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