Final answer:
Using a scale factor of 1 billion shrinks the vast distances of the solar system to manageable sizes; Earth becomes a grape-sized 1.3 cm, the Moon a pea at 40 cm away, and the Sun a large grapefruit with a diameter of approximately 1.39 meters at 12 meters distance.
Step-by-step explanation:
The question deals with the concept of scaling gigantic astronomical distances into more comprehensible, manageable dimensions that can be easily visualized. To achieve this, a scale factor of 1 billion is used. On this scale, the Earth has a diameter of 1.3 centimeters, representing a size similar to a grape. Similarly, the Moon would be the size of a pea with a scaled diameter of 40 centimeters from the Earth. The Sun, when scaled, has a diameter of approximately 1.39 meters, akin to a large grapefruit, and is 12 meters (40 feet) away from Earth, which gives some perspective on their relative sizes and distances in the solar system.
Comparing actual diameters with scaled diameters provides insight into the immense scale of the solar system and helps in visualizing these vast distances. For instance, the Sun's true diameter is about 1.39 million kilometers, but on the scale model, it is represented by a 100 mm diameter sphere. The interactive website mentioned allows further exploration of these scaled distances, facilitating the understanding of the scale of our solar system in a more tangible way.