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) ○ 630 cm ○ 28.5 cm ○ 1.5 cm ○ 570 cm

Explanation:

Step1: Find distance of Neptune in model

Given \(1\ AU = 20\ cm\) and Neptune is \(30\ AU\) from sun. So distance of Neptune from sun in model: \(30\times20 = 600\ cm\).

Step2: Find distance of Mars in model

Mars is \(1.5\ AU\) from sun, so distance of Mars from sun in model: \(1.5\times20 = 30\ cm\) (already given, but confirm).

Step3: Calculate maximum distance between them

When on opposite sides, distance is sum of their distances from sun: \(600 + 30 = 630\ cm\)? Wait, no, wait: Wait, Mars is \(1.5\ AU\), Neptune \(30\ AU\). Wait, the hint says opposite sides, so the distance between them is (distance of Neptune from sun) + (distance of Mars from sun). Wait, but let's recheck: \(1\ AU = 20\ cm\), so Mars: \(1.5\ AU\times20\ cm/AU = 30\ cm\) (correct as given). Neptune: \(30\ AU\times20\ cm/AU = 600\ cm\). When opposite, the distance between Mars and Neptune is \(600 + 30 = 630\ cm\)? Wait, but wait, maybe I misread. Wait, Mars is \(1.5\ AU\) from sun, Neptune \(30\ AU\) from sun. If they are on opposite sides, the distance between them is \(30\ AU + 1.5\ AU = 31.5\ AU\) in real, then convert to model: \(31.5\ AU\times20\ cm/AU = 630\ cm\). Yes, that's correct.

Answer:

630 cm