Lagrange’s planetary equations
E157396
mathematical formulation in celestial mechanics
perturbation theory tool
set of differential equations
Lagrange’s planetary equations are a set of differential equations in celestial mechanics that describe how the orbital elements of a body evolve over time under perturbing forces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lagrange’s planetary equations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382649 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lagrange’s planetary equations Context triple: [Gauss’s planetary equations, relatedTo, Lagrange’s planetary equations]
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A.
Gauss’s planetary equations
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.
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B.
Mécanique céleste
Mécanique céleste is Pierre-Simon Laplace’s landmark multi-volume treatise that reformulated celestial mechanics using Newtonian gravitation and advanced mathematical analysis, profoundly shaping modern astronomy and physics.
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C.
The Tides and Kindred Phenomena in the Solar System
"The Tides and Kindred Phenomena in the Solar System" is a seminal scientific work by George Howard Darwin that analyzes tidal forces and related gravitational effects throughout the solar system using mathematical and physical principles.
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D.
Division on Dynamical Astronomy
The Division on Dynamical Astronomy is a specialized branch of the American Astronomical Society focused on the study of the motions and gravitational interactions of astronomical objects.
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E.
Kepler’s laws of planetary motion
Kepler’s laws of planetary motion are three fundamental principles that mathematically describe how planets orbit the Sun in ellipses, sweep out equal areas in equal times, and relate their orbital periods to their distances from the Sun.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lagrange’s planetary equations Target entity description: Lagrange’s planetary equations are a set of differential equations in celestial mechanics that describe how the orbital elements of a body evolve over time under perturbing forces.
-
A.
Gauss’s planetary equations
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.
-
B.
Mécanique céleste
Mécanique céleste is Pierre-Simon Laplace’s landmark multi-volume treatise that reformulated celestial mechanics using Newtonian gravitation and advanced mathematical analysis, profoundly shaping modern astronomy and physics.
-
C.
The Tides and Kindred Phenomena in the Solar System
"The Tides and Kindred Phenomena in the Solar System" is a seminal scientific work by George Howard Darwin that analyzes tidal forces and related gravitational effects throughout the solar system using mathematical and physical principles.
-
D.
Division on Dynamical Astronomy
The Division on Dynamical Astronomy is a specialized branch of the American Astronomical Society focused on the study of the motions and gravitational interactions of astronomical objects.
-
E.
Kepler’s laws of planetary motion
Kepler’s laws of planetary motion are three fundamental principles that mathematically describe how planets orbit the Sun in ellipses, sweep out equal areas in equal times, and relate their orbital periods to their distances from the Sun.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical formulation in celestial mechanics
ⓘ
perturbation theory tool ⓘ set of differential equations ⓘ |
| appliesTo | two-body orbits with perturbations ⓘ |
| assumes | Keplerian reference orbit plus small perturbations ⓘ |
| basedOn | Lagrange’s variation of parameters method ⓘ |
| canBeWrittenIn |
Gauss’s planetary equations
ⓘ
surface form:
Gauss’s form of planetary equations
vectorial form ⓘ |
| describes |
effects of perturbing forces on orbits
ⓘ
time evolution of orbital elements ⓘ |
| domain |
classical mechanics
ⓘ
dynamical systems ⓘ |
| expressedInTermsOf |
argument of periapsis
ⓘ
eccentricity ⓘ inclination ⓘ longitude of ascending node ⓘ mean anomaly or mean longitude ⓘ semi-major axis ⓘ |
| field |
astrodynamics
ⓘ
celestial mechanics ⓘ orbital mechanics ⓘ |
| goal | predict long-term stability and evolution of orbits ⓘ |
| historicalPeriod | 18th century ⓘ |
| influenced |
analytical theories of planetary motion
ⓘ
modern orbit determination methods ⓘ |
| languageOfOriginalFormulation | French ⓘ |
| mathematicalNature | first-order ordinary differential equations ⓘ |
| namedAfter | Joseph-Louis Lagrange ⓘ |
| relatedTo |
Delaunay variables
ⓘ
Hamiltonian perturbation theory ⓘ canonical perturbation theory ⓘ |
| relates | perturbing accelerations to rates of change of orbital elements ⓘ |
| requires | perturbing potential or perturbing acceleration model ⓘ |
| usedFor |
analysis of periodic orbital variations
ⓘ
analysis of secular orbital changes ⓘ long-term orbit propagation ⓘ mission design in astrodynamics ⓘ study of atmospheric drag effects ⓘ study of non-spherical gravity effects ⓘ study of planetary perturbations ⓘ study of radiation pressure effects ⓘ study of third-body perturbations ⓘ |
| uses | osculating orbital elements ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lagrange’s planetary equations Description of subject: Lagrange’s planetary equations are a set of differential equations in celestial mechanics that describe how the orbital elements of a body evolve over time under perturbing forces.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.