The table gives size and distance data for the planets at a certain point in time. Calculate the scaled size and distance for each planet using a 1 to 10 billion scale model of the solar system.
Planet
Diameter
Distance from Sun
 
Mercury
4880 km  
56.3 million km  
Venus
12 comma 100 km  
108.2 million km  
Earth
12 comma 760 km  
150.3 million km  
Mars
6790 km  
241.8 million km  
Jupiter
143 comma 000 km  
812.4 million km  
Saturn
120 comma 000 km  
1397 million km  
Uranus
52 comma 000 km  
2899 million km  
Neptune
48 comma 400 km  
4499 million km  
Question content area bottom
Part 1
Complete the following table.
​(Type integers or decimals rounded to the nearest tenth as​ needed.)
Planet
Diameter
Distance from Sun
Mercury
  
enter your response here mm   
  
enter your response here m        


To solve this problem, we need to apply the given scale of 1 to 10 billion to both the diameter and distance from the Sun for each planet.

### Conversion Details:
- **Scale:** 1 to 10 billion (1:10,000,000,000)
- This means that every 1 kilometer in real life is scaled down to \( \frac{1}{10,000,000,000} \) kilometers in the model.
- To find the scaled **diameter** in millimeters, we multiply the actual diameter by \( \frac{1}{10,000,000,000} \times 1,000,000 \) to convert to millimeters.
- To find the scaled **distance from the Sun** in meters, we multiply the actual distance by \( \frac{1}{10,000,000,000} \).

### Mercury
- **Diameter:** 4880 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{4880 \, \text{km}}{10,000,000,000} \times 1,000,000 = 0.488 \, \text{mm}
  \]
- **Distance from the Sun:** 56.3 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{56,300,000 \, \text{km}}{10,000,000,000} = 5.63 \, \text{m}
  \]

### Venus
- **Diameter:** 12,100 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{12,100 \, \text{km}}{10,000,000,000} \times 1,000,000 = 1.21 \, \text{mm}
  \]
- **Distance from the Sun:** 108.2 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{108,200,000 \, \text{km}}{10,000,000,000} = 10.82 \, \text{m}
  \]

### Earth
- **Diameter:** 12,760 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{12,760 \, \text{km}}{10,000,000,000} \times 1,000,000 = 1.276 \, \text{mm}
  \]
- **Distance from the Sun:** 150.3 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{150,300,000 \, \text{km}}{10,000,000,000} = 15.03 \, \text{m}
  \]

### Mars
- **Diameter:** 6790 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{6790 \, \text{km}}{10,000,000,000} \times 1,000,000 = 0.679 \, \text{mm}
  \]
- **Distance from the Sun:** 241.8 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{241,800,000 \, \text{km}}{10,000,000,000} = 24.18 \, \text{m}
  \]

### Jupiter
- **Diameter:** 143,000 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{143,000 \, \text{km}}{10,000,000,000} \times 1,000,000 = 14.3 \, \text{mm}
  \]
- **Distance from the Sun:** 812.4 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{812,400,000 \, \text{km}}{10,000,000,000} = 81.24 \, \text{m}
  \]

### Saturn
- **Diameter:** 120,000 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{120,000 \, \text{km}}{10,000,000,000} \times 1,000,000 = 12.0 \, \text{mm}
  \]
- **Distance from the Sun:** 1397 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{1,397,000,000 \, \text{km}}{10,000,000,000} = 139.7 \, \text{m}
  \]

### Uranus
- **Diameter:** 52,000 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{52,000 \, \text{km}}{10,000,000,000} \times 1,000,000 = 5.2 \, \text{mm}
  \]
- **Distance from the Sun:** 2899 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{2,899,000,000 \, \text{km}}{10,000,000,000} = 289.9 \, \text{m}
  \]

### Neptune
- **Diameter:** 48,400 km  
  Scaled Diameter:  
  \[
  \text{Scaled Diameter} = \frac{48,400 \, \text{km}}{10,000,000,000} \times 1,000,000 = 4.84 \, \text{mm}
  \]
- **Distance from the Sun:** 4499 million km  
  Scaled Distance:  
  \[
  \text{Scaled Distance} = \frac{4,499,000,000 \, \text{km}}{10,000,000,000} = 449.9 \, \text{m}
  \]

### Final Table
Here is the complete table with scaled sizes and distances:

| Planet   | Diameter (mm) | Distance from Sun (m) |
|----------|---------------|-----------------------|
| Mercury  | 0.488         | 5.63                  |
| Venus    | 1.21          | 10.82                 |
| Earth    | 1.276         | 15.03                 |
| Mars     | 0.679         | 24.18                 |
| Jupiter  | 14.3          | 81.24                 |
| Saturn   | 12.0          | 139.7                 |
| Uranus   | 5.2           | 289.9                 |
| Neptune  | 4.84          | 449.9                 |

Would you like further explanations on how these values were calculated? Here are some related questions you might consider:

1. What would be the scaled diameter of the Sun using the same scale?
2. How would the model change if the scale was 1 to 5 billion instead?
3. What is the ratio of the scaled distances between Mars and Jupiter?
4. How does the scaled distance of Neptune compare to that of Earth?
5. How does the diameter of Jupiter compare to that of Earth in the scaled model?

**Tip:** Always double-check your unit conversions when working with scales to avoid common errors.

Learn how to calculate the scaled size and distance of planets using a 1 to 10 billion scale model of the solar system. This problem involves proportional reasoning and unit conversions. Suitable for Grades 6-8.

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