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)

1.5 cm
1.5 cm

630 cm
630 cm

28.5 cm
28.5 cm

570 cm
570 cm

Answer 1

Answer:

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Answer 2

A scale drawing is a drawing of a real object such that the sides are accurately reduced or enlarged

Part A;

The maximum distance between Mars and Neptune, $d_m$ = 630 cm

Part B; Please find attached, the drawing of the planets, Mars and Neptune, located as far apart as  possible

The reason the above value and drawing are correct is as follows:

Part A

The given parameters are;

The distance Mars is away from the Sun, D₁ = 1.5 AU

In the scale model Mars at d₁ = 30 cm from the Sun

The scale of the drawing is 1 AU = 20 cm

The distance of Neptune from the Sun, D₂ = 30 AU

The maximum distance between Mars and Neptune

The required parameter:

To find the maximum possible distance that can be drawn between Mars and Neptune

Solution:

The distance between Neptune and the Sun, on the scale drawing, d₂, is found as follows;

The scale of the drawing, s = 20 cm/(1 AU)

d₂ = D₂ × s

∴ d₂ = 30 AU × 20 cm/(1 AU) = 600 cm

The maximum distance between Mars and Neptune, $d_m$ = d₁ + d₂

$d_m$ = 30 cm + 600 cm = 630 cm

The maximum distance between Mars and Neptune, $d_m$ = 630 cm

Part B:

Please find attached the required drawing of the planets located as far as possible, created with MS Visio

Learn more about scale drawing here:

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