Data Model of Kepler's Second Law of Planetary Motion

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SUMMARY

The discussion focuses on deriving Kepler's Second Law of Planetary Motion, which states that a planet sweeps out equal areas in equal times. The user seeks to validate this law through real-world orbital data and calculations involving calculus and numerical approximation techniques. The suggestion includes utilizing Newton's laws to model a two-body problem, where one body is significantly larger than the other, to facilitate the analysis. This approach will enable the user to compare theoretical results with empirical data effectively.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Proficiency in calculus, particularly area calculations
  • Familiarity with Newton's laws of motion
  • Knowledge of numerical approximation methods
NEXT STEPS
  • Research how to apply calculus to derive area under a curve in orbital mechanics
  • Learn about numerical methods for approximating integrals, such as the trapezoidal rule
  • Explore data sources for real-world planetary orbital data
  • Study the two-body problem in classical mechanics to understand its implications on Kepler's laws
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Students and researchers in physics or mathematics, particularly those focused on celestial mechanics, differential equations, and numerical analysis.

icecats
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Hello,
I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for a couple of planets and calculate the area at a couple of different parts of the orbit, proving that they are the same. How could I do this using calculus, numerical approximation, or similar?
Thanks
 
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You could make it up based on Newton's laws for a two body problem with one body much bigger than the other.
 

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