Question

In constructing a scale model solar system with a 1 to 10 billion scale ratio, analyze the scaled size and distance for the planet Mercury. Given that Mercury has a diameter of 4880 km and is located 56.6 million km from the Sun, calculate the corresponding scaled dimensions for both size and distance. Discuss the methodology and mathematical procedures involved in establishing the scale model, and elucidate the implications of using a 1 to 10 billion scale ratio in accurately representing the size and relative distances of celestial bodies within the solar system.

Answer 1

To construct a scale model of the solar system with a 1 to 10 billion scale ratio, we can calculate the scaled size and distance for Mercury. The scaled diameter of Mercury would be 0.488 mm and the scaled distance from the Sun would be 5.66 cm. Using a 1 to 10 billion scale ratio accurately represents the size and relative distances of celestial bodies in the solar system.

Step-by-step explanation:

In constructing a scale model of the solar system with a 1 to 10 billion scale ratio, we can analyze the scaled size and distance for the planet Mercury. Given that Mercury has a diameter of 4880 km and is located 56.6 million km from the Sun, we can calculate the corresponding scaled dimensions for both size and distance.

To establish the scale model, we divide the actual diameter and distance of Mercury by the scale factor of 10 billion. This gives us a scaled diameter of 0.488 mm and a scaled distance of 5.66 cm.

Using a 1 to 10 billion scale ratio allows us to accurately represent the size and relative distances of celestial bodies within the solar system. It ensures that the model is proportionally reduced and maintains the same ratios as the actual solar system, allowing for a better understanding of the vast scales involved in astronomy.