Solar System Model

Question

I'm doing a solar system model project where both the distance from the sun and size of the planet have to be on the same scale. For the background of my model I've cut 100 squares of black paper that are 4 x 4.5 inches, and have already decided that the scale is done by squares and have done all the math for the distance (Mercury is 1 square away from the sun, Venus is 1.8 squares, etc.) but how could I make the actual size of the planet to scale using this method?

Answer 1

There's a website that allows you to enter the diameter of the sun that you want to use in the scale model, and it will calculate the diameter of all the planets, as well as the orbital radius.

http://www.exploratorium.edu/ronh/solar_system/

 

What you will find is that there is no practical way to have the diameter of the planets be on the same scale as the orbital radius. For example, if you enter 1 inch for the sun diameter, you will get 0.001 inch for the diameter of Pluto and 354 feet for the orbital radius of Pluto (assuming you are considering Pluto to be a planet).  So the range is 0.001 inch to 354 feet (4248 in).  That is a ratio of 4248/0.001 = 4.25million.  Even if you eliminate Pluto, the range is unacceptably large.

 

One compromise would be to have the orbital radius use one scale (which you have already planned out) and the diameter of the planets use a different scale.

Answer 2

One major obstacle is as follows:

 

If the sun is modeled by a sphere of diameter 10 centimeters, then the earth must be modeled with diameter of just under 1 millimeter and the two must be modeled as just over 10 meters apart. In turns, it would result in placing Neptune at about 300 meters from the sun.

Answer 3

Mercury is 3.598 x 10¹⁰ miles from the sun. 

You have set one square equal to 3.598 x 10¹⁰ miles

The diameter of Mercury is 3.032 x 10³ miles.

There fore your scale model of Mercury would be (3.032 x 10³) / (3.598 x 10¹⁰) of one square.

That is 8.4 x 10^-6 or 0.0000084 of a square.

Do you think you need to increase your scale?

Answer 4

Use the area of one square?

 

Area = 4 in x 4.5 in

        = 18 in²

 

1 square = 18 in²