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Table of Contents
Appendix
A.1 SI Units
We typically denote numerical values in scientific notation with a number in the interval $[1,10)$, multiplied by a power of ten, followed by a combination of the following units:
| time | second | s , sec |
|---|---|---|
| length | meter | m |
| mass | kilogram | kg |
Occasionally, the power of ten is indicated by one of the following abbreviations
| d | dezi | $10^{-1}$ | |||
|---|---|---|---|---|---|
| c | centi | $10^{-2}\qquad\qquad$ | h | hekto | $10^2$ |
| m | milli | $10^{-3}\qquad\qquad$ | k | kilo | $10^3$ |
| $\mu$ | micro | $10^{-6}$ | M | mega | $10^6$ |
| n | nano | $10^{-9}$ | G | giga | $10^9$ |
| n | pico | $10^{-12}$ | T | tera | $10^{12}$ |
| f | femto | $10^{-15}$ | P | peta | $10^{15}$ |
A.2 Orders of magnitude
Length
\begin{align} \label{eq:times} 1 \, \text{parsec} = 1 \: \text{pc} \simeq 3 \times 10^{16} \: \text{m} \\ 1 \, \text{light year} \simeq 10^{16} \, \text{m} \\ 1 \, \text{astronomical unit} = 1 \: \text{AU} \simeq 1.5 \times 10^{11} \: \text{m} \end{align}
Time
\begin{align} \label{eq:times} 1 \, \text{year} \simeq \pi \times 10^7 \, \text{s} \end{align}
Speed
\begin{align} \text{speed of light} && c_L &= 3 \times 10^8 \: \text{m/s} \\ \text{speed of sound} && c_S &= 3 \times 10^2 \: \text{m/s} \end{align}
Acceleration and gravity
\begin{align} \text{gravitational acceleration on Earth } && g &= 9.81 \:\text{m/s}^2 \simeq 10 \text{m/s}^2 \\ \text{gravitational acceleration on Moon} && g_{moon} &= 1.62 \:\text{m/s}^2 \simeq g/6 \\ \text{gravitational constant} && G &= 7 \times 10^{-11} \:\text{m}^3 / \text{kg s}^2 \\ \end{align}
Mass
\begin{align} \text{electron} && m_\text{e} &= 9 \times 10^{-31} \: \text{kg} \\ \text{proton, neutron, hydrogen atom} && m_\text{p} &= 1.7 \times 10^{-27} \: \text{kg} \\ \nonumber \\ \text{Earth} && m_\text{earth} &= 6 \times 10^{24} \: \text{kg} \\ \text{Sun} && m_\text{sun} &= 2 \times 10^{30} \: \text{kg} \end{align}
\text{neutron} && m_\text{n} &= 1.7 \times 10^{-27} \: \text{kg}
\text{hydrogen atom} && m_\text{hydrogen} &= 1.7 \times 10^{-27} \: \text{kg}
Density
\begin{align} \text{lab vaccum} && \rho_\text{sun} &= 10^{-17} \: \text{kg/m}^{3} \\ \text{air} && \rho_\text{air} &= 1 \: \text{kg/m}^{3} \\ \text{petroleum} && \rho_\text{water} &= 8 \times 10^2 \: \text{kg/m}^{3} \\ \text{water} && \rho_\text{water} &= 10^3 \: \text{kg/m}^{3} \\ \text{Sun} && \rho_\text{sun} &= 1.4 \times 10^3 \: \text{kg/m}^{3} \\ \text{steel} && \rho_\text{steel} &= 8 \times 10^3 \: \text{kg/m}^{3} \\ \text{lead} && \rho_\text{lead} &= 11 \times 10^3 \: \text{kg/m}^{3} \\ \text{plutonium} && \rho_\text{lead} &= 20 \times 10^3 \: \text{kg/m}^{3} \\ \nonumber \\ \text{universe} && \rho_\text{sun} &= 10^{-27} \: \text{kg/m}^{3} \\ \text{Sun} && \rho_\text{sun} &= 1.4 \: \rho_\text{water} \\ \text{Moon} && \rho_\text{moon} &= 3.3 \: \rho_\text{water} \\ \text{Mars} && \rho_\text{mars} &= 3.3 \: \rho_\text{water} \\ \text{Earth} && \rho_\text{earth} &= 5.5 \: \rho_\text{water} \\ \text{white dwarf star} && \rho_\text{white dwarf} &= 10^9 \: \text{kg/m}^{3} \\ \text{neutron star} && \rho_\text{nucl} &= 4 \times 10^{17} \: \text{kg/m}^{3} \\ \end{align}
Pressure
\begin{align} \text{outer space} && p_\text{space} &= 10^{-18} \: \text{Pa} \\ \text{lab vacuum} && p_\text{vacuum} &= 10^{-13} \: \text{Pa} \\ \text{Mars} && p_\text{Mars} &= 10^3 \: \text{Pa} \\ \text{normal atmospheric pressure} && p_\text{air} &= 10^5 \: \text{Pa} = 1 \:\text{bar} \\ \text{Titan} && p_\text{Titan} &= 1.5 \times 10^5 \: \text{Pa} = 1.5 \:\text{bar} \\ \text{bicycle tire} && p_\text{bicycle} &= 4 \times 10^5 \: \text{Pa} = 4 \:\text{bar} \\ \text{espresso machine} && p_\text{espresso} &= 10^6 \: \text{Pa} \\ \text{Venus} && p_\text{Venus} &= 9 \times 10^6 \: \text{Pa} = 90 \:\text{bar} \\ \text{high heels} && p_\text{heels} &= 10^7 \: \text{Pa} \\ \text{deepest ocean} && p_\text{ocean} &= 10^8 \: \text{Pa} \\ \text{create diamond} && p_\text{diamond} &= 10^{10} \: \text{Pa} \\ \text{Earth center} && p_\text{Earth} &= 4 \times 10^{11} \: \text{Pa} \\ \text{Sun center} && p_\text{Sun} &= 3 \times 10^{16} \: \text{Pa} \end{align}
See the The Physics Factbook for lists with other estimates, and background information.
A.3 Solar System
The solar system has $1.0014$ solar masses, which amounts to about $2 \times 10^{30}\, \, \text{kg}$. The Earth-Sun distance is $1 \, \text{AU} \simeq 500 \, \text{light second} \simeq 1.5 \times 10^{11}\, \, \text{m}$.
| object | Sun | Mecury | Venus | Earth | Mars | Jupiter | Saturn | Uranus | Neptun |
|---|---|---|---|---|---|---|---|---|---|
| distance | $0.005$ | $0.387098$ | $0.723332$ | $1$ | $1.523679$ | $5.2044$ | $9.5826$ | $19.2184$ | $30.11$ |
| radius | $109$ | $0.3829$ | $0.9499$ | $1$ | $0.533$ | $11.209$ | $9.449 $ | $4.007$ | $3.883$ |
| mass | $333,000$ | $0.055$ | $0.815$ | $1$ | $0.107$ | $317.8$ | $95.159$ | $14.536$ | $17.147$ |
| period | $0.240846$ | $0.615198$ | $1$ | $2.1354$ | $11.862$ | $29.4571$ | $84.0205$ | $164.8$ |
Properties of Sun and planets of our solar system, provided in multiples of the Earth values. The distance referes to the semi-major axis in AU. For the sun the distance denotes the sun surface, i.e., its radius. }
| object | Moon | Ceres | Pluto | Eris |
|---|---|---|---|---|
| distance | $0.00257$ | $2.769$ | $39.482$ | $67.864$ |
| radius | $0.2727$ | $0.073$ | $0.1868$ | $0.1825$ |
| mass | $0.0123$ | $0.00016$ | $0.00218$ | $0.0028$ |
| period | $0.08085$ | $4.61$ | $247.94$ | $559.07$ |
Properties of the Moon and dwarf planets of our solar system. The properties of the Moon refer to its distrance to and period around Earth. Ceres is the largest object in the meteorite belt between Mars and Jupiter. Eris is a dwarf planet in the Kuiper belt that is larger in mass than Pluto.