So far, June's chill is one for the records

The cloudy, chilly and rainy open to June here has been the talk of the town. So far this June is running more than 12 degrees cooler than last year, and the clouds, rain and chilly lake winds have been persistent. The average temperature at O'Hare International Airport through Friday has been only 59.5 degrees: nearly 7 degrees below normal and the coldest since records there began 50 years ago.

6 The increase of the Astronomical Unit

6.1 The observation

From the analysis of radiometric measurements of distances between the Earth and the major planets including observations from Martian orbiters and landers from 1961 to 2003 a secular increase of the Astronomical Unit of approximately 10 m/cy has been reported (36) (see also the article (37) and the discussion therein).

6.2 Search for explanation

Time–dependent gravitational constant and velocity of light This increase cannot be explained by a time–dependent gravitational constant G because the ˙ G/G needed is larger than the restrictions obtained from LLR.

It has also been speculated that a time–dependent change in the velocity of light can be responsible for this effect. Indeed, if the speed of light becomes smaller, than ranging will simulate a drift of distances. However, a inspection of Kepler’s third law
T2 4π2
a3 = GM⊙

(17)
12

shows that, if one replaces the distance a by a ranging time a = ct, then effectively the quotient G/c3 appears. Only this combination of the gravitational constant and the speed of light governs the ratio between the orbit time, in our case the orbit time of the Earth. Consequently, a time–dependent speed of light is equivalent to a time–dependent gravitational constant. Since the latter has been ruled out to be possibly responsible for an increase of the Astronomical Unit, also a time–dependent speed of light has to be ruled out.

Cosmic expansion The influence of cosmic expansion by many orders of magnitude too small, see Sec.9.2. Neither the modification of the gravitational field of the Sun nor the drag of the planetary orbits due to the expansion is big enough to explain this drift.

Clock drift An increase of ranged distances might also be due to a drift of the time scale of the form t → t + αt2 for α > 0. This is of the same form as the time drift needed to account for the Pioneer anomaly. From Kepler’s third law one may ask which α is suitable in order to simulate the increase of the Astronomical Unit. One obtains α ≈ 3 · 10−20 s−1 what is astonishing close to the clock drift needed for a clock drift simulation of the pioneer anomaly, see Eq.(16) and below.
7 The quadrupole and octupule anomaly Recently an anomalous behavior of the low–l contributions to the cosmic microwave background has been reported. It has been shown that (i) there exists an alignment between the quadrupole and octupole with > 99.87% C.L. [38], and (ii) that the quadrupole and octupole are aligned to Solar system ecliptic to > 99% C.L. [39]. No correlation with the galactic plane has been found.

The reason for this is totally unclear. One may speculate that an unknown gravitational field within the Solar system slightly redirects the incoming cosmic microwave radiation (in the similar way as a motion with a certain velocity with respect to the rest frame of the cosmological background redirects the cosmic background radiation and leads to modifications of the dipole and quadrupole parts). Such a redirection should be more pronounced for low–l components of the radiation. It should be possible to calculate the gravitational field needed for such a redirection and then to compare that with the observational data of the Solar system and the other observed anomalies.

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8.2 Other anomalies?
There is one further observation which status is rather unclear bit which perhaps may fit into the other observations. This is the observation of the return time of comets: Comets usually come back a few days before they are expected when applying ordinary equations of motion. The delay usually is assigned to the outgassing of these objects. In fact, the delay is used for an estimate of the strength of this outgassing. On the other hand, it has been calculated in (44) that the assumption that starting with 20 AU there is an additional acceleration of the order of the Pioneer anomaly also leads to the effect that comets come back a few days earlier. It is not clear whether this is a serious indications but a further study of the trajectories of comets certainly is worthwhile.