To find the astronomical unit distance between Jupiter and Uranus, we first need to establish the relationship between the distances given.
We know:
- The distance between Jupiter and Saturn is 4.3 AU.
- The distance between Saturn and Uranus is 38.8 cm, but we don't have a direct astronomical unit distance for that yet.
Explore the scale:
- Let's assume 1 AU corresponds to a certain number of centimeters in the scale model.
- We're given that the distance between Jupiter and Saturn is 17.2 cm, so we can calculate 1 AU in the model.
The scale from Jupiter to Saturn in the model translates to: \[ \text{Distance in AU} = \frac{\text{Model distance (cm)}}{\text{Actual distance (AU)}} \] \[ 4.3 \text{ AU} = 17.2 \text{ cm} \] \[ 1 \text{ AU} = \frac{17.2 \text{ cm}}{4.3 \text{ AU}} \] \[ 1 \text{ AU} = 4 \text{ cm/AU} \]
Now, the distance from Saturn to Uranus in AU can be calculated:
- First, we convert the distance from Saturn to Uranus to AU using the scale.
- 38.8 cm would be converted as follows: \[ \text{Distance in AU} = \frac{38.8 \text{ cm}}{4 \text{ cm/AU}} = 9.7 \text{ AU} \]
Now, add the distance from Jupiter to Saturn (4.3 AU) to the distance from Saturn to Uranus (9.7 AU): \[ \text{Distance from Jupiter to Uranus} = 4.3 \text{ AU} + 9.7 \text{ AU} = 14 \text{ AU} \]
Thus, the astronomical unit distance between Jupiter and Uranus is 14 AU.