To determine the maximum possible distance between Mars and Neptune in a scale model, we first need to understand their real average distances from the Sun and then decide on a scale for the model.
Real Average Distances:
- Distance from the Sun to Mars: Approximately 227.9 million km.
- Distance from the Sun to Neptune: Approximately 4.5 billion km (4,500 million km).
Calculation of Maximum Distance Between Mars and Neptune:
The maximum distance between Mars and Neptune can be calculated as follows:
\[ \text{Maximum Distance} = \text{Distance to Neptune} - \text{Distance to Mars} \] \[ \text{Maximum Distance} = 4,500 \text{ million km} - 227.9 \text{ million km} \] \[ \text{Maximum Distance} \approx 4,272.1 \text{ million km} \]
Scale Model:
To create a scale model, you need to decide on a scale. For example, if you choose a scale of 1:1 billion, then:
- In the scale model: \[ \text{Maximum Distance in Model} = \frac{4,272.1 \text{ million km}}{1,000,000,000} \] \[ = 4.2721 \text{ km} \]
You can choose different scales depending on the dimensions of your model. For example, at a scale of 1:10 billion, the distance would be 0.42721 km (or 427.21 meters).
In summary, the maximum distance in a scale model of the solar system depends on how you choose to scale it down.