Gauss’s planetary equations
E29372
Gauss’s planetary equations are a set of differential equations in celestial mechanics that describe how a planet’s orbital elements change over time under the influence of perturbing forces.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical formulation in celestial mechanics
→
set of differential equations → |
| appliesTo |
Keplerian orbital elements
→
asteroid orbits → cometary orbits → osculating orbital elements → planetary orbits → satellite orbits → |
| assumes |
perturbing forces small compared to central gravity
→
two-body Keplerian reference orbit plus small perturbations → |
| category |
orbital perturbation theory
→
|
| describes |
time evolution of orbital elements
→
variation of orbital elements under perturbations → |
| domain |
classical mechanics
→
|
| expressedIn |
non-singular form for non-circular, non-equatorial orbits
→
|
| field |
astrodynamics
→
celestial mechanics → orbital mechanics → |
| governs |
time derivative of argument of periapsis
→
time derivative of eccentricity → time derivative of inclination → time derivative of longitude of ascending node → time derivative of mean anomaly → time derivative of semi-major axis → |
| historicalPeriod |
19th century
→
|
| mathematicalForm |
first-order ordinary differential equations
→
|
| namedAfter |
Carl Friedrich Gauss
→
|
| relatedTo |
Lagrange’s planetary equations
→
variation of parameters method → |
| relates |
perturbing accelerations to rates of change of orbital elements
→
|
| requires |
gravitational parameter of central body
→
|
| usedFor |
analytical orbit perturbation analysis
→
effect of atmospheric drag on low Earth orbits → effect of non-gravitational forces on orbits → effect of solar radiation pressure on orbits → effect of third-body perturbations → long-term orbital evolution studies → spacecraft trajectory design → |
| usedIn |
long-term stability analysis of planetary systems
→
mission analysis → orbit determination → |
| uses |
normal perturbing acceleration
→
perturbing acceleration components → radial perturbing acceleration → transverse perturbing acceleration → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Carl Friedrich Gauss
→
|
hasConceptNamedAfter |