Table of Symbols
The symbols used in this document are summarized in the Table of Symbols along with their units. Throughout the document, symbols in bold will represent vectors, and scalars otherwise. The symbols are listed in alphabetical order. For vector quantities, the units shown are for each component of the vector.
| Symbol | Description | Units |
|---|---|---|
| \({a_{\text{x}1}}\) | X-acceleration of the first star | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{x}2}}\) | X-acceleration of the second star | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{y}1}}\) | Y-acceleration of the first star | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{y}2}}\) | Y-acceleration of the second star | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(\boldsymbol{a}\text{(}t\text{)}\) | Acceleration | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(E\) | Energy | \({\text{J}}\) |
| \(\boldsymbol{F}\) | Force | \({\text{N}}\) |
| \({\boldsymbol{F}_{\boldsymbol{g}}}\) | Force of gravity | \({\text{N}}\) |
| \(G\) | Gravitational constant | \(\frac{\text{m}^{3}}{\text{kg}\text{s}^{2}}\) |
| \(i\) | Index | – |
| \(m\) | Mass | \({\text{kg}}\) |
| \({m_{1}}\) | Mass of the first star | \({\text{kg}}\) |
| \({m_{2}}\) | Mass of the second star | \({\text{kg}}\) |
| \({m_{\text{max}}}\) | Maximum stellar mass | \({\text{kg}}\) |
| \({m_{\text{min}}}\) | Minimum stellar mass | \({\text{kg}}\) |
| \(n\) | Number of bodies | – |
| \(\boldsymbol{p}\text{(}t\text{)}\) | Position | \({\text{m}}\) |
| \({r_{12}}\) | Separation distance | \({\text{m}}\) |
| \({r_{\text{max}}}\) | Maximum initial distance from origin | \({\text{m}}\) |
| \(t\) | Time | \({\text{s}}\) |
| \({t_{\text{final}}}\) | Final time | \({\text{s}}\) |
| \({t_{\text{max}}}\) | Maximum simulation time | \({\text{s}}\) |
| \({v_{\text{max}}}\) | Maximum initial speed | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{x}1}}\) | X-velocity of the first star | \(\frac{\text{m}}{\text{s}}\) |
| \({{v_{\text{x}1}}^{0}}\) | Initial x-velocity of the first star | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{x}2}}\) | X-velocity of the second star | \(\frac{\text{m}}{\text{s}}\) |
| \({{v_{\text{x}2}}^{0}}\) | Initial x-velocity of the second star | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{y}1}}\) | Y-velocity of the first star | \(\frac{\text{m}}{\text{s}}\) |
| \({{v_{\text{y}1}}^{0}}\) | Initial y-velocity of the first star | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{y}2}}\) | Y-velocity of the second star | \(\frac{\text{m}}{\text{s}}\) |
| \({{v_{\text{y}2}}^{0}}\) | Initial y-velocity of the second star | \(\frac{\text{m}}{\text{s}}\) |
| \(\boldsymbol{v}\text{(}t\text{)}\) | Velocity | \(\frac{\text{m}}{\text{s}}\) |
| \({x_{1}}\) | X-position of the first star | \({\text{m}}\) |
| \({{x_{1}}^{0}}\) | Initial x-position of the first star | \({\text{m}}\) |
| \({x_{2}}\) | X-position of the second star | \({\text{m}}\) |
| \({{x_{2}}^{0}}\) | Initial x-position of the second star | \({\text{m}}\) |
| \({y_{1}}\) | Y-position of the first star | \({\text{m}}\) |
| \({{y_{1}}^{0}}\) | Initial y-position of the first star | \({\text{m}}\) |
| \({y_{2}}\) | Y-position of the second star | \({\text{m}}\) |
| \({{y_{2}}^{0}}\) | Initial y-position of the second star | \({\text{m}}\) |
Table of Symbols