Find the age of the universe based upon Hubble's initial works Age of Universe (1/Ho) x (3.08 x 1019 km/Mpc) x (1 year/3.15 x 10' sec) = %3D %3D %3 (1/563 km/sec/Mpc) x (3.08 x 1019 km/Mpc) x (1/3.15 x 10' sec) 1.7 yrs
Find the age of the universe based upon Hubble's initial works Age of Universe (1/Ho) x (3.08 x 1019 km/Mpc) x (1 year/3.15 x 10' sec) = %3D %3D %3 (1/563 km/sec/Mpc) x (3.08 x 1019 km/Mpc) x (1/3.15 x 10' sec) 1.7 yrs
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![### Determining the Hubble Constant and the Age of the Universe
#### Calculating Hubble's Constant (Ho)
To find Hubble's Constant (\(H_0\)), follow these steps:
1. **Draw a Best Fit Line:** Draw a line that best fits the points on the data plot. This line represents the relationship between the velocity (Y-axis) of the galaxies and their distance (X-axis).
2. **Calculate the Slope:** Use the slope formula, which in this context represents Hubble's Constant.
\[
H_0 = \text{slope} = \frac{\text{velocity}}{\text{distance}} = \frac{\text{change in } Y}{\text{change in } X} = \frac{Y_2 - Y_1}{X_2 - X_1}
\]
Given the values:
\[
\frac{350}{0.6} = \textbf{583 km/sec/Mpc}
\]
#### Finding the Age of the Universe
To determine the age of the universe based on Hubble's initial work, follow these steps:
1. **Understanding Unit Conversions:**
- 1 Mpc (Megaparsec) = \(3.08 \times 10^{19}\) km
- 1 year = \(3.15 \times 10^7\) seconds
2. **Formula for Age of the Universe:**
\[
\text{Age of Universe} = \left( \frac{1}{H_0} \right) \times (3.08 \times 10^{19} \text{ km/Mpc}) \times \left( \frac{1 \text{ year}}{3.15 \times 10^7 \text{ sec}} \right)
\]
Substituting \(H_0 = 583 \text{ km/sec/Mpc}\):
\[
\text{Age of Universe} = \left( \frac{1 \text{ sec}}{583 \text{ km/Mpc}} \right) \times (3.08 \times 10^{19} \text{ km/Mpc}) \times \left( \frac{1 \text{ year}}{3.15 \times 10^7 \text{ sec}} \right)
\]
3. **Simplifying](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81152691-2184-4c83-8479-c547a590b68f%2Ff128c7ba-b8d4-4bf0-8ca7-c655b915648e%2Faqbbz5_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Hubble Constant and the Age of the Universe
#### Calculating Hubble's Constant (Ho)
To find Hubble's Constant (\(H_0\)), follow these steps:
1. **Draw a Best Fit Line:** Draw a line that best fits the points on the data plot. This line represents the relationship between the velocity (Y-axis) of the galaxies and their distance (X-axis).
2. **Calculate the Slope:** Use the slope formula, which in this context represents Hubble's Constant.
\[
H_0 = \text{slope} = \frac{\text{velocity}}{\text{distance}} = \frac{\text{change in } Y}{\text{change in } X} = \frac{Y_2 - Y_1}{X_2 - X_1}
\]
Given the values:
\[
\frac{350}{0.6} = \textbf{583 km/sec/Mpc}
\]
#### Finding the Age of the Universe
To determine the age of the universe based on Hubble's initial work, follow these steps:
1. **Understanding Unit Conversions:**
- 1 Mpc (Megaparsec) = \(3.08 \times 10^{19}\) km
- 1 year = \(3.15 \times 10^7\) seconds
2. **Formula for Age of the Universe:**
\[
\text{Age of Universe} = \left( \frac{1}{H_0} \right) \times (3.08 \times 10^{19} \text{ km/Mpc}) \times \left( \frac{1 \text{ year}}{3.15 \times 10^7 \text{ sec}} \right)
\]
Substituting \(H_0 = 583 \text{ km/sec/Mpc}\):
\[
\text{Age of Universe} = \left( \frac{1 \text{ sec}}{583 \text{ km/Mpc}} \right) \times (3.08 \times 10^{19} \text{ km/Mpc}) \times \left( \frac{1 \text{ year}}{3.15 \times 10^7 \text{ sec}} \right)
\]
3. **Simplifying
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