Can a Binary Star system be possible where in one star is stationary and the other star revolves around it? (Just like a planet revolving a star. i.e planets in the system and the star revolving around their own center of masses to balance the system).

# [Physics] Binary Star system with one star stationary

orbital-motionplanetsstars

#### Related Solutions

They are sometimes also called double planets and they're more widespread in fiction than in observations. I don't think that there is any new instability that would appear for the system of double planets orbiting a star and that wouldn't be present for other, more asymmetric pairs of planets. Obviously, the tidal forces would be really large if the planets were close enough to each other. But because the tidal forces go like $1/r^3$, it's enough to choose the distance that is 5 times larger than the Earth-Moon distance and the tidal forces from the other Earth would be weakened 125 times and would already be as weak as they are actually from the Moon now (with a lower frequency).

One must realize that the systems with two or several planets are rather rare and the condition that the mass of the leading two planets is comparable is even more constraining.

Imagine that each of the two planets has a mass that is uniformly distributed between 1/20 of Earth's mass (like Mercury) and 300 Earth masses (like Jupiter) on the log scale. The interval goes from the minimum to the maximum that is 6,000 times heavier. That's more than 12 doublings, $2^{12}=4,096$. So if you pick the first planet to be at a random place on that interval of masses (uniformly at the log scale), the probability that the second planet's mass (which is independent) differs by less than the factor of $\sqrt{2}$ from the first mass is about $1/12$.

Only $1/12$ of systems that look like a pair of planets will be this symmetric. And the number of pairs of planets - even asymmetric ones – is rather low, indeed. The reason is really that during the violent eras when Solar-like systems were created, rocks had large enough velocities and they flew in pretty random directions so they were unbound at the end. It's just unlikely to find two large rocks in the same small volume of space: compare this statement with some high-temperature, high-entropy configurations of molecules in statistical physics.

It's also rather unlikely that a collision with another object creates two objects that will orbit one another. After all, the two-body orbits are periodic so if the two parts were in contact during the collision, they will collide again after one period (or earlier). Equivalently, the eccentricity of the orbit is likely to be too extreme which will lead to a fast reunification of the two new planets. Moreover, even if something would place the two newly created planets from a "divorce" on a near-circular orbit, perhaps a collision with a second external object (good luck), it's very unlikely that such an orbit will have the right radius, like the 1 million km I was suggesting in the case of the hypothetical double Earth above. If the two objects are too close, the tidal forces will be huge and (at least for some signs of the internal angular momentum) they will gradually make the planets collapse into one object again. And if the energy with which the planets are ejected from one another is too high, no bound state will be created at all. So the initial kinetic energy of the newborn 2 planets would have to be almost exactly tuned to their gravitational potential energy (without the minus sign) and that's generally unlikely, too.

## Best Answer

Well, motion is relative so you can choose a frame of reference where one is stationary. If you do though, it makes the equations of motion quite complicated.

Even in our solar system, the Sun isn't stationary. It orbits the center of mass of the whole solar system (barycenter), just as each planet orbits the center of mass.

The center of mass of our solar system moves relative to the sun due to the motion of the Sun and planets. Here is a graph:

(Source)

So you could potentially call a body in a system where the barycenter stays inside that body "stationary" but that's not technically correct, no matter how lopsided the masses of the bodies are. For example:

The larger mass will still always move relative to the system barycenter.