Three Body Problem - Earth, Sun, and Moon

In summary, the conversation discusses the challenges and potential solutions for solving the three body problem involving the sun, earth, and moon. The participants mention the limitations of using the restricted three body problem solution due to the moon's gravitational effects and suggest turning to numerical solutions for more accuracy. They also discuss the benefits of using a force model for potential addition of non-gravitational forces. The analytical results from the circular restricted three-body problem are deemed insufficient for this specific system due to its high mass ratio. The conversation concludes by mentioning the potential for simulation of this system in astronomy studies.
  • #1
metgt4
35
0
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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  • #2
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?
 

1. What is the Three Body Problem?

The Three Body Problem refers to the mathematical problem of predicting the motion of three celestial bodies, such as the Earth, Sun, and Moon, based on their gravitational interactions with each other. It is a complex problem that has been studied by scientists for centuries.

2. Why is the Three Body Problem important?

The Three Body Problem is important because it allows us to better understand the dynamics of the solar system and other celestial bodies. By studying the interactions between three bodies, we can gain insights into the larger scale behavior of the universe and make predictions about future events.

3. What makes the Three Body Problem difficult to solve?

The Three Body Problem is difficult to solve because it is a non-linear system, meaning that small changes in initial conditions can lead to drastically different outcomes. Additionally, the gravitational forces between the three bodies are constantly changing as they move, making it a highly complex and unpredictable problem to solve.

4. How have scientists attempted to solve the Three Body Problem?

Scientists have used various mathematical and computational methods to try and solve the Three Body Problem. Some have developed analytical solutions, while others have used numerical simulations and computer models to approximate the behavior of the three bodies. However, a perfect solution to the problem has yet to be found.

5. What is the significance of the Three Body Problem in astronomy?

The Three Body Problem is significant in astronomy because it has helped us understand the motions and interactions of celestial bodies, such as the Earth, Sun, and Moon, in our solar system. It has also led to advancements in our understanding of gravity and the laws of motion, which have implications for many other areas of science and technology.

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