Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:appendix:magnitudes

Appendix 2. Orders of magnitude

Length

\begin{align} \label{app-eq:length} 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}

Surface area

\begin{align} 1 \, \text{km}^2 &= 1000000 \, \text{m}^2 &= 1 \times 10^{10} \text{cm}^2 \\ 1 \, \text{m}^2 &= 10000 \, \text{cm}^2 \\ \\ 1\, \text{cm}^2 &= 0,0001 \, \text{m}^2 \\ 1\, \text{m}^2 &= 1 \times 10^{-6} \text{km}^2 \end{align}

Time

\begin{align} \label{eq:times} 1 \, \text{year} \simeq \pi \times 10^7 \, \text{s} \\ 1 \, \text{day} &= 24 \, \text{hour} &= 1440 \, \text{min} &= 86400 \, \text{sec} \\ 1 \, \text{hour} &= 60 \, \text{min} &= 3600 \, \text{sec} \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} \\ \\ \text{average human speed} && v_{human} &= 7\text{km/h} &= 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} \\ \\ \text{average human weight} && m_{human} &= 80 \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}

\begin{align} 1 \, \text{t} &= 1000 \,\text{kg} &= 1000000 \, \text{g} \\ 1 \, \text{kg} &= 1000 \,\text{g} &= 1000000 \, \text{mg} \\ 1 \, \text{g} &= 1000 \, \text{mg} \end{align}

volume

\begin{align} 1 \, \text{m}^3 &= 1000000 \, \text{cm}^3 \\ 1 \, \text{l} &= 1000 \, \text{cm}^3 \\ 1\, \text{ml} &= 1 \, \text{cm}^3 \end{align}

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.

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book/appendix/magnitudes.txt · Last modified: 2022/10/14 06:48 by adam