- #1
Freeman Dyson
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Homework Statement
Convert astronomical objects into money based on their radius. This is how it works. The Earth is worth one penny. $.01 The Earth's radius is 6,378 km. So 6,378 km equal one penny in this system. So the sun, which has a radius of 696,000 km. We divide that by 6,378. Which is 109 cents. So the sun is worth 1.09
Solar System is 40 AU. I want this in km. AU is 1.5 x 10^8 km. So do 40 times 1.5 x 10^8 =6,000,000,000km or 6 x 10^9. So then I divide 6 x 10^9 by 6.378 x 10^3. And I get 940,733 cents. Drop 2 decimals to convert to dollars and I get $9,407 for the price of the solar system.
I believe those are right. Anyway, it is the bigger ones that I am having problems with. Next is the Milky Way. Milky way is 50,000 light years away.
Homework Equations
The Attempt at a Solution
So this is how I am going about the Milky Way one. Probably wrongly. I want to convert the those 50,000 light years into km. Or do I? Anyway, I'll try it. A light year is 10 trillion km. So I multiply 50,000 by 10 trillion. 5 x 10^4 x 1 x 10^13. So that is 5 x 10^17. Now I divide this by 6.378 x 10^3 and get .78394481 x 10^14. Now what? Should I get rid of some exponents? Maybe 783 x 10^9? Which is 78,300,000,000,000 cents. Take out two points to convert to dollars and you have $783,000,000,000 as the cost of the Milky Way, Is this correct? Is there a better way to do it?