Anomalies in orbital measurements of Mercury and the moons of Jupiter are today known to result from Relativity and the speed of light *c*. A discrepancy of 43^{″}/cyr in Mercury’s 5600^{″}precession is a sign of General Relativity. An anomaly in observations of Jupiter’s moons was predicted by Roemer from the finite speed of light. All possibilities being considered, the lunar anomaly may have a cosmological origin.

This author’s hypothesis may be summarized simply:

where *t* is age of the Universe, *GM* is the gravitational constant multiplied by a constant with dimensions of mass.

Speed of light *c* would then be given by:

c\left(t\right)={\left(GM\right)}^{1/3}{t}^{-1/3}

(7)

\dot{c}\left(t\right)=\left(-1/3\right){\left(GM\right)}^{1/3}{t}^{-4/3}

(8)

\frac{\dot{c}}{c}=-\frac{1}{3t}=-0.24\times {10}^{-10}y{r}^{-1}

(9)

where age of Universe *t* is estimated at 13.7Gyr, the constants *GM* cancel.

By theory, when *t* was small *c* was enormous and the Universe would have expanded like a “Bang.” As age *t* increases, *c* would slow due to gravitation and continue to slow at a tiny rate today. This model has been suggested to precisely fit the non-linear redshifts of distant Type Ia supernovae [12], the *4.507034%* proportion of bayons and other puzzles. Cosmology makes a surprising but testable prediction: Time for laser light to return would increase each year, making the Moon appear to recede faster as measured by LLRE.

Apparent lunar distance would increase proportional to decrease in *c*:

\frac{\dot{a}}{a}=-\frac{\dot{a}}{c}=\frac{1}{3t}

(10)

\dot{a}=\frac{a}{3t}=\frac{384,400km}{3\left(13.7\text{Gyr})\right)}

(11)

where age of Universe *t* is estimated at *13.7 Gyr*, apparent distance is predicted to increase an additional 0.935*cm*/*yr,* precisely accounting for the anomaly.From LLRE and accounting for the speed of light, actual recession rate would be:

\dot{a}=3.82\pm .07cm/yr-0.935cm/yr

(13)

\dot{a}=2.88\pm .07cm/yr

(14)

This value is in *1σ* agreement with eclipse records, Mansfield sedimentary data and numerical simulation. If one of these three datasets were found to contain error, the other two would agree with prediction.

Variation of *ċ*/*c* = 0.24 × 10^{− 10}
*yr*^{− 1} equals − 0.72*cm*/sec *yr*, too small to have been detected by previous experiments. For example, a survey by Iorio [13] using data on planetary orbits limits cdot/c to (0.5 ± 2) × 10^{− 7}
*yr*^{− 1}, more than 3 orders of magnitude greater. Iorio [14] has also written about a change in lunar orbital eccentricity. A change in semimajor axis could be interpreted as a change in eccentricity. However as lunar orbital angular momentum increases the semimajor and semiminor axes would both change proportionately. Iorio finds no known physical basis for an eccentricity change.

An apparent change in the astronomical unit of 15 ± 4*m*/*cyr* has been cited by Krasinsky et al. [15] Although planetary observations contain many possible sources of error, the apparent change is of similar order of magnitude to the lunar orbit anomaly. The discrepancy in AU could also be partially due to change in *c*. On the Moon we have the advantage of laser reflectors, providing a more precise standard of measurement.