AstroShire County: ASTROSHIRE MATHEMATICS

In order for the AstroShire to have been made possible, various mathematical questions had to be solved. On this page, there are five main math questions that are discussed, broken down into simple and comprehensible steps, and visualized in statistical imagery.

WHAT IS THE SCALE?

Before we begin let's define the word "scale". A "scale", in its simplest form is the relative size or extent of an object. To "bring something to scale" means to make something's size equal to that of another and use that as a new basis of measure. In order to do this, an equation has to be made that can create this equality.

For example: If I wanted to bring the Empire State Building to scale with a mouse as if the mouse were a human, I have to make an equation that makes the mouse equal to the size of a human.

1 inch tall Mouse = 5 foot tall Human

By doing that, we have created a ratio - ( 1 : 5 ) "One for every five". Using this equation, I can bring the 1,454 foot Empire State Building to scale with the 1 inch mouse.

Step 1: Divide 1,454 feet (building) by 5 feet (human), giving us 290 and 8/10.

Step 2: Multiply 1 inch (mouse) by 290.8 to get 290.8 inches.

Step 3: Convert inches to feet to get 24.2 feet.

Below is a diagram of the above math problem:

These mathematics can be applied to many other things as well.

Let's apply it to the AstroShire!

Since the main question of the problem we just did was "What would the height of the ESB be if a human were the size of a mouse", here is the question made for the AstroShire:

"Where would the planets of the solar system be located in our county and what would their masses be if miles equaled astronomical units?"

Since we already know that in order for us to create the scale, we need to have an equation, two values that equal each other. The equation is already stated in the question:

miles = astronomical units

To build off of that, we need to have a formula. The basic formula for scales and proportions is:

a = b ( c / d )

a = scale in units

Now we need to find some numbers to plug into the formula.

miles = astronomical units

1 mile = 92,960,00 miles

5,280 feet = 92,960,000 miles

With these numbers, we can create the AstroShire Scale formula:

WHAT IS THE DISTANCE?

Now that we have found the formula with which we can find the scale in the AstroShire County, let's learn about its uses. The first and most useful application is finding the distance of the planets from the sun. To do this, things can be done is two ways. Either we can use the formula or simply convert the distance into AU. Let's use Mercury as an example:

Mercury's astronomical distance in miles: x = 36,000,000 mi.

Mercury's astroshire distance in feet: y = ???

y = 5280 ( 36,000,000 / 92,960,000)

y = 5280 ( 0.36 x 10^8 / 0.9293 x 10^8 )

y = 5280 ( 0.36 / 0.9296 )

y = 5280 ( 0.39 )

y = 2059.2

Mercury's astroshire distance in feet = 2059.2 feet ( 0.39 miles )