User:JohnOwens/Orbital variables
|
|
From external pages
How the variables are used (& re-used) on some of the pages I refer to.
Mars Academy (http://www.marsacademy.com/orbmect/orbles1.htm)
Kind of cheesy name, but what the heck.
| <math>F<math> | force |
| <math>m_1, m_2<math> | mass of objects 1 & 2 |
| <math>G<math> | gravitational constant |
| <math>d<math> | distance (scalar) |
| <math>r<math> | distance (scalar) |
| <math>\bar{r}<math> | displacement (vector) |
| <math>\mu<math> | <math>G\,m_1<math> |
| <math>K_e<math> | kinetic energy |
| <math>W<math> | work |
| <math>P_e<math> | potential energy |
| <math>F_g<math> | gravitational force |
| <math>E<math> | mechanical energy |
| <math>\bar{A}, \bar{B}<math> | arbitrary vectors |
| <math>A, B<math> | their magnitudes |
| <math>\alpha<math> | the angle between <math>\bar{A}<math> and <math>\bar{B}<math> |
| <math>\beta<math> | complement of α |
| <math>\bar{v}<math> | velocity, <math>\bar{r}'<math> |
| <math>v<math> | speed |
| <math>t<math> | time |
| <math>k<math> | specific mechanical energy |
| <math>\bar{p}<math> | momentum |
| <math>\bar{L}<math> | angular momentum |
| <math>\bar{h}<math> | specific angular momentum, <math>{\bar{L} \over m}<math> |
| <math>\bar{a}, \bar{b}, \bar{c}<math> | arbitrary vectors |
| <math>\bar{k}<math> | vector constant of integration |
| <math>\gamma<math> | angle between <math>\bar{r}<math> and <math>\bar{k}<math> |
| <math>p<math> | semilatus rectum |
| <math>a<math> | semimajor axis |
| <math>c<math> | (distance between foci)/2 |
| <math>\mbox{d}<math> | directrix of a conic section |
| <math>x<math> | distance between directrix and focus |
| <math>\theta<math> | angle to <math>\bar{r}<math> |
| <math>e<math> | eccentricity |
| <math>r_p, r_a<math> | distance at periapsis and apoapsis |
| <math>v_p, v_a<math> | velocity/speed at periapsis and apoapsis |
World of Physics (http://scienceworld.wolfram.com/physics/Two-BodyProblem.html)
| <math>m_1, m_2<math> | mass of objects 1 & 2 |
| <math>M<math> | <math>m_1 + m_2<math> |
| <math>\mathbf{r}_1, \mathbf{r}_2<math> | radius of objects 1 & 2 |
| <math>\mu<math> | reduced mass <math>{m_1\,m_2 \over m_1 + m_2} \equiv {m_1\,m_2 \over M}<math> |
| <math>\mathbf{r}<math> | displacement from body 1 to body 2, <math>\mathbf{r}_2 - \mathbf{r}_1<math> |
| <math>\mathbf{p}<math> | momentum |
| <math>a<math> | distance between bodies, <math>r_1 + r_2<math> |
| <math>G<math> | gravitational constant |
| <math>\mathbf{L}<math> | angular momentum, <math>\mathbf{r} \times \mathbf{p}<math> |
| <math>\mathbf{h}<math> | angular momentum per mass, <math>{\mathbf{L} \over m} \equiv {\mathbf{r} \times \mathbf{p} \over m} = {\mathbf{r} \times \mathbf{r'}}<math> |
| <math>h<math> | magnitude of <math>\mathbf{h}<math> |
| <math>\theta<math> | angle from arbitrary direction |
| <math>A<math> | area |
| <math>t<math> | time |
| <math>E<math> | orbital energy |
| <math>\mathcal{E}<math> | specific energy |
| <math>\mathbf{A}<math> | Laplace-Runge-Lenz vector, <math>\mathbf{r'} \times \mathbf{h} - {G\,M\,\mathbf{r} \over r}<math> |
| <math>e<math> | eccentricity |
| <math>v<math> | velocity/speed |
| <math>p<math> | semilatus rectum |
| <math>u<math> | <math>{1 \over r}<math> |
| <math>B<math> | arbitrary constant |
| <math>\theta_0<math> | arbitrary constant |
| <math>a<math> | semimajor axis |
| <math>\theta_0<math> | argument of pericenter |
| <math>a \equiv 2 E<math> | |
| <math>b \equiv 2 G M m<math> | |
| <math>c \equiv h^2 m<math> | |
| <math>A(r) \equiv 2 \sqrt{a (a r^2 + b r - c)}<math> | |
| <math>B(r) \equiv \ln{\left[b + 2 a r + A(r)\right]}<math> | |
| <math>C(r) \equiv A(r) + b B(r)<math> | |