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

28.5 cm
28.5 cm

570 cm
570 cm

630 cm
630 cm

1.5 cm
1.5 cm

1 answer

To find the maximum possible distance between Mars and Neptune in the scale model, we will first convert their distances from the sun into centimeters based on the given scale.

  1. Distance of Mars from the Sun:

    • Mars is 1.5 AU away from the sun.
    • Using the scale where 1 AU = 20 cm,

    \[ \text{Distance of Mars} = 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \]

  2. Distance of Neptune from the Sun:

    • Neptune is 30 AU away from the sun.
    • Again, using the scale of 1 AU = 20 cm,

    \[ \text{Distance of Neptune} = 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \]

  3. Finding the Maximum Distance:

    • To find the maximum distance between Mars and Neptune when they are on opposite sides of the sun, we simply add the distances from the sun:

    \[ \text{Maximum distance} = \text{Distance of Mars} + \text{Distance of Neptune} \] \[ \text{Maximum distance} = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]

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

The correct response is:

630 cm