# Misc science info

From Christoph's Personal Wiki

This article will be about miscellaneous science information that I have not organized just yet.

## Contents

## The Six Great Stages of Evolution on Earth

- From the origin of life to the ”Last Common Ancestor"
- Prokaryote diversification
- Unicellular eukaryote diversification
- Multicellularity
- Invasion of the land
- Appearance of intelligence and technology.

## Back of the Envelope Calculations (BotEC)

see: wikipedia:Fermi problem

It is a good practice to use the following steps when performing BotEC's:

- Formula(s)
- formula(s) that provide a roadmap to the upcoming calculations. The formula should include names for any quantity that will be estimated, and should give units of measurement (in parentheses). Conversion factors (e.g. bits/Byte) can appear without a name.
- Estimates
- Estimates of the quantities appearing in the formula. There should be a very brief justification of the estimate if it is not obvious. You should use "wiggley equal signs" to indicate approximations.
- Calculation(s)
- Calculations in which the estimates and known facts are substituted into the formula.

### Example #1: Calculate the bandwidth needed for full screen video

- Formula
- Bandwidth (Bytes/sec) = ScreenSize(dots/image) x RefreshRate (images/sec) x Information (Bytes/dot)

- Estimates
- ScreenSize ~= 1,000,000 dots/image (estimating a 1000x1000 screen)
- RefreshRate ~= 30 images/second (so eye won't see flicker)
- Information = 3 Bytes/dot (one Byte each for R, G, B)

- Calculation
- Bandwidth ~= 10^6 dots/image x 30 images/sec x 3 Bytes/dot = 90x10^6 Bytes/sec ~=
**100 MByte/sec**

### Example #2: AU / ly

- Calculate the number of astronomical units (AU) in a light-year (ly)

Speed of light ~= 300,000 km/sec Seconds in a year = 60 X 60 X 24 X 365.25 = 31,557,600 Distance traveled in a year = speed in km/sec X seconds = 9,467,280,000,000 km = 1 Light Year 1 AU = 149,598,500 km Number of AU in 1 ly = (9,467,280,000,000 km) / (149,598,500 km) = 9,467,280,000 / 149,598.5 = = 946728 / 15 = 63115.2 AU/ly --------------------------------------------------------- c = speed of light = 2.99792458E+8 m/s y = seconds per (tropical) year = 31556926 cy = one lightyear in meters = 9.460528412641E+15 meters au = one astronomical unit = 1.49597870691E+11 meters # There are cy/au astronomical units in one lightyear. cy/au = 63239.7 # If you use the Julian year instead of the tropical year # to calculate the number of meters in a light-year, then y = 31557600 cy = 9.46073047258E+15 meters cy/au = 63241.1 --------------------------------------------------------- 1 light-year = 63.241 × 10^3 AU = 63,241 AU 1 AU = 149,597,870,700 metres = 149.60 x 10^6 km = 149.60 x 10^9 m 1 AU ~= 499 seconds ~= 8.32 minutes for light to travel this distance 1 light-year = 9460730472580800 metres (exactly) 1 year = 365.25 days (exactly) 1 year = 86400 SI seconds, totaling 31,557,600 seconds) = pi x 10^7 s speed of light = 299792458 m/s --------------------------------------------------------- speed of light in AU/hr: 2.998 x 10^8m/s = (2.998x10^8 m/s)/(1000 m/km) = 2.998 x 10^5 km/s = (2.998x10^5 km/s)*(3600 s/h) = 10792.8 x 10^5 km/h = 1.07928 x 10^9 km/h = (1.07928 x10^9 km/h)(1/(1.50 x 10^8 km/Au) = 0.71952 x10^1 Au/ h= 7.1952 Au/h, ~= 7.20 AU/h (at 3 significant figures) # the accuracy of the least accurate data "1.50 x10^8 km/Au"

### Misc examples

- Victor Weisskopf's pamphlet
*Modern Physics from an Elementary Point of View*.^{[1]}In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.

- Land area for use by humans:

Each family get a piece of land of area A = 30m x 30m = 10^3 m^2 (or about 1/4 acre). Therefore, all of us together will use a total land area of A = 6 x 10^9 people * (1 family)/(3 people) * (10^3 m^2)/(family) = 2 x 10^12 m^2 (when one multiplies numbers in scientific notation, one multiplies the coefficients and adds the exponents. In this case, 10^9 x 10^3 = 10^(9+3) = 10^12.) This is 2 x 10^6 km^2 (two million square kilometres); around the area of Alaska or twice the area of Egypt, which is about 1% of the surface area of the Earth.

## External links

- Being Isaac Newton: Computer derives natural laws from raw data
- The Six Great Stages of Evolution on Earth -- Is There a Seventh?