Question

system
she calculates that the distance between the earth and the moon should be about 10 centimeters in her model. a should the sun be from the earth in frannys model?
a. 15 centimeters
b. 2.0 meters
c. 50 meters
d. 20 centimeters

Explanation:

Step1: Recall real-world distance ratios

The real average distance between Earth and Moon is ~$3.84 \times 10^8$ m, and Earth to Sun is ~$1.5 \times 10^{11}$ m. Calculate the ratio:
$$\frac{\text{Earth-Sun distance}}{\text{Earth-Moon distance}} = \frac{1.5 \times 10^{11}}{3.84 \times 10^8} \approx 390.6$$

Step2: Apply ratio to model distance

Model Earth-Moon distance = 10 cm. Multiply by the ratio:
$$10\ \text{cm} \times 390.6 = 3906\ \text{cm} = 39.06\ \text{m}$$
This value is closest to 50 meters.

Answer:

C. 50 meters