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Use this paragraph: In a scale model of the solar system, the sun is placed at the center and the planets are shown orbiting in circles around it. Mars is 1.5 AU away from the sun and in the model, it appears at 30 cm from it which means that 1 AU = 20 cm. Likewise, Neptune is 30 AU away from the sun. What is the maximum possible distance that can be drawn between Mars and Neptune in the scale model? Hint: Two planets are as far apart as possible when they are on directly opposite sides of the sun from each other. Draw a picture with the planets as far apart as possible. (1 point) Responses 1.5 cm 1.5 cm 630 cm 630 cm 570 cm 570 cm 28.5 cm

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To determine the maximum possible distance between Mars and Neptune in the scale model, we first need to convert their distances from the sun into the scale used in the model.

  1. Convert the distances of Mars and Neptune from AU to cm:

    • Mars is 1.5 AU away from the sun: \[ \text{Distance of Mars in cm} = 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \]
    • Neptune is 30 AU away from the sun: \[ \text{Distance of Neptune in cm} = 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \]

  2. Calculate the maximum distance between Mars and Neptune:

    • If Mars and Neptune are on directly opposite sides of the sun, the maximum distance between them is: \[ \text{Maximum distance} = \text{Distance of Mars} + \text{Distance of Neptune} \] \[ \text{Maximum distance} = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]

Thus, the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 630 cm.