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

1.5 cm
1.5 cm

630 cm
630 cm

570 cm
570 cm

28.5 cm

Answer 1

To determine the maximum possible distance between Mars and Neptune in the scale model, we can start with the scale established in the paragraph.

1 AU is represented in the model as 20 cm, so we can calculate the distances of Mars and Neptune from the sun in the model:

• Mars is 1.5 AU away from the sun: \( 1.5 \text{ AU} \times 20 \text{ cm/AU} = 30 \text{ cm} \)

• Neptune is 30 AU away from the sun: \( 30 \text{ AU} \times 20 \text{ cm/AU} = 600 \text{ cm} \)

Now, for the maximum distance between Mars and Neptune when they are on opposite sides of the sun, we can add their distances from the sun:

• Distance between Mars and Neptune: \( 30 \text{ cm} + 600 \text{ cm} = 630 \text{ cm} \)

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