On Tuesday, November 6, 2012 2:03:14 AM UTC+8, Bill Owen wrote:
Peter Riedt wrote:

Calculating the EXACT mass of the sun



The relationship r*v^2 determines the mass of the sun by the distance of a planet from the sun (r in m) and the square of its speed (v in m/sec) exactly if the known velocity is adjusted for eccentric orbits. The adjusted velocities for nine planets are shown in the following table. All produce the standard value of GM with a deviation of 0.000000000000000000%. GM (1.327158270.E+20) is calculated from the Codata values G = 6.674E-11 and M = 1.988550E+30.

r/m v/msec adjusted v r*v^2=GM

MER 5.791000E+10 47,870 47,872 1.327158270.E+20

VEN 1.082100E+11 35,020 35,021 1.327158270.E+20

EAR 1.496000E+11 29,780 29,785 1.327158270.E+20

MAR 2.279200E+11 24,130 24,131 1.327158270.E+20

JUP 7.785700E+11 13,070 13,056 1.327158270.E+20

SAT 1.427000E+12 9,690 9,644 1.327158270.E+20

URA 2.871000E+12 6,810 6,799 1.327158270.E+20

NEP 4.497100E+12 5,430 5,432 1.327158270.E+20

PLU 5.913000E+12 4,720 4,738 1.327158270.E+20



Peter Riedt





I see a few problems with this analysis.



1) The distance r is given to four or five significant digits, the

velocity v likewise. The quantity r*v^2 should therefore be given to no

more than five significant digits.



2) What is the adjustment for eccentricity?



3) What about perturbations from the other planets? Jupiter's mass is

about 1/1000 that of the Sun. For Uranus, Neptune and Pluto it almost

makes sense to add Jupiter's mass to the Sun's mass when working out

their r*v^2. (Certainly the inner four planets can be treated that way

under some circumstances.)



4) We can measure the product G*Msun quite well from radio tracking of

spacecraft. The most recent value (JPL planetary ephemeris DE425) is

1.3271244004E20 m^3/s^2, good to at least 10 digits. This differs from

the value above in the 6th significant digit.



5) Even though we know G*Msun very well, we don't know the sun's mass at

all well, because we don't know the value of G to more than four digits.

CODATA's currently recommended value is 6.67384E-11 +/- 0.00080E-11,

with a relative accuracy of 1.2E-4.



-- Bill Owen

Bill, it is not an analysis; it is a calculation using a variant of Kepler's third planetary law. The remarkable thing about it is that for nine planets each result is identical in terms of GM and therefore the values of G and M are validated regardless of the number of significant digits. The adjustments to v are minimal, they range from 1m/sec to 46m/sec. They were necessary because rv^2is for circular orbits and all planets are ellipses due to perturbations. I will never doubt again that G represents a true constant. G will be part of my theory of the cause of gravity. Kepler and Cavendish were geniuses.

Peter Riedt