gravity derivations
- normal gravity at sea level from latitude - symbol - description - unit - variable name - \(g\) - normal gravity at sea level - \(\frac{m}{s^2}\) - gravity {:} - \(\phi\) - latitude - \(degN\) - latitude {:} - The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[\begin{eqnarray} g & = & 9.7803253359 \frac{1 + 0.00193185265241{\sin}^2(\frac{\pi}{180}\phi)} {\sqrt{1 - 0.00669437999013{\sin}^2(\frac{\pi}{180}\phi)}} \end{eqnarray}\]
- gravity at specific altitude - symbol - name - unit - variable name - \(a\) - WGS84 semi-major axis - \(m\) - \(b\) - WGS84 semi-minor axis - \(m\) - \(f\) - WGS84 flattening - \(m\) - \(g_{h}\) - gravity at specific height - \(\frac{m}{s^2}\) - gravity {:,vertical} - \(g\) - normal gravity at sea level - \(\frac{m}{s^2}\) - gravity {:} - \(GM\) - WGS84 earth’s gravitational constant - \(\frac{m^3}{s^2}\) - \(z\) - altitude - \(m\) - altitude {:,vertical} - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\omega\) - WGS84 earth angular velocity - \(rad/s\) - The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all. \begin{eqnarray} m & = & \frac{\omega^2a^2b}{GM} \\ g_{h} & = & g \left[ 1 - \frac{2}{a}\left(1+f+m-2f{\sin}^2(\frac{\pi}{180}\phi)\right)z + \frac{3}{a^2}z^2 \right] \\ \end{eqnarray}
- gravity at earth surface - symbol - name - unit - variable name - \(a\) - WGS84 semi-major axis - \(m\) - \(b\) - WGS84 semi-minor axis - \(m\) - \(f\) - WGS84 flattening - \(m\) - \(g_{surf}\) - gravity at surface altitude - \(\frac{m}{s^2}\) - surface_gravity {:} - \(g\) - normal gravity at sea level - \(\frac{m}{s^2}\) - gravity {:} - \(GM\) - WGS84 earth’s gravitational constant - \(\frac{m^3}{s^2}\) - \(z_{surf}\) - surface altitude - \(m\) - surface_altitude {:} - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\omega\) - WGS84 earth angular velocity - \(rad/s\) - The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \begin{eqnarray} m & = & \frac{\omega^2a^2b}{GM} \\ g_{surf} & = & g \left[ 1 - \frac{2}{a}\left(1+f+m-2f{\sin}^2(\frac{\pi}{180}\phi)\right)z + \frac{3}{a^2}z^2 \right] \\ \end{eqnarray}