Two body problem - effective particle

In summary, the "two body problem" in science refers to a scenario where two objects interact with each other through gravitational forces. An "effective particle" is a hypothetical object used to simplify calculations in this problem. It can be solved using mathematical equations and is significant in understanding the motion of objects in space. However, the model has limitations such as assuming point masses and not accounting for external factors.
  • #1
maria clara
58
0
as for the center of mass, the position vector is Rcm=[tex]\frac{m1r1+m2r2}{m1+m2}[/tex]
and Vcm is determined in a similar way (it is simply the time derivative of Rcm).

But what is the radius vector of the effective particle (with the reduced mass)?
is it simply the vectoric sum of the two radius vectors?


thanks
 
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  • #2
sorry, I didn't mean the sum, but the difference, r1-r2.
 

Related to Two body problem - effective particle

What is the "two body problem" in science?

The "two body problem" refers to a specific scenario in classical mechanics where two objects, usually of significant mass, interact with each other through gravitational forces. This problem is often used to model the orbit of planets and satellites around a central object, such as the sun.

What is an "effective particle" in the context of the two body problem?

In the two body problem, an "effective particle" is a hypothetical object that is used to simplify the calculation of the gravitational interaction between two bodies. It is a mathematical construct that represents the combined mass and position of the two bodies, allowing for easier analysis of their motion.

How is the "two body problem" solved?

The "two body problem" can be solved using mathematical equations and principles from classical mechanics, such as Newton's laws of motion and the law of universal gravitation. These equations can be used to determine the position, velocity, and acceleration of the two bodies at any given time.

What is the significance of the "two body problem" in science?

The "two body problem" is significant in science because it allows us to understand and predict the motion of objects in space, such as planets and satellites. It also serves as a basis for more complex problems involving multiple bodies, such as the three-body problem.

What are some limitations of the "two body problem" model?

One limitation of the "two body problem" model is that it assumes the bodies being studied are point masses with no size or shape. This does not accurately represent real-world objects, which can have varying shapes and sizes. Additionally, the model does not take into account external factors such as the gravitational pull of other objects, which can affect the motion of the two bodies in the system.

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