To find the astronomical unit (AU) distance between Jupiter and Uranus, we first need the distances between Jupiter and Saturn, and between Saturn and Uranus in AU.
We know that:
- The distance between Jupiter and Saturn is 4.3 AU (this is given).
- The distance from Saturn to Uranus in the scale model is 38.8 cm.
To find the distance in AU from Saturn to Uranus, we need to determine how the distances in the scale model correspond to actual astronomical units.
The scale model gives us:
- The distance between Jupiter and Saturn in the scale model = 17.2 cm corresponds to 4.3 AU.
We can use this to find the scale (AU per cm): \[ \text{Scale} = \frac{4.3 , \text{AU}}{17.2 , \text{cm}} \approx 0.250 , \text{AU/cm} \]
Now, we can convert the distance from Saturn to Uranus in the scale model (38.8 cm) into AU: \[ \text{Distance from Saturn to Uranus in AU} = 38.8 , \text{cm} \times 0.250 , \text{AU/cm} = 9.7 , \text{AU} \]
To find the total distance from Jupiter to Uranus, we add the distance from Jupiter to Saturn and the distance from Saturn to Uranus: \[ \text{Distance between Jupiter and Uranus} = 4.3 , \text{AU} + 9.7 , \text{AU} = 14 , \text{AU} \]
The astronomical unit distance between Jupiter and Uranus is 14 AU.
So the correct response is: 14 AU.
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