Size Comparison - How big would the earth be?

by Scotty Long
(Union City Tenessee)

I have a question I would like answered from a purely math perspective. Let me see if I can explain what I am wanting.

GOD = (diameter of known universe)
My thinking is that God would have to be at least as big as everything we know.

Then I want to scale that number down to the size of an average human being.

My question is how big would the earth be using the scale determined by how big God would be if he is at least as big as the known universe.

For example using this scale I imagine it would be similar to me holding a grain of sand thus my equation would look something like this:

God equals man

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Nov 02, 2012

Scaled Down Diameter of Earth
by: Staff

Answer

Part I

A proportion can be applied to answer your question

Direct Proportions:

         A direct proportion between two variables means that one variable is a constant multiple of the other variable.

         The terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

         The equation for your question looks like this:

             y = kx

         k is a constant. It is called the “constant of variation”.

      To solve for k:

             y/x = k

         The constant of variation means that DIVIDING the value of ONE VARIABLE BY THE value of the OTHER variable is a CONSTANT value (k, the constant of variation). (This can be applied to your problem).

             The diameter of the earth divided by the diameter of the universe is a ratio (or proportion), a k value which I will name “k₁”.

             The height of a human divided by the diameter of the universe is a different ratio, another k value which I will name “k₂”.

             If I understand your question correctly, it is: if you scale the universe down to the size of an average human, what would the diameter of the earth be? In other words, you want to compute what the size of the earth would be using the ratio “k₁” (similar to you holding a grain of sand).

             There is some difference of opinion as to what the diameter of the universe is. For the sake of argument, I am going to assume the universe is 93 billion light years in diameter.

             Light travels a distance of 3.10384842519685 ✕ 10¹⁶ feet in 1 year.

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Nov 02, 2012

Scaled Down Diameter of Earth
by: Staff

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Part II

             Therefore, the diameter of the universe in feet is: (3.10384842519685 ✕ 10¹⁶ feet per light year) * (93 ✕ 10⁹ light years) = 2.8865790354331*10²⁷ feet

             Unfortunately the earth is not a perfect sphere. The diameter at the equator is slightly larger than the diameter between the north and south poles. I’m going to assume the diameter of the earth is 7,926 miles.

             Therefore, the diameter of the earth in feet is: (7926 miles) * (5280 feet per mile) = 41849280 feet

             The average height of a human varies greatly. The average height of men and women is not the same, the average height varies by geographical location and race, and the average height varies by age. I’m going to arbitrarily assume the average height of a human is: 5 feet 9 inches. This is equivalent to 5.75 feet.

         On this basis, the constant of variation k₁ = (41849280 feet)/( 2.8865790354331*10²⁷ feet) = 1.4497881224209 ✕ 10^-20.

         If the diameter of the universe is scaled down to the average height of a human, the diameter can be calculated as follows:

         Diameter of scaled down earth = k₁ * (average height of human)

         Diameter of scaled down earth = (1.4497881224209 ✕ 10^-20) * (5.75 feet)

         Diameter of scaled down earth = 8.3362817039202 ✕ 10^-20 feet

Final Answer

         If the diameter of the universe is scaled down to the average height of a human, the diameter of the scaled down earth is:

             8.3362817039202 ✕ 10^-20 feet

             This size is equivalent to 2.5408986633549*10^-14 microns. This size is smaller than the diameter of a strand of spider web (2 – 3 microns), smaller than a particle of smoke (0.01 – 1 microns), and smaller than the diameter of an oxygen atom (0.0005 microns)

Thanks for writing.

Staff
www.solving-math-problems.com

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Size Comparison - How big would the earth be?

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