how do you scale a solar system model? in the model, how far away from the earth would be the sun?
the average Earth-Sun distance is 1.5E8 km
~solar diameter is 1.4E6 km
so the Earth is about a hundred times farther from the Sun
... than the sun is across
To scale a solar system model, you need to determine a suitable scale factor that allows you to represent all the celestial bodies accurately.
The scale factor is a ratio comparing the size of the actual solar system to the size of your model. For instance, if you choose a scale factor of 1:10 billion, it means that every 1 unit in your model represents 10 billion units in the actual solar system.
To determine the distance between Earth and the scaled model's Sun, you will need the average distance from Earth to the Sun, known as an astronomical unit (AU). The average distance from Earth to the Sun is approximately 93 million miles or 150 million kilometers.
Using the scale factor, you can calculate the distance between Earth and the scaled model's Sun by dividing the actual distance by the scale factor. For example, if you choose a scale factor of 1:10 billion, the distance between Earth and the scaled model's Sun would be:
(93 million miles) / (10 billion) = 0.0093 miles or (150 million kilometers) / (10 billion) = 0.015 kilometers.
Remember to convert the units appropriately based on your preference (miles or kilometers).
So, in the model with a scale factor of 1:10 billion, the Sun would be located about 0.0093 miles or 0.015 kilometers away from the Earth.
To scale a solar system model, you need to proportionally reduce the distances and sizes of the celestial objects so that they fit within the model's constraints. Here's how you can do it:
1. Determine the size of your model: First, decide on the scale you want for your solar system model. For example, you might choose a scale where 1 centimeter represents 1 million kilometers.
2. Determine the size of the Sun: Look up the actual diameter of the Sun, which is approximately 1.4 million kilometers. If you chose a scale of 1 centimeter to 1 million kilometers, the diameter of your model sun would be 1.4 centimeters.
3. Determine the distance between the Earth and the Sun: The average distance between the Earth and the Sun is about 150 million kilometers. Using the same scale (1 centimeter to 1 million kilometers), the distance between the Earth and the Sun in your model would be 150 centimeters, or 1.5 meters.
Therefore, in your scaled solar system model, the distance between the Earth and the Sun would be 1.5 meters.
Remember, these values can be adjusted based on the size of your model and the available space. Also, keep in mind that the other planets and objects within the solar system should be scaled accordingly to maintain proportionality.