# Misc science info

## The Six Great Stages of Evolution on Earth

1. From the origin of life to the ”Last Common Ancestor"
2. Prokaryote diversification
3. Unicellular eukaryote diversification
4. Multicellularity
5. Invasion of the land
6. 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. 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.
```