Three Body Problem - Earth, Sun, and Moon

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SUMMARY

The discussion focuses on solving the three-body problem specifically for the Sun, Earth, and Moon. It establishes that the Moon's gravitational influence disqualifies the use of the restricted three-body problem solution due to its significant mass. Participants agree that numerical solutions are essential for accurate trajectory predictions, allowing for the incorporation of additional forces such as solar wind and light pressure. The conversation highlights the inadequacy of analytical results from the circular restricted three-body model in this scenario.

PREREQUISITES
  • Understanding of the three-body problem in celestial mechanics
  • Familiarity with numerical methods for solving differential equations
  • Knowledge of gravitational forces and their effects on celestial bodies
  • Basic principles of orbital mechanics
NEXT STEPS
  • Research numerical integration techniques for celestial mechanics
  • Explore the use of software tools like MATLAB or Python libraries for simulating orbital dynamics
  • Study the effects of non-gravitational forces on celestial trajectories
  • Investigate the historical context and solutions of the three-body problem in astronomy
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in celestial mechanics and the dynamics of the Sun-Earth-Moon system will benefit from this discussion.

metgt4
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How would you go about solving the three body problem in the case of our sun, earth, and moon? The moon's gravitational effects are enough to rule out using the restricted three body problem solution, right? So if given a set of initial conditions, how would one find equations for the motions of each of these bodies?
 
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If you want a trajectory with any kind of accuracy I would say that you need to turn to numerical solutions, which luckily are fairly easy do to in this case. Numerical solutions using the force model also has the benefit that you can add non-gravitational forces like solar wind and light pressure in the same framework later if you like (well, that of course not that relevant for the moon I guess).

The analytical results you can get from the circular restricted three-body do require the third body to be of insignificant mass and since the earth-moon system has one of the highest mass ratios in the solar system, I would, like you, say that requirement clearly is not satisfied.

Perhaps others here can offer more insight - I'm sure simulation of the Sun-Earth-Moon system must be a well practised exercise for astronomy majors?
 

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