Question

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 1.5 cm 1.5 cm 28.5 cm 28.5 cm 630 cm 630 cm 570 cm

Answer 1

To determine the maximum possible distance between Mars and Neptune in the scale model, we first need to establish the distances of both planets from the sun in the scale of 1 AU = 20 cm.

1. Distance of Mars from the Sun:

   • Mars is 1.5 AU away from the sun.
   • In the model: \( 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \) (which matches the given distance in the paragraph).

2. Distance of Neptune from the Sun:

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

3. Maximum Distance Between Mars and Neptune:

   • For the maximum distance, the two planets should be on opposite sides of the sun. Therefore, this is figured out by summing their distances from the sun: \[ \text{Maximum Distance} = \text{Distance from Sun to Mars} + \text{Distance from Sun to Neptune} \] \[ = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm}. \]

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