Actually, the web page I cited doesn’t say Earth orbits the Sun-Jupiter barycenter. It says Earth orbits the solar system’s barycenter (which is pretty close to the Sun-Jupiter barycenter but it’s not the same thing).
Can you point me to a web page that agrees with you that this statement “is just wrong” [your words]? Because I googled the question “Earth orbits the barycenter of what?”. Naturally, there are multiple sources which completely ignore the barycenter and merely say that Earth orbits the Sun. I also found several sources which ignore the rest of the solar system and talk about the Earth-Sun barycenter. But looked at five who discussed the solar system’s barycenter and all five of them said yes the Sun and Earth and all the objects in the solar system orbit the barycenter of the solar system. I can’t find a single source (outside this thread) that says the solar system has a barycenter but Earth doesn’t orbit it.
But you could also say that the Earth orbits the Earth-Moon barycenter. And what barycenter does the Moon orbit around?
Objects behaving like all of their mass is at the center of mass only works when the mass distributions are spherically symmetric. The Solar System isn’t.
Depends on what you mean by “alignment”. The Jupiter/Sun barycenter is above the “surface” of the sun by thousands of miles. This is the point that the two orbit around. Thus, if Jupiter and Earth are in alignment (shortest distance between them), I would expect the Sun to be farther away, not closer.
The Earth/Moon barycenter goes through the body of the Earth (about a thousand miles down from the surface closest to the moon), so one would say Earth rotates around it while the moon orbits it.
My answer: On a short time scale of weeks, Earth and Luna orbit the Earth-Luna barycenter. But on a longer time scale of months, both Earth and Luna are orbiting the barycenter of the solar system. Luna’s orbit around the solar system is a series of a dozen or so loops whose center is the barycenter of the solar system. On an even longer time scale of MegaYears, everything in our Galaxy, including Luna, is orbiting the barycenter of the Galaxy. It just makes lots of little loops and twirls along the way.
This kinda caught me off-guard as well … my understanding is that if we treat the Earth and Moon as point-sources of force, then these two points orbit around the barycenter of this system, and it’s the barycenter that orbits the Sun … meaning the Earth wobbles a bit as it revolves around the Sun …
Then, by extension to a 12 or 18 body system, each of these body’s force vector is pointed at the combined barycenter of the whole system … just add the forces from the Sun, Jupiter, Saturn etc etc etc (as measured from the Earth/Moon barycenter) and this should point to the solar system’s barycenter, not the center of gravity of the Sun …
Why would all these 18 point sources of gravity have be symmetric relative to each other? … they are symmetric within themselves but I don’t see the need for them to be symmetric to each other …
… or does this have to do with the near impossibility of solving the 18-body gravity equations? …
I am not questioning your judgement in the slightest, but I am interested in knowing how you made your determination. Can you shed some light on this (PM me if you prefer)?
You have the period too long by a factor of 2. Jupiter’s period is 12 years. So if its opposition (point where it’s in the opposite direction from the sun) is in April, a year later when the Earth comes around to opposition again, Jupiter will have traveled 1/12th of its orbit. So Earth has to travel 1/12th of an additional orbit to catch up. That is, an extra month, so the opposition will be in May in this case. So for Jupiter, the period from one opposition to the next (the synodic period) is 13 months. The conjuction point (point where Jupiter is in the same direction as the Sun) will be half that, 6 1/2 months after opposition. In this case, that’ll be in October or November.
The Earth is a small speck that orbits the sun, with distant Jupiter pulling on the whole set. So to a first approximation, Jupiter pulls BOTH Sun and Earth closer to it, with no effect on the Earth-Sun distance.
To a second approximation, there would be the tidal effects. Tidal effects always pull a body apart. So Jupiter actually pulls the Earth and Sun apart from each other periodically by a very very tiny amount, with a 6 month period.
Note that from the point of view of the Moon’s orbit around the Sun it is not a bunch of loops. If you draw the Moon’s orbit around the Sun you get something fairly close to a circle (okay, an ellipse). It is everywhere concave. Not remotely loopy.
Stand on the surface of the Moon, right in the middle of the Earth-facing side. The Earth-Moon barycenter will be directly above you. The Moon will be directly below you. If you let go of something, which way does it fall, towards the barycenter or towards the Moon?
The net force vectors don’t all point to the barycenter. I can’t explain why they don’t, because there’s no reason why they would. Individual components of the net force point towards individual objects, and then you add up all of those components to get the net force.
I’ve been looking for a good cite. I think Chronos and Frankenstein Monster have explained the issue well, but I haven’t found an authoritative citation yet.
This is an N-body problem (or 3-body if you just consider Sun, Earth and Jupiter). It doesn’t follow Kepler’s laws. You can’t reduce it into a 2-body problem by replacing 2 objects with 1 at their barycenter.
Let’s simplify the problem and imagine just three bodies: the Sun, Earth, and Jupiter. Would it be fair to say that the Sun and Earth both orbit the Sun-Earth barycenter but Jupiter and the Sun-Earth system orbit the Sun-Earth-Jupiter barycenter? If that’s the case, then it seems logical to me that Earth actually orbits the Sun-Mercury-Venus-Earth-Luna barycenter whereas Jupiter orbits the Sun-Mercury-Venus-Earth-Luna-Mars-Asteroids-Jupiter barycenter. But all the sources I’ve found say that Earth and Jupiter both orbit the solar system barycenter.
Can anyone find some actual emperical data on measuring the Earth-Sun distance to an accuracy level which could detect deviations away from the numbers predicted by the Earth-Sun elipse, caused by the position of Jupiter (if such deviation exists)? If the emperical data shows no deviation, that would support the claim that Jupiter doesn’t affect the Earth-Sun distance.
That’s a great idea, and finally led me to a good citation. Here’s a chart of the perihelion and aphelion dates, times and distances for a hundred year period Earth at Perihelion and Aphelion: 2001 to 2100. The variability of perihelion and aphelion distances is a few thousand kilometers, not hundreds of thousands of kilometers even though sometimes perihelion occurs when Jupiter is on one side of the Sun (relative to Earth) and sometimes on the other side.
This pen in front of me is on the Moon’s side of the Earth/Moon barycenter, I let it go it falls towards Earth because the gravity force is so much stronger … maybe I’m thinking barycenter means something else … because it’s just a point in space, not “treating it as a point”, but in fact, it is a point … no mass, no gravity, no nothing … there’s no reason for the net force vector to point at the barycenter except that this net force vector has to point someplace, and if not the barycenter, then where? …
I’ve given too much thought to this, so please excuse my repeating what sbunny posted above … I’m wording this a little different, but the question is the same … we’re at the Sun and we experience a gravity force vector pointed towards the Earth AND a second force vector pointed towards the Moon … now the Sun can only have one acceleration vector, so we ADD the two gravity force vectors to get a resultant force vector and use this to calculate our acceleration vector … this resultant vector points towards the barycenter at all times …
You seem to be claiming that the Earth is following the ellipse and I’m claiming the Earth has 13 distinct wobbles per year in and out of this ellipse … I haven’t bothered with a citation thinking the Wikipedia article “Perturbation” is good enough for this hijack … noting that I agree 100% none of this is relevant to the effects of Jupiter on the Earth’s climate short of a billion year time interval, and even at this long period the effect may well be within instrumentation error …
Please note your reference here clearly states “(although in reality neither of the bodies are truly stationary, as they both orbit the center of mass of the whole system—about the barycenter)” … this seems to support what sbunny is claiming …
ETA: From Andy L’s citation: “Due of the gravitational perturbation of the Moon (and to a much lesser extent the planets), Earth’s actual distance at perihelion can vary from 0.9831914 AU (147,083,346 km) to 0.9833860 AU (147,112,452 km). This is a range of 0.0001946 AU (29,106 km), which corresponds to about 2.28 times the 12,756 km equatorial diameter of Earth.”
You really think a three body problem is simplifying things? Even I (admittedly more form the book of the same name than any formal education that included it) know how difficult a three body problem is.
Question from an ignorant one here: it would seem to me that the barycenter is everchanging, which is part of what makes it so complicated. Is that an incorrect understanding?
No, this is just saying the TWO bodies orbit around each other’s barycenter. Even when we approximate the 3-body problem by assuming that the 3rd body is too small to affect the other two, the third body follows a path that isn’t quite circular or elliptical. If it’s very close to one body, it will be very close to a circular orbit around that body. E.g. the Apollo spacecraft started out in a nearly circular orbit around the earth, and ended up in a nearly circular orbit around the Moon.
