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
28.5 cm
28.5 cm
1.5 cm
1.5 cm
630 cm
630 cm
570 cm
570 cm
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page 13 of 13
The maximum possible distance that can be drawn between Mars and Neptune in the scale model is 28.5 cm.
To find the maximum possible distance that can be drawn between Mars and Neptune in the scale model, we need to determine the distance between them when they are on directly opposite sides of the sun from each other.
Given that Mars is 1.5 AU away from the sun and in the model it appears at 30 cm, and that 1 AU is equal to 20 cm in the model, we can calculate the distance between Mars and the sun in centimeters by multiplying the AU distance by the scale factor:
Distance between Mars and the sun = 1.5 AU * 20 cm/AU = 30 cm
Now, since Neptune is 30 AU away from the sun, we can calculate its distance from the sun in centimeters using the same scale factor:
Distance between Neptune and the sun = 30 AU * 20 cm/AU = 600 cm
To find the maximum possible distance that can be drawn between Mars and Neptune in the scale model, we can subtract the distance from Mars to the sun from the distance from Neptune to the sun:
Maximum possible distance between Mars and Neptune = Distance between Neptune and the sun - Distance between Mars and the sun = 600 cm - 30 cm = 570 cm
Therefore, the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 570 cm.