Ask a New Question
Menu

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 28.5 cm 28.5 cm 570 cm

1 answer

To determine the maximum possible distance between Mars and Neptune in the scale model, we first calculate their actual distances from the sun in astronomical units (AU) and convert those distances to centimeters using the given scale (1 AU = 20 cm).

  1. Calculate the distance of Mars from the sun in centimeters:

    • Mars is 1.5 AU from the sun.
    • Distance from the sun in the scale model: \( 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \)

  2. Calculate the distance of Neptune from the sun in centimeters:

    • Neptune is 30 AU from the sun.
    • Distance from the sun in the scale model: \( 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \)

  3. Calculate the maximum distance between Mars and Neptune:

    • When Mars and Neptune are on opposite sides of the sun, the total distance between them is the sum of their distances from the sun.
    • Maximum distance = Distance from Mars to sun + Distance from Neptune to sun
    • Maximum distance = \( 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \)

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