2-body Definition and 25 Threads

I encounter a function that I don‘t know in the calculation of Relativistically invariant 2-body phase space integral: in this equation, ##s##is the square of total energy of the system in the center-of-mass frame(I think) I don't know what the function ##\lambda^{\frac{1}{2}}## is. There are...

How do you go about writing down the energy momentum tensor for the 2-body problem. Just looking for the approach.

Hi, I was trying to solve the classical two body problem with Lagrangian Principle. I replaced the angular velocity before taking the partial derivatives (which respect to the distance to the virtual particle) and the result was completely different. I would like to ask, therefore, which...

Hi I am confused about certain aspects of deriving the planetary orbit equation by considering it as 2-body problem. I will ask my first question now before i get to my other questions. In the David Tong notes on "Dynamics & Relativity" he states that a particle in central force potential...

Hi With the 2-body problem relating to planetary orbits i have encountered the following ; the gravitational force on the reduced mass acts towards the large mass(Sun) and since it is a central force it exerts no torque about the fixed centre(Sun) so angular momentum is conserved. Conservation...

Other than compact binaries, are there conditions where 2-body inspirals circularize? 3-body? Thx

Homework Statement Two-body problem given as $$\ddot{\textbf{r}}+\frac{GM}{r^2}\frac{\textbf{r}}{r}=0$$ $$\textbf{h}=\textbf{r}\times\dot{\textbf{r}}$$ where the moment of the momentum vector mh Homework Equations The vector solution to the above equation may be obtained by first taking the...

I'm having a ... "discussion" on another forum about capture and ejection of bodies. My opponents believe that, for one example, the sun can capture an object that has entered the SS from outside its g-well (i.e. on a hyperbolic trajectory) - without requiring a third body to steal its energy...

Homework Statement In a 2-body scattering event, A + B → C + D, it is convenient to introduce the Mandelstam variables, s ≡ −(PA + PB)2 , t ≡ −(PA − PC) 2 , u ≡ −(PA − PD) 2 , where PA,...,D are the 4-momenta of the particles A, . . . , D respectively, (· · ·) 2 = (· · ·) · (· · ·) denotes a...

I understand that in a 2-body system a circular orbit is gravitationally stable in General Relativity. In Newtonian dynamics, an elliptical orbit is also stable, but is this also true in GR? I understand that the orbit precesses, but I do not intend that to change my meaning regarding stability...

I was wondering are there any experiments to distinguish between 2 and 3-body decays? For example, consider decay of the muon and the pion: The pion only emits 1 muon neutrino ("missing energy") and 1 muon. The muon however, emits 1 muon neutrino, 1 electron neutrino and 1 electron. How is...

I have been looking at the problem of 2 point masses connected by a spring in polar coordinates. The problem is solved using the center of mass coordinate R and the relative coordinate r where M=total mass and m=reduced mass. The Euler-Lagrange equations then give equations for P(a vector) and...

How do you solve the Kepler Problem for a 2-body system where m1<<m2 with a given velocity and position vector resulting in a new velocity and position for a certain time interval?

Homework Statement A ball of mass M traveling at non-relativistic speed v elastically collides with a stationary ball of mass m. (a)Show that the maximum speed which the second ball can have is: 2Mv/(M+m)(b)What is the minimum speed?The Attempt at a Solution (a) Method 1 Go into ZMF...

Hi, I'm new to this forum and I've got a question. In all articles I've found about the two body problem, they first start off by writing the distances between the masses as one function r(t) and one function R(t) (which is just simple the position of the reference frame). *note: i use initial...

Homework Statement Assume that recombination of atoms proceeds at the gas-kinetic rate of collisions. Compare the recombination rates for a 2-body and 3-body reaction, such as in the formation of O2. (hint: you may want to use production rate equations and calculate the number density of...

Homework Statement A comet is released from rest at a distance r_max from the sun. Therefore it has no angular momentum. We can assume the sun is a point mass ( i.e. sun's radius is zero ). How long does it take for the comet to hit the sun? Let m = comet mass let M_s = sun's mass...

I'd like to get back into theoretical physics as a retiree. I last worked on the relativistic 2-body problem over 25 years ago. I've been reading Trump and Schieve's text on classical relativistic dynamics and I'm wondering has the classical 2-body relativistic problem been solved. I realize...

2-body problems--Need help calculating! A 20 kg block (A) rests on a frictionless table; a cord attached to the block extends horizontally to a pulley at the edge of the table. A 10 kg mass (B) hangs at the end of the cord. a) Clearly draw and label the force vectors acting on each object. b)...

Homework Statement I'm trying to solve the 2-body problem analytically by following this book: http://books.google.com/books?id=imN_8IuZ8l8C&lpg=PR1&dq=David%20Betounes%20Differential%20equations&pg=PA60#v=onepage&q&f=false" (note: the book preview is not complete, but you can find pages 69-73...

What are the equations of motion for two charges where the two charges are the only sources for the EM field? (No background field) What I'm looking for is given two particles of mass m_1 and m_2 with respective position vectors x_1 and x_2, what are f_1 and f_2 such that...

I just have a quick question about a binary star system consisting of 2 starts of unequal masses. Is the period of rotation of the 2 masses about their centre of mass equal? Do they both take the same amount of time to complete 1 revolution about the centre of mass?

Well, my biggest q, isn't exactly about the 2-body, it's more like 3-body I guess. What I'm trying to accomplish here is to say that we can not ignore a small third mass orbiting around a sun-like object. I have the Sun-Like Object and another object (L) orbiting around it, now L is...

Hello, everyone. Here is my question and my thoughts on it: Suppose we lived in a bizarre world in which gravitation, instead of being an inverse square law, were an inverse cube law. (a) In this world, show that the 2-body problem can be brought to a central force problem in a plane P by...

A little question: as a planet (such as jupiter) orbits the sun, both the planet, and the sun orbit the same point of the centre of mass. how do you calculate where that centre of mass is? (2 body problem only) thanks DH