# Orbital mechanics question - 2 bodies **URL:** \ **Category:** Factual Questions\ **Created:** [August 22, 2001, 9:10pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615 "2001-08-22T21:10:14Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 22, 2001, 9:10pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/1 "2001-08-22T21:10:14Z")
Suppose you have two bodies of equal mass in space (like a binary star system) are they each orbiting the other in a manner of speaking? Now suppose one of them is maybe half the mass of the other; the bigger one is still going to move about (it won’t act as if it’s nailed to a fixed point in space, will it? so are they still orbiting each other now? suppose again that now one of the bodies is 1/100th of the size of the other; again the smaller one is going to do most of the moving, but the big one isn’t entirely stationary, are they orbiting each other now? You can see where I’m going here; I’m not trying to justify a geocentric view of the solar system, but it must be true that the earth’s gravity moves the sun a tiny bit. The question is, I suppose, can the pair of bodies of equal mass be truly described as orbiting each other, or is there another term for it? ---
**Author:** ![Race\_Bannon](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Race\_Bannon](https://boards.straightdope.com/u/Race_Bannon)\ **Post date:** [August 22, 2001, 9:29pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/2 "2001-08-22T21:29:25Z")
> [@](#): > > \*Originally posted by Mangetout \* > \*\*Suppose you have two bodies of equal mass in space (like a binary star system) are they each orbiting the other in a manner of speaking? > … > You can see where I’m going here; I’m not trying to justify a geocentric view of the solar system, but it must be true that the earth’s gravity moves the sun a tiny bit. > > The question is, I suppose, can the pair of bodies of equal mass be truly described as orbiting each other, or is there another term for it? \*\* You have the right idea. Binary stars of equal mass could each move in a circle around an empty point in space, midway between them. And as one star gets larger with respect to the other, this “center” moves closer, and even inside of, the larger one. Think of two figure skaters with their hands joined, spinning around each other. This kind of thing should lead you to consider what is really meant by the word “orbit”. In commmon conversation, the word kind of implies that the satellite is in an elliptical path, outside the atmosphere of the planet. But in the general _astrodynamical_ sense, the word just refers to the natural motion of two (or maybe more) objects under the influence of their own gravity (only). In this sense, and orbit could be and ellipse, or parabola, or a hyperbola. The paths of multiple objects are more complicated, as you guessed. In this sense, a thrown baseball is “in orbit” if we neglect the aerodynamic effects. It just so happens that its orbit intersects the earth’s surface rather soon. ---
**Author:** ![Podkayne](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Podkayne](https://boards.straightdope.com/u/Podkayne)\ **Post date:** [August 22, 2001, 9:32pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/3 "2001-08-22T21:32:44Z")
In a two-body system, _both_ bodies orbit the center of mass of the system. The center of mass of the Sun-Jupiter system is just slightly outside the surface of the Sun. This does indeed cause the Sun to move about the center of mass, at a velocity of about 12.5 meters per second. The highly technical term for this motion is “wobble.” This is how we find planets around other stars. The Doppler shift of the star’s spectrum reveals its motion about the barycenter. ---
**Author:** ![Race\_Bannon](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Race\_Bannon](https://boards.straightdope.com/u/Race_Bannon)\ **Post date:** [August 22, 2001, 9:33pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/4 "2001-08-22T21:33:22Z")
I should have mentioned - the tiny motions of stars as they are perturbed by unseen planets is one of the best ways such planets can be detected. ---
**Author:** ![Race\_Bannon](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Race\_Bannon](https://boards.straightdope.com/u/Race_Bannon)\ **Post date:** [August 22, 2001, 9:36pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/5 "2001-08-22T21:36:25Z")
…but Podkayne beat me to it… ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [August 22, 2001, 9:37pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/6 "2001-08-22T21:37:00Z")
> [@](#): > > The question is, I suppose, can the pair of bodies of equal mass be truly described as orbiting each other, or is there another term for it? Technically, the two bodies (if spherical) are both in elliptical orbits about the same point, called the centre of mass. Kepler’s Laws then apply to both bodies, using the centre of mass as the focus. When the masses are equal, this centre of mass lies halfway between them. Otherwise it is closer to the heavier of the two. The lighter is then in a bigger elliptical orbit than the heavier one. For a very large and a small body, the centre of mass can lie inside the larger. The heavier’s orbit then looks much like a sort of wobble. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 22, 2001, 9:39pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/7 "2001-08-22T21:39:25Z")
So except in practical useful terms, it’s not quite right to say that the earth orbits the sun, but rather all of the bodies in the solar system revolve around their collective centre of mass? Haha, so you see, science is wrong and theref…sorry. ---
**Author:** ![micco](https://avatars.discourse-cdn.com/v4/letter/m/5f8ce5/32.png) [@micco](https://boards.straightdope.com/u/micco)\ **Post date:** [August 22, 2001, 9:41pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/8 "2001-08-22T21:41:37Z")
First you have to define “orbit”. > [@](#): > > Orbit: a path described by one body in its revolution around another It is certainly true that any two bodies with mass have a gravitational force between them, but an orbit would involve making a complete circuit around the other body. The earth orbits the sun. The earth’s gravitational attraction will cause the sun to wobble somewhat, but the path of that wobble won’t encompass the earth, to the sun doesn’t orbit the earth. ---
**Author:** ![Podkayne](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Podkayne](https://boards.straightdope.com/u/Podkayne)\ **Post date:** [August 22, 2001, 9:46pm UTC](https://boards.straightdope.com/t/orbital-mechanics-question-2-bodies/77615/9 "2001-08-22T21:46:40Z")
If you said “The Earth revolves about the solar system barycenter,” unless you were trying to make a specific point about some fiddly point of celestial motion, everyone would look at you funny, even though you’re technically correct. “The Earth orbits the Sun,” suffices in most ordinary problems.