Greetings all. Due to perceived inadequacies, I here submit for your consideration a revised version of my earlier post -- From Paul Deema Fri May 23 15:16:51 2008. World/Moon system From Neville Jones Mon May 19 20:02:46 2008 "Diagrams, comments, thoughts, one-way tickets to the Gulag, ... toss them all into the pot and let's see what comes out." Version 2. First a few simplifications - The Earth's orbit is a circle; the Moon's orbit is a circle; The Moon's orbit lies in the plane of the ecliptic; the Earth/Moon barycentre is at the centre of gravity of the Earth. Next, some approximate dimensions - One day = 86400 s; one year = 365.25 days; the Earth's orbit has a radius of 150 * 10^6 km; the Moon's orbit has a radius of 384 * 10^3 km; the Earth revolves at 360/365.25 = 0.986 deg/day; the Moon revolves at 360/27.322 = 13.2 deg/day; the Earth has an orbital velocity of 30 km/s; the Moon has an orbital velocity of 1.0 km/s. A body in orbit about the Sun at a distance 150 * 10^6 km, which does not rotate on its axis (inclined at 0 deg wrt the plane of its orbit) experiences a 'day' of one year duration with the Sun rising over the western horizon and setting over the eastern horizon. The shadow of a sundial will record a traverse of 0.986 deg/day from East to West. Should the body of the previous paragraph rotate in a prograde direction on its axis once per year, then a sundial shadow will neither advance nor retreat from a fixed position. Again the same body, but rotating in the same direction at a rate of twice per year -- the shadow will now advance from West to East at a rate of 0.986 deg/day. Change the body's rotation rate to once per 27.322 days ie 13.2 deg/day and the shadow will move from East to West at a rate of 13.2 - 0.986 = 12.214 deg/day. This second term -- 0.986 -- is the 360 deg of the orbit divided by the number of days to achieve one revolution. This body will have an orbital velocity of 30 km/s. If we increase the orbital velocity to 31 km/s, then the time for one orbit is reduced to 365.25 * 30/31 = 353.468 days and the orbital radial velocity increases to 1.018 deg/day. If the body is still rotating at once per 27.322 days, then the shadow will advance at a rate of 13.2 - 1.018 = 12.182 deg/day. At 29 km/s orbital velocity, the corresponding figures are 365.25 * 30/29 = 377.845 days orbital period and 0.953 deg/day revolution. Shadow advance then, will be 13.2 - 0.953 = 12.247 deg/day. The difference is therefore 12.247 - 12.182 = 0.065 deg/day -- an eminently measurable difference. Now the purists may cry foul because we all know that if an orbiting body is travelling faster, then its orbit radius will be less, and conversely, if slower then the radius will be greater. However, if the body we have been discussing is the Moon and it is orbiting the Earth at a distance of 384 * 10^3 km, and the Earth/Moon barycentre is orbiting the Sun, then at full moon it will be travelling at Earth orbital velocity plus Moon orbital velocity, while at new moon it will be travelling at Earth orbital velocity minus Moon orbital velocity. Its average velocity would therefore be 30 km/s. Under these conditions we should see the rate of advance of the shadow at new moon to be 0.065 deg/day faster than at full moon. Should the Universe however be centred on the Earth with the Moon and the Sun orbiting it, the Moon's radial velocity would be constant and so the rate at which the shadow advances would be constant. A real test would of course need to take into account the fact that both orbits in question are in fact ellipses, that they are not in the same plane and that the orientation of the Luna orbit major axis remains fixed while its angle to the Sun is constantly varying. I'm sure there will be other things which have not occurred to me but I am also sure that -- if I have the mechanics properly sorted -- this effect is eminently measurable. That we cannot immediately rush out and do the experiment matters not -- science is in the habit of making predictions which routinely take decades or centuries to demonstrate or destroy. Finally, the Earth/Moon barycentre is not at the Earth's centre of gravity -- there is an offset of about 4700 km. While the effect is greatly reduced, it seems to me that the rate of shadow advance could, under these conditions, also be shown to differ slightly between new moon and full moon on the Earth. Paul D Get the name you always wanted with the new y7mail email address. www.yahoo7.com.au/mail