In a scale model of the Solar System, the distance between Jupiter and Saturn is 17.2 cm. While the distance between Saturn and Uranus is 38.8 centimeters, the astronomical unit distance between Jupiter and Saturn is 4.3 AU. What is the astronomical unit between jupiter and uranus
To find the astronomical unit (AU) between Jupiter and Uranus, we need to determine the ratio between the scale model distances and the actual distances in the Solar System.
The ratio of the scale model distance between Jupiter and Saturn to the astronomical unit distance between Jupiter and Saturn is equal to the ratio of the actual distance between Jupiter and Saturn to 1 AU.
Let's say the scale model distance between Jupiter and Uranus is x cm.
From the given information, we have:
17.2 cm / 4.3 AU = x cm / (actual AU between Jupiter and Uranus)
To solve for the actual AU between Jupiter and Uranus, we can use the concept of cross-multiplication:
17.2 cm * (actual AU between Jupiter and Uranus) = 4.3 AU * x cm
17.2 cm * (actual AU between Jupiter and Uranus) = 4.3 AU * 38.8 cm
(actual AU between Jupiter and Uranus) = (4.3 AU * 38.8 cm) / 17.2 cm
(actual AU between Jupiter and Uranus) ≈ 9.712 AUs
Therefore, the astronomical unit distance between Jupiter and Uranus is approximately 9.712 AU.