## Fermi Questions C

Magikarpmaster629
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### Re: Fermi Questions C

Unome wrote:Current question, since we need some activity:
Adi1008 wrote:How far, in Planck lengths, would New Horizons travel in the time it takes for our Solar System to make one orbit around the center of the Milky Way?
Since I'm considering helping write questions for this event:
-Planck length is about e-19 meters
-Solar system goes around the milky way in 2.5e7 years; one year is e7 seconds, so 2.5e14 s
-I don't know much about New Horizons or a way to estimate it, so I'll say its velocity is about 0.01c, or 3e6 m/s
-Multiplying velocity by the change in time, we get e20 meters, or e39 Planck lengths
[b]Fermi Answer: 39[/b]
-So I was WAAAAYYYY off in my estimate of Planck's length (must have been thinking of electron charge), it's e-35 m
-Solar system estimate was spot on, and the seconds to years was pretty close too
-Real velocity of New Horizons was 6e7 m/s, so not too bad?
-Multiplying out we get 5e57 Planck lengths
[b]Final Answer: 57[/b] (maybe I'll just stick to Astronomy...)
I want to destroy the world by flooding every country's capital city! How many buckets of water would it take me to create flooding conditions in every world capital?

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### Re: Fermi Questions C

Magikarpmaster629 wrote:I want to destroy the world by flooding every country's capital city! How many buckets of water would it take me to create flooding conditions in every world capital?
The question is a little vague. I'll assume that you're attempting to raise the sea level to a sufficient height to flood all of the capitals.
- The highest capital city of a country is probably around a mile. Accounting for the extra land volume, I'll just go with 1 km as an approximation.
- The earth has a radius of 6E4 km, so this is solving for a disk volume.
- The surface layer of water can be approximated with a disk. Earth surface area is 4 pi r^2 so ~4E10 km.
- This gives a volume of 4E19 cubic meters, or 4E22 liters.
- The average bucket probably isn't quite enough to lower than below 5E21, so:
Fermi Answer: 22
- The highest altitude capital city is La Paz (Bolivia) at an elevation of 3.64 km
- Ignoring land volume, a disk from sea level has a volume of 1.8577E21 liters. Subtracting land volume (1.25E20 liters) we get 1.73E21 liters.
- Apparently an average bucket is ten liters, so
Fermi Answer: 20
How many orbits does Pluto make in the time i takes for the solar system to orbit the galactic center once?
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### Re: Fermi Questions C

Unome wrote:How many orbits does Pluto make in the time i takes for the solar system to orbit the galactic center once?
This is a ratio between the period of the solar system around the Milky Way (roughly 2.5E8 years) and the period of Pluto around the Sun (2.48E2 years). [b]Fermi Answer: 6[/b]
[url=https://www.wolframalpha.com/input/?i=(period+of+solar)%2F(period+of+pluto)]Wolfram Alpha[/url] gives a [b]Fermi Answer: 6[/b]
How many neutrons need to spontaneously decay $(\mathrm{n^0} \rightarrow \mathrm{p^+} + \mathrm{e^-} + \bar{\mathrm{\nu_e}})$ in order to equal the energy output of Betelgeuse (a red supergiant) over the course of one day?
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