Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:appendix:solar-system [2022/10/11 21:47] – [Time] jvbook:appendix:solar-system [2022/10/11 22:03] (current) jv
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-====== Appendix ====== +====== Appendix 3.  The Solar System  =====
- +
-===== 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. 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} +
- +
-<wrap hide> +
-\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}  \\ \\ +
-</wrap> +
- +
- +
-==== 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 [[https://hypertextbook.com/facts/|The Physics Factbook]]  +
-for lists with other estimates, and background information. +
- +
- +
- +
-===== A.3  Solar System  =====+
  
 The solar system has $1.0014$ solar masses, The solar system has $1.0014$ solar masses,
 which amounts to about $2 \times 10^{30}\, \, \text{kg}$. which amounts to about $2 \times 10^{30}\, \, \text{kg}$.
 +
 The Earth-Sun distance is $1 \, \text{AU} \simeq 500 \, \text{light second} \simeq 1.5 \times 10^{11}\, \, \text{m}$. The Earth-Sun distance is $1 \, \text{AU} \simeq 500 \, \text{light second} \simeq 1.5 \times 10^{11}\, \, \text{m}$.
  
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 +~~DISCUSSION|Typos and suggestions for additional entries~~
  
book/appendix/solar-system.1665517649.txt.gz · Last modified: 2022/10/11 21:47 by jv