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
630 cm
630 cm
1.5 cm
1.5 cm
28.5 cm
28.5 cm
570 cm
The maximum possible distance that can be drawn between Mars and Neptune in the scale model is 570 cm
To find the maximum possible distance between Mars and Neptune in the scale model, we need to consider that they are as far apart as possible when they are on directly opposite sides of the sun from each other. In this case, the distance between Mars and Neptune will be equal to the sum of their distances from the sun.
From the paragraph, we know that Mars is 1.5 AU away from the sun, which corresponds to 30 cm in the scale model. Similarly, Neptune is 30 AU away from the sun. Therefore, we can calculate the maximum possible distance between Mars and Neptune by adding their distances from the sun in the model.
The distance between Mars and Neptune in the scale model = distance of Mars from the sun + distance of Neptune from the sun
= 30 cm (distance of Mars from the sun) + 30 AU (distance of Neptune from the sun)
= 30 cm + 30 AU × 20 cm/AU (converting AU to cm using the scale)
By substituting the value of 1 AU = 20 cm, we can calculate the maximum possible distance:
= 30 cm + 30 AU × 20 cm/AU
= 30 cm + 600 cm
= 630 cm
Therefore, the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 630 cm.