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

570 cm
570 cm

28.5 cm
28.5 cm

1.5 cm
1.5 cm

630 cm

Answer 1

To calculate the maximum possible distance between Mars and Neptune in the scale model, we need to consider their distances from the sun and the scale conversion factor.

1. Mars is 1.5 AU away from the sun. Scale distance of Mars from the sun: \( 1.5 , \text{AU} = 1.5 \times 20 , \text{cm} = 30 , \text{cm} \)

2. Neptune is 30 AU away from the sun. Scale distance of Neptune from the sun: \( 30 , \text{AU} = 30 \times 20 , \text{cm} = 600 , \text{cm} \)

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

\[ \text{Distance} = \text{Distance from Mars to the sun} + \text{Distance from Neptune to the sun} = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]

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