To find the maximum possible distance between Mars and Neptune in the scale model, we first need to determine their positions in relation to the sun.
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Distance of Mars from the Sun:
- Mars is 1.5 AU away from the sun, which in the scale model is: \[ 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \]
- So, Mars is positioned 30 cm from the sun.
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Distance of Neptune from the Sun:
- Neptune is 30 AU away from the sun. In the scale model, this distance is: \[ 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \]
- Thus, Neptune is placed 600 cm from the sun.
To find the maximum distance between Mars and Neptune when they are on opposite sides of the sun, we add the distances from the sun:
\[ \text{Distance}_{\text{max}} = \text{Distance from Sun to Mars} + \text{Distance from Sun to Neptune} \]
Calculating this:
\[ \text{Distance}_{\text{max}} = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]
Therefore, the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 630 cm.