To determine the maximum possible distance between Mars and Neptune in a scale model, we need to consider their average distances from the Sun. The average distance from the Sun to Mars is about 227.9 million kilometers, and for Neptune, it's approximately 4.5 billion kilometers.
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First, calculate the maximum distance in kilometers when Mars and Neptune are on opposite sides of the Sun: \[ \text{Maximum distance} = \text{Distance to Mars} + \text{Distance to Neptune} \] \[ = 227.9 \text{ million km} + 4500 \text{ million km} = 4727.9 \text{ million km} \]
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Now, we need to know the scale of the model. However, assuming that the options provided are based on a set scale model where distances have already been converted into centimeters, we can determine which of the options matches the maximum distance calculated above.
The options are given in centimeters:
- 630 cm
- 28.5 cm
- 1.5 cm
- 570 cm
If we consider a typical astronomical scale model, 1 astronomical unit (AU) is about 150 million kilometers. The distance in AU for Mars and Neptune can be calculated as follows:
- Mars: approximately 1.52 AU
- Neptune: approximately 30.07 AU
Now, when they are on opposite sides of the Sun: \[ \text{Distance in AU} = 1.52 \text{ AU} + 30.07 \text{ AU} \approx 31.59 \text{ AU} \]
If we were to convert this distance to centimeters using a common astronomical scale where \( 1 \text{ AU} \approx 1 \text{ cm} \) to simplify: \[ 31.59 \text{ AU} \approx 31.59 \text{ cm} \text{ in a smaller scale model.} \]
Given the options, we see there's no conversion directly leading us to the expected values based on 1.52 AU and 30.07 AU. However, if aligning the logical distances further and interpreting the scale for distances beyond the common size of such models, a distance of 630 cm is plausible in larger scale representations of the solar system.
Ultimately, based on common astronomical scaling practices and the understanding of opposite and away placement in a model, the maximum possible distance in the given options should be:
630 cm