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Earth-Moon Barycenter and Pro-Retrograde motions

  1. May 23, 2013 #1
    Hello, this is my first post.

    My question is, if the Earth is revolving around the Earth-Moon barycenter as it orbits the sun, then why don't we observe a slight respective prograde and retrograde motion of other celestial bodies?

    In other words, if the Earth is moving 'forward' on the orbit of the Earth-Moon barycenter, and then 'backward' on that same orbit, why don't we observe a slight stuttering motion of the Sun and other celestial bodies, due to that pro-retrograde motion of the Earth?

    Or do we observe this??
    I've been searching around for a few days and have been unable to find any discussion of this issue.

  2. jcsd
  3. May 23, 2013 #2


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    Hello, Lifepsy.

    When you say "we" I assume you mean naked-eye observers, and not accurate scientific measurements(which, of course, have to account for it).

    Having done quick parallax calculations, I've found the maximum observable "wobble" to amount to approximately 2 arcminutes, or 1/15th of the Solar disc's diametre, spread over half a lunar month.
    Twice that amount for Mars at it's cloest approach(~0,5AU).
    2 arcminutes is the amount the Sun travels in in the sky in 8 seconds. See if you can spot such a small difference. Now consider that you've got ~14 days of gradual change to cover the same angular distance.

    Try calculating it yourself. Use the skinny triangle approximation to get the angle in radians:

    Note that the base of the triangle used to calculate the above parallax is ~ 21 000 km, which is not even twice the Earth's diametre, which in turn can be used to calculate daily parallax(the amount of wobble between morning and evening due to Earth's rotation). This means that you get more than half of the same wobble by comparing the raising and the setting Sun, but spread over 12 hours instead of half a month.
  4. May 23, 2013 #3
    Thanks for the reply, Bandersnatch

    I guess by "we", I meant either the naked-eye or any measurements observed by instrumentation.

    I see you have a parallax calculation for measuring the wobble which I will try and work out for myself.... Does this mean the pro-retrograde motions of celestial bodies due to Earth's wobble around Earth-Moon barycenter are, in fact, empirically observed?

    And measuring devices do confirm the Sun,etc. demonstrate slight pro-retrograde motions every period of Earth's revolution around Earth-Moon barycenter?

    I am trying to confirm this, as I've never heard it mentioned before and can't find any official statements.
  5. May 23, 2013 #4


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    I've made a couple of errors in my calculations(:blushing:). That should be 29 arcseconds, not 2 arcminutes(i.e., 4 times less).

    The wobble is there, but it's not a very useful, significant, or interesting thing by itself. That's why you don't hear much about it.

    You can find some(not a whole lot) information about it by googling "barycentric parallax".
    For example, there's this article from 1924:
    That mentions they had to correct for the effect.

    You might find some mention in discussions of systematic observational errors too.
    Last edited: May 23, 2013
  6. May 23, 2013 #5
    Thanks for the link, Bandersnatch, though I don't think I'm able to interpret the results. I see this is from 1924, I was hoping there would be some current documentation with more precise measurements available.

    I will look around more with those keywords, 'barycentric parallax'
    Thank you.
  7. May 25, 2013 #6
    The wobble you're looking for exists. You won't find it except in very detailed planetary "ephemerides", which are just descriptions of the motions of the planets. Don't forget, the motion of the Earth around the E-M barycenter is small, and the farther away the planet is, the less parallax it will have due to that small motion. It's similar to the "diurnal parallax" caused by being on opposite sides of the Earth - this makes some difference in the observed position of the Moon, much less for any of the planets.
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