# Questions tagged [binary-stars]

Binary stars are a system of two stars rotating around their center of mass, as opposed to single stellar systems such as our solar system.

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### How to convert from polarization modes ($h_{+}$, $h_{×}$) to obtain spin-weighted spherical harmonic $h_{lm}$ as a function of $h_{+}$, $h_{×}$?

This question arises from a discussion in the thread How to convert from plus and cross polarization modes ($h_{+}$, $h_{×}$) to spin-weighted spherical harmonic $h_{lm}$? I was looking for a ...
1 vote
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### Gravitational wave radiation power from dimensional analysis

Let us try to find a formula for the power emitted through gravitational waves (GW) from a binary system in quasi circular orbit. The relevant quantities are the Newton's constant $G_N$, speed of ...
154 views

### Are orbital eccentricities in a binary system always the same?

Some excercises on Kepler laws and binary system use this relation $$\frac{r_1}{r_2} = \frac{a_1}{a_2},$$ where $r$ is the distance from the center of mass to each object and $a$ is the semi-major ...
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### How do astronomers calculate the mass of celestial bodies light year from Earth?

I have read in many scientific stuff that mass of this planet or that stars is about '$n$' times the mass of Sun. I have gone through many websites and videos on YouTube but didn't find the right ...
2k views

### Time dilation effects at the center of a binary black hole system

Imagine two identical black holes in a circular orbit, and Alice is smack-dab in the middle of the system (at the barycenter). Bob is at infinity. Let's assume that Alice and Bob are stationary ...
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### How would I see if there is a transit in this light curve?

I am trying to detect if some binary star systems have exoplanets orbiting them. I've been completing this project for many weeks now, and have managed to write some code that will plot light curves ...
1 vote
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### How likely is it that a typical pair of black holes will eventually merge?

Gravitational wave observatories have found many pairs of black holes merging. I understand that before they were working there were estimates of the rate at which they ought to be found. To me it ...
118 views

### Can two relativistic black holes' event horizons overlap and separate again?

I have read this question: What I have not seen is a purely classical argument for the non-separation of a black hole merger. One can obviously take the time reversed spacetime manifold of a merger ...
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### Gauge independence of the gravitational-wave frequency and gauge dependence of the binary separation?

In the seminal paper by Cutler & Flanagan (1994), which uses multi-timescale analysis to derive waveforms in the post-Newtonian approximation without spin effects, they state that, "In Eq. (...
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### Why isn't the two-body problem in General Relativity completely solvable?

I do know that approximate solutions to the two-body problem come in the form of the equations of motion in the Schwarzschild metric plus post-Newtonian power radiated. However, I am more interested ...
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### Black holes: Is merger inevitable when horizons touch?

I watched a simulation of the binary black hole merger of 2019 April 12 https://www.ligo.caltech.edu/video/ligo20200420v1 When the "apparent horizons" (their terminology; are those ...
1 vote
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### Dissipation caused by Gravitational Wave Emission

Two massive bodies orbiting each other can lose energy through gravitational wave emission until colliding. Can a single massive body, moving with constant velocity with respect to an observer, lose ...
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### Is there an approximate expression for the force between two black holes?

Just curious: is there an approximate expression for the gravitational attraction between two Schwarzschild black holes of masses $M$ and $m$, held without relative speed at some center to center ...
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### As of 2021 in how many binary systems has the period decrease due to gravitational waves been measured?

I am searching for data for the period decrease of binary systems due to gravitational waves. I am aware of three systems in which it was possible to measure this period decrease: The Hulse-Taylor ...
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### Gravitational waves in the post-Newtonian expansion

I have spent some time trying to understand gravitational waves in the context of the post-Newtonian expansion. As far as I understand it, the general relativistic equation of motion can be ...
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### Should the stars of a relativistic binary system have tangential acceleration?

Should the stars of a relativistic binary system have tangential acceleration?
1 vote
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### Why in binary star system the 2 bodies revolve around their center of mass?

Can you prove it mathematically? Is it just an observation? I know the force between them is $\frac{Gm_1m_2}{r^2}$. Centripetal force on any one of them is $\frac{mv^2}{r_1}$, where $r_1$ is radius of ...
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### An apparent paradox in General relativity using a binary black hole

Note: Quantum gravity effects are ignored in this question. Imagine 2 black holes each with mass $m$ approaching each other and after some time the Event Horizons (EHs) of both black holes touch each ...
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### Relationships between G magnitude, Johnson V magnitude, and spectral type of stars?

I'm simulating a population of binary stars for a summer research project. I'm adding uncertainties to my simulated observables such as angular position and radial (line of sight) velocity. I'm using ...
1 vote
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### Why are wide binary systems assumed to contain negligible dark matter?

I'm doing a project that simulates wide binaries to do gravity tests, specifically a dark matter vs MOND test. I've come across similar papers, and their justification for using wide binaries for this ...
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### Would the 2 orbiting black holes emit gravitational waves?

Would the 2 orbiting black holes emit gravitational waves even if they are moving at a constant speed in orbits? Here, can we consider the changing direction of black holes in their orbits as ...
1 vote
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### Find semi-minor axis of elliptical binary orbit given semi-major axis and mass ratio

I'm working on a simulation of binary stars. I'm using Kepler's Laws to solve for the angular velocity given the semi-major axis $a$ and the masses $m_1$ and $m_2$ of the two objects in an elliptical ...
1 vote
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### Could two planets trapped between two stars orbit each other?

Say there are two stars, each exerting and equal force on a point in the midde of them. For simplicity, we'll say the two stars have the same mass and are equidistant from the point. Now suppose that ...
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### Angular momentum orientation of the orbits of the two stars with respect to the Solar System

Happen to see this in Wiki... The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, ...
1 vote
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### Specific gravitational wave polarisation direction for "edge-on" binary system

The gravitational wave signal from a binary system approaching merger consists of a mixture of the two $h_+$ and $h_\times$ orthogonal polarisation states. If the binary is "face-on" (with ...
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### Original reference for Binary star system orbital seperation decay rate due to GW emission

Could someone please point me in the direction of who first derived the equation for the orbital separation decay rate of two point masses in a binary system due to the emission of gravitational waves:...
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### Binary stars orbiting around each other are equidistant [closed]

This is a problem that was given to me in my Classical Mechanics course: J.S.Plaskett's star is one of the most massive stars known at present. It is a binary star, that is, it consists of two stars ...
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### Solving for the mass of the larger star in a binary star system. (Larger star is much larger, so orbit is essentially circular)

I'm a teaching assistant for a class on Newtonian mechanics, and was confronted with a way of solving for the larger mass in this two-star system that gets the right symbolic solution, but seems to ...
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### Can Binary Stars Escape Each Other?

updated 8/27/2020 While the recession of our Moon from the Earth may slow and even stop, (see When will the Moon reach escape velocity?) binary star systems will (1) never stop experiencing mutual ...
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### Definition of eclipsing binaries?

In the second minimum (the 3rd step) there is a smaller decrease in light intensity. For this to happen, wouldn't you need to be looking at the plane of orbit from above rather than directly along the ...
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### Gravitational force between astronomical bodies in a binary system

If two celestial bodies of similar mass form a binary system and both have fairly relativistic velocities does in that case gravity act with delay and does the picture shown present the problem in the ...
1 vote
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### Keplerian orbital elements of a binary system: computing the eccentricity vector and angular momentum vector

I have been given a binary system and know a few of the keplerian orbital elements such as ...
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### Ratio of masses of double star problem

I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 2 of chapter 1 is as follows: The two components of a double star are observed to move in circles of radii ...
1 vote
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I don't think context is needed but to make sure: I'm doing a homework exercise on binary system. P is the orbital period and E the energy of the system. The following is in the solution when trying ...
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### How do tidal forces change gravitational waves

If there is a binary of two neutron stars, they are going to be deformed because of the tidal forces. I suppose that it will cause a change in the movement of the stars and that will cause a change in ...
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### Eccentricity of two bodies in an unbound orbit

There seems to be two definitions of an eccentricity of orbiting bodies, one for when it’s not bound and the other for when it is bound (Keplerian binary). When the binary is bound there is a simple ...
1 vote
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### Derive hamiltonian from equations of motion

Is there a method for deriving the hamiltonian given that you know the equations of motion? For example given the equation (equation 5 in paper linked) they simply the derive the Hamiltonian in ...
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### Discerning binary stars

What is the minimum magnification that one would need to discern a pair of binary stars if viewed from Earth? Are there factors other than magnification that matter? If so, why?
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### In which direction would gravitational waves be emitted when two black holes colide?

Imagine two black holes on the x-axis coming together at the origin (not rotating around each other, just falling towards each other). In which direction would the most intense gravitational waves be ...
5k views

### Why do gravitational waves circularize a binary?

I understand that a binary orbiting around one another will circularize due to the emission of GWs due to Peters equations and that highly eccentric binaries evolve faster. But GW emission also ...
1 vote
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### Are there any black hole neutron star binary?

Has a black hole-neutron star binary aver been observed? I mean observed in any way: gravitationally, through eclipse, or any other means. EDIT Thanks to the comment to this question, we know that ...
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### How does the mass loss in a binary system affect the semi-major axis of the orbit?

It is common that during the stellar evolution one of the stars in a binary system would transfer mass into the the other, resulting in the increase of mass of one star and decrease of mass of the ...
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### Why does mass (gas) transfer between binary stars cause them to move apart?

Some binaries, like Algol binaries, move monotonically apart from each other as one steals gas from the other. Why? On a naive level, shouldn't friction and such cause the two stars to move (rotate?,...
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### Existence and evolution of P-type "asymmetrical binaries"

I'm not sure how those are called so let me explain what I mean by "P-type asymmetrical binaries" - I'm thinking of two stars of very different masses (originally) that orbit each-other fairly closely....
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### Free fall and gravitational waves

If you take the Earth-Moon system, from what I understand, the Moon for instance is in free fall towards the Earth-Moon center of mass. However Einstein's equivalence principle says that a body in ...
1 vote
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### Roche lobes in binary star systems

While studying mass transfer in binary star systems, I came across the concept of Roche lobes and the role of the inner Lagrangian point $L_1$, as shown in the adjoining figure. However, I am having ...
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### What happens to the accretion disk when two black holes merge?

I'm aware that accretion disks around black holes are formed from the swirling mass of matter that is slowly being stripped of its atoms, but what happens to it when two black holes merge? I was ...
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### Position vector of an eccentric binary

For a circular, equatorial ($z=0$) Newtonian binary, the position can be clearly written as, $$x_i = r(\cos \Omega t, \sin \Omega t, 0)$$ for orbital frequency $\Omega$. My question is how would ...