"The dipole signal seen by an observer moving with speed v relative to the rest frame of the CMB is T_0 v/c, where T_0 is the absolute temperature of the CMB, and c is the speed of light. Thus, additional sources of error that could affect the absolute calibration of the WMAP data include errors in the determination of WMAP’s velocity with respect to the solar system barycenter (the point of reference for the COBE dipole) and errors in the absolute temperature of the CMB. The velocity of WMAP is routinely measured with respect to geocentric inertial coordinates (GCI) with an accuracy of < 1 cm s
-1. The velocity of the Earth is determined from the JPL ephemeris with similar accuracy."
http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/syserr/wmap_syserr.pdf
Pity rattis, (s)he will have to build and launch a space probe like WMAP to convince him/herself that the Earth moves around the barycentre (so Jupiter's, Saturn's etc motion is included), as measured against the CMB.
Canute's model of the universe will have not only horribly complex orbits of the solar system planets (and asteroids, comets etc), but a very odd semi-annual ~2.73 K blackbody that goes round the Earth is just the same plane as the Sun does, but is clearly not connected to the Sun!
In principle, you could make observations of the CMB from the surface of the Earth, but ...
So, other indicators of semi-annual motion?
- pulsars (you have to know where you are wrt the barycentre to get the timing right - in fact, rattis could build a telescope, fit a webcam and good clock, and measure the Earth's motion quite accurately, all by looking at M1, the Crab pulsar!)
- (BTW, really good, coordinated observations by LBI radio telescopes will also show the ~200 million year motion of the solar system around Sag A*)
- doppler signals etc from the Voyagers and Pioneers (I think there's only one still broadcasting)
- fast binary timing (this is a variation on pulsars, but with quite different objects, and different physics)
- interstellar meteor streams (yes, we do have samples of particles from other stellar systems, burning up in the atmosphere every few seconds)
- doppler shifts in stars all around the celestial sphere, with a 6 months' period, and a magnitude which exactly matches a model of the Earth in orbit around the barycentre, in a plane pole at coordinates (\alpha, \delta), ellipticity e, nodes at ...