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.

Question

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

630 cm
630 cm

28.5 cm
28.5 cm

570 cm
570 cm

1.5 cm
1.5 cm

Answer 1

To find the maximum possible distance that can be drawn between Mars and Neptune in the scale model, we first need to determine their distances in the model.

1. Distance of Mars from the Sun:

   • Mars is 1.5 AU from the Sun.
   • In the model, 1 AU = 20 cm.
   • Therefore, the distance from the Sun to Mars in the model is: \[ 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \]

2. Distance of Neptune from the Sun:

   • Neptune is 30 AU from the Sun.
   • Therefore, the distance from the Sun to Neptune in the model is: \[ 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \]

3. Maximum distance between Mars and Neptune:

   • When Mars and Neptune are on opposite sides of the Sun, the maximum distance between them can be calculated by adding the distances from the Sun: \[ 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]

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