I'm prepared to believe that changes in the Sun's barycentre can slightly affect its radiation spectrum and hence Earth's climate. But photons, bouncing from pillar to post, take about 100,000 years to travel from inner regions of the Sun to its surface where they escape as radiation.
So to try and correlate barycentric effects with present day climate changes, scientists should work out the positions of planets (especially Jupiter and Saturn), and thus the barycentre, that time in the past rather than now.
The snag is that photon escape time is only an average. So you'd need to average over such a broad time window that any supposed barycentric effects would be smoothed out to practically nothing.
So to try and correlate barycentric effects with present day climate changes, scientists should work out the positions of planets (especially Jupiter and Saturn), and thus the barycentre, that time in the past rather than now.
The snag is that photon escape time is only an average. So you'd need to average over such a broad time window that any supposed barycentric effects would be smoothed out to practically nothing.

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