Question

make sure to write down your calculations with units!
scale = model size/real size
model size = real size * scale
1 m = 1000 m
1 au = 149,600,000 km
name of planet uranus
diameter 31518 miles
distance from the sun (average) in km 2,872,500,000
distance from the sun (average) in au 19.2
at a scale of 1m/1au, how far from the sun will the model planet be?
19.2 au×1m/1au = 19.2 m
at a scale of 1m/1au, how large will the model planet be?
31518/149600000 0.0022 km
at a scale where the sun is 1.0 m in diameter, how large would the model planet be?
at a scale where the sun is 1.0 m in diameter, how far would the model be from it?

Explanation:

Step1: Convert diameter from miles to km

1 mile = 1.60934 km, so 31518 miles * 1.60934 km/mile = 50749.71 km

Step2: Calculate model size for 1m/1AU scale (diameter)

First, note 1 AU = 149600000 km. Scale is 1m/1AU. Model size = real size scale. So, $\frac{50749.71}{149600000}$ km 100 cm/km = 0.0339 cm

Step3: Calculate model - Sun distance for Sun - 1m diameter scale

Let's assume we need to find a new scale based on the Sun's real diameter (1391000 km) and model Sun diameter (1m). New scale = 1m/1391000 km. Distance from Sun to Uranus is 2872500000 km. Model distance = 2872500000 km * $\frac{1m}{1391000 km}$ = 2065.06 m

Step4: Calculate model size for Sun - 1m diameter scale (diameter)

Real diameter of Uranus is 50749.71 km. Model size = 50749.71 km * $\frac{1m}{1391000 km}$ = 0.0365 m = 3.65 cm

Answer:

• At a scale of 1m/1AU, model - Sun distance: 19.2 m
• At a scale of 1m/1AU, model diameter: 0.0339 cm
• At a scale where the Sun is 1.0 m in diameter, model diameter: 3.65 cm
• At a scale where the Sun is 1.0 m in diameter, model - Sun distance: 2065.06 m