High School Astronomy
EQUATIONS
|
INFORMATION
|
$$ \large
D = \frac{\alpha d}{206265} $$
|
\(\\ \textbf{D} = diameter \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} object \hspace{4 pt} (km) \\ {\alpha} = angular \hspace{4 pt} size \hspace{4 pt} of \hspace{4 pt} object \hspace{4 pt} (arcsec) \\ \textbf{d} = distance \hspace{4 pt} to \hspace{4 pt} object \hspace{4 pt} (km)\) |
|
$$ \large
F = ma $$
|
\(\\ \textbf{F} = force \hspace{4 pt} on \hspace{4 pt} an \hspace{4 pt} object \hspace{4 pt} (N) \\ \textbf{m} = mass \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} object \hspace{4 pt} (kg) \\ \textbf{a} = acceleration \hspace{4 pt} of \hspace{4 pt} object \hspace{4 pt} (m \hspace{2 pt} s^{-2})\) |
|
$$ \large
F = G \left( \frac{m_1 m_2}{r^2} \right ) $$
|
\( \textbf{F} = gravitational \hspace{4 pt} force \hspace{4 pt} between \\ \hspace{6 pt} masses \hspace{4 pt} (N)\\ \textbf{G} = gravitational \hspace{4 pt} constant \hspace{7 pt} \\ \hspace{8 pt} (6.67384 x 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2}) \\ {m_\#} = mass \hspace{4 pt} of \hspace{4 pt} object \hspace{4 pt} \# \hspace{4 pt} (kg)\\ \textbf{r} = distance \hspace{4 pt} between \hspace{4 pt} objects \hspace{4 pt} (m)\) |
|
$$ \large
T^2 = \left ( \frac{4\pi^2}{G(m_1 + m_2)} \right ) a^3 $$
|
\(\\ \textbf{T} = orbital \hspace{4 pt} period \hspace{4 pt} (s) \\ \textbf{G} = gravitational \hspace{4 pt} constant \hspace{7 pt} \\ \hspace{8 pt} (6.67384 x 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2}) \\ {m_\#} = mass \hspace{4 pt} of \hspace{4 pt} object \hspace{4 pt} \# \hspace{4 pt} (kg)\\ \textbf{a} = semi-major \hspace{4 pt} axis \hspace{4 pt} (m)\) |
|
$$ \large L = mvr $$
|
\(\\ \textbf{L} = angular \hspace{4 pt} momentum \hspace{4 pt} (kg \hspace{2 pt} m^2 \hspace{2 pt} s^{-1}) \\ \textbf{m} = mass \hspace{4 pt} (kg) \\ \textbf{v} = velocity \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \\ \textbf{r} = distance \hspace{4 pt} from \hspace{4 pt} point \hspace{4 pt} of \hspace{4 pt} rotation \hspace{4 pt} (m)\) |
|
$$ \large
\frac{m_1}{m_2} = \frac{r_2}{r_1} = \frac{a_2}{a_1} $$
|
\(\\ {m_\#} = mass \hspace{4 pt} of \hspace{4 pt} star \hspace{4 pt} \# \hspace{4 pt} (M_{sun}) \\ {r_\#} = distance \hspace{4 pt} from \hspace{4 pt} the \hspace{4 pt} center \hspace{4 pt} of \hspace{4 pt} mass \hspace{4 pt} \\ \hspace{11 pt} to star \# (A.U.) \\ {a_\#} = semi-major \hspace{4 pt} axis \hspace{4 pt} of \hspace{4 pt} orbit \hspace{4 pt} (A.U.)\) |
|
$$ \large
\frac{m_1}{m_2} = \frac{v_2}{v_1} $$
|
\(\\ {m_\#} = mass \hspace{4 pt} of \hspace{4 pt} star \hspace{4 pt} \# \hspace{4 pt} (M_{sun}) \\ {v_\#} = radial \hspace{4 pt} velocity \hspace{4 pt} of \hspace{4 pt} star \hspace{4 pt} \# \hspace{4 pt} (km \hspace{2 pt} s^{-1})\) |
|
$$ \large v_{orb} = \sqrt{\frac{GM}{r}} $$
|
\(\\ {v_{orb}} = escape \hspace{4 pt} velocity \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \\ \textbf{G} = gravitational \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{8 pt} (6.67 \hspace{2 pt} x \hspace{2 pt} 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2}) \\ \textbf{M} = mass \hspace{4 pt} of \hspace{4 pt} planet \hspace{4 pt} (kg) \\ \textbf{r} = distance \hspace{4 pt} from \hspace{4 pt} center \hspace{4 pt} of \\ \hspace{3 pt} gravity \hspace{4 pt} (m)\) |
|
$$ \large v_{esc} = \sqrt{\frac{2GM}{r}} $$
|
\(\\ {v_{esc}} = escape \hspace{4 pt} velocity \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \\ \textbf{G} = gravitational \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{8 pt} (6.67 \hspace{2 pt} x \hspace{2 pt} 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2}) \\ \textbf{M} = mass \hspace{4 pt} of \hspace{4 pt} planet \hspace{4 pt} (kg) \\ \textbf{r} = distance \hspace{4 pt} from \hspace{4 pt} center \hspace{4 pt} of \\ \hspace{3 pt} gravity \hspace{4 pt} (m)\) |
|
$$ \large
L = A \sigma T^4 = 4\pi R^2 \sigma T^4 $$
|
\(\\ \textbf {L} = luminosity \hspace {4 pt} (W)\\ {\sigma} = Stefan-Boltzmann \hspace {4 pt} constant \hspace {1 pt} (5.67 \hspace {4 pt} x \hspace {4 pt} 10^{-8} \hspace {4 pt} W \hspace {2 pt} m^{-2} \hspace {2 pt} K^{-4}) \\ \textbf{A} = surface \hspace{4 pt} area \hspace {4 pt} (m^2) \\ \textbf {T} = temperature \hspace {4 pt} (K)\\ \textbf {R} = radius \hspace {4 pt} of \hspace {4 pt} the \hspace {4 pt} star \hspace {4 pt} (m)\) |
|
$$ \large
F = \frac{L}{A} = \frac{L}{4 \pi R^2} = \sigma T^4 $$
|
\(\\ \textbf {F} = flux\hspace {4 pt}(W \hspace{2 pt} m^{-2})\\ \textbf {L} = luminosity \hspace {4 pt} (W)\\ \textbf{A} = surface \hspace{4 pt} area \hspace {4 pt} (m^2) \\ \textbf {R} = radius \hspace {4 pt} of \hspace {4 pt} the \hspace {4 pt} star \hspace {4 pt} (m) \\ {\sigma} = Stefan-Boltzmann \hspace {4 pt} constant \hspace {1 pt} (5.67 \hspace {4 pt} x \hspace {4 pt} 10^{-8} \hspace {4 pt} W \hspace {2 pt} m^{-2} \hspace {2 pt} K^{-4}) \\ \textbf {T} = temperature \hspace {4 pt} (K)\\\) |
|
$$ \large
c = \nu \lambda $$
|
\(\\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.00 \hspace{2 pt} m \hspace{2 pt} s^{-2}) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (Hz) \\ {\lambda} = wavelength \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (m)\) |
|
$$ \large
E = h\nu = \frac{hc}{\lambda} $$
|
\( \textbf{E} = energy \hspace{4 pt} of \hspace{4 pt} a \hspace{4 pt} photon \hspace{4 pt} (J) \\ \textbf{h} = Planck's \hspace{4 pt} constant \hspace{4 pt} (6.625 \hspace{2 pt}x \hspace{2 pt} 10^{-34} J \hspace{2 pt} s ) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} light \hspace{4 pt}(Hz) \\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.0 \hspace{2 pt} x \hspace{2 pt} 10^8 \hspace{4 pt} m \hspace{2 pt} s^{-1}) \\ {\lambda} = wavelength \hspace{4 pt} (m) \) |
|
$$ \large
\frac{v_r}{c} = \frac{\Delta \lambda}{\lambda_0} = \frac{\lambda - \lambda_0}{\lambda_0} $$
|
\(\\ {v_r} = radial \hspace{4 pt} velocity \hspace {4 pt}(km/s) \\ \textbf{c} = speed \hspace {4 pt}of \hspace {4 pt} light \hspace{4 pt}(km/s) \\ {\lambda} = observed \hspace {4 pt} wavelength \hspace {4 pt}(km/s) \\ {\lambda_0} = emitted \hspace {4 pt} wavelength \hspace{4 pt}(km/s) \\ \) |
|
$$ \large
R_{Sch} = \frac{2GM}{c^2} $$
|
\(\\ {R_{Sch}} = Schwarzchild \hspace {4 pt} radius \hspace {4 pt} (km)\\ \textbf {G} = gravitational \hspace {4 pt} constant \hspace {4 pt} \\ \hspace{8 pt}(6.67384 \hspace{2 pt} x \hspace{2 pt} 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2}) \\ \textbf{M} = mass \hspace {4 pt} of\hspace {4 pt} the\hspace {4 pt} object \hspace {4 pt} (kg) \\ \textbf{c} = speed \hspace {4 pt} of \hspace {4 pt} light \hspace {4 pt}(km/s) \) |
|
$$ \large v = H_0 d $$
|
\(\\ \textbf{v} = velocity \hspace {4 pt} (km \hspace{2 pt} s^{-1}) \\ {H_0} = Hubble's \hspace {4 pt}constant \\ \hspace{12 pt}(\sim 68 \hspace{4 pt}km \hspace{2 pt} s^{-1} \hspace{2 pt} Mpc^{-1}) \\ \textbf{D} = proper \hspace{4 pt} distance \hspace{4 pt} (km) \) |
|