomers discovered that more-distant galaxies move away from the Earth more rapidly than do nearer ones. Why? To answer this question, make a model of the problem by drawing three equally spaced dots along a line; the dot at one end represents the Earth, and the other two represent galaxies. "Stretch" the line by drawing the line and dots again, but this time make the line twice as long. This stretching represents Universe expansion. Notice that the dots are now farther apart. Using the following equation for velocity (Velocity \(=\) Distance/Time) \(-\) if you pretend that it took 1 second to stretch the line (so Time \(=1\) second), measurement of the distance that each galaxy moved relative to the Earth allows you to calculate velocity.

Short answer

The model of the expanding universe demonstrates that more-distant galaxies move away from Earth more rapidly than nearer ones. By stretching the line, Galaxy 1 moves a distance of "d" and Galaxy 2 moves a distance of "2d." Since it took 1 second to stretch the line, Galaxy 1's velocity is d units per second and Galaxy 2's velocity is 2d units per second. This shows that as the universe expands, more-distant objects appear to move away faster due to the proportional increase in distances.

Step-by-step solution

Draw the initial model

Draw a line with three equally spaced dots. Label the dot at one end as "Earth" and the other two dots as "Galaxy 1" and "Galaxy 2". The distances between Earth and Galaxy 1, and between Galaxy 1 and Galaxy 2 are equal and can be represented as "d".

Stretch the line

Draw the line again, but this time make it twice as long. The dots will now be farther apart. The distances between Earth and Galaxy 1, and between Galaxy 1 and Galaxy 2 are now both "2d".

Calculate the distances each galaxy moved

To calculate the distances each galaxy moved, subtract their initial distances from their final distances. For Galaxy 1: Final distance - Initial distance = \(2d - d = d\) For Galaxy 2: Final distance - Initial distance = \(2(2d) - 2d = 2d\)

Calculate the velocities using the equation for velocity

Given that it took 1 second to stretch the line, the time (t) is 1 second. Using the velocity equation (Velocity = Distance/Time), calculate the velocities for both galaxies. For Galaxy 1: Velocity = Distance/Time = \(d/1\) = d (units per second) For Galaxy 2: Velocity = Distance/Time = \(2d/1\) = 2d (units per second)

Observe the relationship between distance and velocity

From the calculated velocities, we can observe that more-distant galaxies move away from Earth more rapidly than do nearer ones. The velocity of Galaxy 2 (2d units per second) is twice as fast as the velocity of Galaxy 1 (d units per second), even though the initial distances between Earth and both galaxies were equal. This occurs because the expansion of the universe causes all distances to increase proportionally, making more-distant objects appear to move away faster.

Key concepts

Galaxy Movement

The movement of galaxies is a fascinating phenomenon that has captivated astronomers for decades. It's important to understand that galaxies do not move through space in the way that a car moves along a road. Instead, it is the very fabric of space itself that is expanding, carrying galaxies along with it. This means that galaxies are not traveling through space so much as they are being swept along by the space that's stretching out between them.

As a result of this expansion, galaxies that are farther away from us appear to move away faster than those that are closer. Returning to our exercise, when we 'stretched' the line representing space to twice its original length, Galaxy 2, being farther from Earth initially, moved through a greater distance than Galaxy 1, which was closer. This is a simplified model helping us visualize how universe expansion affects galaxy movement, and it leads us into the broader implications of these observations, encompassing concepts such as the Big Bang and the ultimate fate of the universe.

Hubble's Law

Hubble's Law is a fundamental concept in cosmology that describes the relationship between the distances of galaxies from Earth and their velocities. Formulated by Edwin Hubble in 1929, it states that galaxies are moving away from us at speeds proportional to their distance. This means that, the farther away a galaxy is, the faster it appears to be moving away.

In mathematical terms, Hubble's Law is often expressed as \( v = H_0 \cdot d \), where \( v \) is the velocity at which a galaxy is moving away from Earth, \( d \) is the galaxy's distance from Earth, and \( H_0 \) is the Hubble constant, a value that represents the rate of expansion of the universe. The exercise we explored earlier provides insight into this law, showing that by doubling the distance due to 'stretching' space, the velocity of the galaxies relative to Earth also increases. This directly reflects Hubble's observation that more distant galaxies exhibit higher recession velocities.

Cosmology

Cosmology is the study of the universe as a whole, including its origins, structure, evolution, and eventual fate. It encompasses the grandest scales of space and time, aiming to understand the entire cosmos from the very beginning to the far future. Cosmologists use theories and observations to explore the properties and behaviors of the universe, including the expansion we've been discussing.

Cosmology brings together many aspects of physics and astronomy to interpret high-level phenomena, such as the Big Bang, dark energy, dark matter, and the cosmic microwave background radiation. Through models and equations, like that of Hubble's Law, we gain insights into how the universe works on a fundamental level. The motion of galaxies is one piece of a much larger puzzle in which cosmologists are fitting together the history and the extensive, dynamic nature of the cosmos that surrounds us.