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NOT TO SCALE
The diameter of the sun is 1,391,000 km. The diameter of the moon is 3,475 km. The distance from Earth to the sun is 149,600,000 km.
How far would the moon have to be from Earth for the moon to appear the same size as the sun?
The class is going to make a scale drawing of the planets in the solar system and their distances from Earth. Your teacher will assign you a planet to draw. A circle with a diameter of 1 meter represents the sun.
| object | average diameter (km) |
average orbit radius (km) |
scaled diameter (cm) |
scaled orbit radius (cm) |
|---|---|---|---|---|
| sun | 696,340 | 0 | ||
| Mercury | 4,879 | 57,900,000 | ||
| Venus | 12,104 | 108,200,000 | ||
| Earth | 12,756 | 149,600,000 | ||
| Mars | 6,792 | 227,900,000 | ||
| Jupiter | 142,984 | 778,600,000 | ||
| Saturn | 120,536 | 1,433,500,000 | ||
| Uranus | 51,118 | 2,872,500,000 | ||
| Neptune | 49,528 | 4,495,100,000 |
Imagine that Earth is about the size of the period at the end of this sentence. That’s a diameter of 0.3 mm.
To make a scaled copy of this figure so that its new height is 3 cm instead of 8 cm, we could start calculating what the lengths of different parts of the figure would be. One way to calculate the measurements of the scaled copy is to multiply every length in the original figure by the scale factor to find the corresponding length in the scaled copy. For example, the radius of the head is 1.3 cm. Because , the radius of the scaled head is about 0.5 cm.
The length of segment is 2.4 cm. How long is segment ? Instead of multiplying by the scale factor we could use equivalent ratios. Because then . So is 0.9 cm.