Question

part d the sun has a diameter of approximately 1,391,400 kilometers. how big would the sun be in your scaled - down model of the solar system? explain how you scaled the suns diameter to fit into your model, and describe how its size compares to the planets.

Explanation:

Step1: Choose a scale

Let's assume we choose a scale such that 1 cm in our model represents 100,000 km in reality.

Step2: Calculate the scaled - down diameter of the Sun

The actual diameter of the Sun is \(d = 1,391,400\) km. Using the scale factor \(s=\frac{1}{100000}\), the scaled - down diameter \(D\) of the Sun is \(D=\frac{1391400}{100000}=13.914\) cm.

Step3: Compare with planets

In our solar system, the largest planet is Jupiter with a diameter of about 139,822 km. In our scale, Jupiter's diameter would be \(\frac{139822}{100000}=1.39822\) cm. The Sun's scaled - down size is much larger than the planets. For example, Earth has a diameter of about 12,742 km, which in our scale would be \(\frac{12742}{100000}=0.12742\) cm. So the Sun is still by far the largest object in our scaled - down model.

Answer:

First, we choose a scale (e.g., 1 cm represents 100,000 km). Then we calculate the scaled - down diameter of the Sun as 13.914 cm. Comparing with planets, Jupiter (the largest planet) has a scaled - down diameter of 1.39822 cm and Earth has 0.12742 cm. The Sun is much larger than the planets in the scaled - down model.