Question

data table
galaxy | distance (millions of ly) | velocity (thousands of km/sec)
a | 0 (milky way = here) | 0
b | 800 | 21,000
c | 400 | 10,000
d | 1600 | 51,000
e | | __,000
f | | __,000
g | | __,000
h | | __,000
i | | __,000
j | | __,000
k | | __,000
l | | __,000
m | | __,000
n | | __,000
o | | __,000
p | | __,000
q | | __,000
r | | __,000

□ use the data on previous page to fill out the distance and velocity columns of the table!
□ then, plot each point on the graph and label it with the letter for that galaxy. galaxy a has already been done for you.
□ use the graph to answer the questions!

galaxy distance vs. velocity graph
hubbles law

? as the distance increases, the velocity ________.

? explain how the graph and data supports (or does not support) the big bang theory- which states the universe is expanding at a faster and faster rate:

Explanation:

First Question (As the DISTANCE INCREASES, the VELOCITY ______):

Looking at the trend from the given data (Galaxy A has distance 0 and velocity 0; other galaxies with increasing distance have increasing velocity values like Galaxy B: distance 800, velocity 21,000; Galaxy C: distance 400, velocity 10,000; Galaxy D: distance 1600, velocity 51,000) and the graph's setup for Hubble's Law (which relates galaxy distance and recessional velocity), as distance (from Milky Way) increases, velocity (recessional) increases.

1. Hubble's Law Basics: Hubble's Law is \( v = H_0 d \), where \( v \) is recessional velocity, \( d \) is distance, and \( H_0 \) is Hubble's constant. If the universe is expanding at an accelerating rate (as Big Bang theory with dark energy suggests), the graph of velocity vs. distance should show a curve that gets steeper (or if we consider the simple linear Hubble's Law, a linear trend, but acceleration would mean deviation from strict linearity over large distances, though for this data - if we plot the points:

• Galaxy A: (0,0)
• Galaxy B: (800, 21000)
• Galaxy C: (400, 10000)
• Galaxy D: (1600, 51000)
• Calculate the slope (Hubble's "constant" approximation) between A and B: \( \frac{21000 - 0}{800 - 0} = 26.25 \) (thousand km/sec per million LY)
• Between A and C: \( \frac{10000 - 0}{400 - 0} = 25 \)
• Between A and D: \( \frac{51000 - 0}{1600 - 0} = 31.875 \)
• The increasing slope (or the trend of higher distance galaxies having higher velocity - distance ratios) suggests that as distance increases, velocity is increasing at a faster rate (since the slope is increasing, meaning for each additional million LY, the velocity is increasing by more). This aligns with the Big Bang theory's implication of an expanding (and accelerating) universe, as galaxies farther away (more distance) are moving away faster, which is consistent with the universe expanding at an increasing rate.
• If the graph were a straight line with constant slope, it would be a steady expansion, but the slight increase in slope (from the given data points) or the general trend of velocity increasing with distance (and the rate of increase of velocity with distance being positive/ increasing) supports the idea that the universe is expanding faster as distance (and time, since light takes time to reach us) increases, which is part of the Big Bang theory's description of cosmic expansion.

Answer:

Increases

Second Question (Explain how the graph and data supports (or does not support) the BIG BANG THEORY - which states the universe is expanding at a faster and faster rate):