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

28.5 cm
28.5 cm

1.5 cm
1.5 cm

570 cm
570 cm

630 cm

Answer 1

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

• Mars is 1.5 AU away from the sun. In the model, this translates to: \[ 1.5 \text{ AU} \times 20 \text{ cm/AU} = 30 \text{ cm} \]

• Neptune is 30 AU away from the sun. In the model, this translates to: \[ 30 \text{ AU} \times 20 \text{ cm/AU} = 600 \text{ cm} \]

Now, if Mars and Neptune are on directly opposite sides of the sun, the maximum distance between them (d) can be calculated by adding their distances from the sun: \[ d = \text{Distance from Sun to Mars} + \text{Distance from Sun to Neptune} \] \[ d = 30 \text{ cm} + 600 \text{ cm} = 630 \text{ cm} \]

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