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Answer :
The scale that Rob should use for his models is 1: 5 × 10^10. This means that every 1 unit in the model represents 5 × 10^10 units in reality.
What is the ratio between the distance in the model and the real distance between the two objects?
To work out the scale that Rob should use for his models of the Sun and Jupiter, we need to find the ratio between the distance in the model and the real distance between the two objects.
Let's first convert the real distance between Jupiter and the Sun from kilometers to meters:
8 × 10^8 km = 8 × 10^11 m
Now, we can use this real distance and the desired distance between the models of 16 m to find the scale. Let's call the scale "1:n".
We can set up a proportion as follows:
model distance / real distance = 1 / n
where the model distance is the distance between the models in Rob's scale model and the real distance is the distance between Jupiter and the Sun in reality.
Plugging in the values we have:
16 m / (8 × 10^11 m) = 1 / n
Solving for n:
n = (8 × 10^11 m) / 16 m = 5 × 10^10
So, the scale that Rob should use for his models is 1 : 5 × 10^10. This means that every 1 unit in the model represents 5 × 10^10 units in reality.
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