Venus

Venus data are as follows,

radius = 6052 km, mass  = 4.867E24 kg, orbit radius = 108208000 km, average orbit speed = 35.02 kms^-1, gravity 8.87 kms^-2.

Velocity at the aphelion (108939000*0.0000113)^(0.5) = 35.086 kms^-1

Velocity at the perihelion (107477000*0.0000113)^(0.5) = 34.850 kms^-1

Based on the model previously developed, the two final rotating vectors are,

vi = ( 35.086 + 34.850)/2 = 34.968 kms^-1

vp = 35.086 - 34.968 = 0.118 kms^-1

The perpendicular component suggest that Venus was captured with very little initial velocity.

The centripetal force keeping Venus in orbit is,

\({F}_{v}\) = (35.02)^2/108208000 = 0.0000113 kms^-2.

which can be calculated theoretically base on surface gravity,

\({F}_{v}\)=\(\frac{{M}_{v}}{{M}_{v}+{M}_{s}}{g}_{v}\) = 0.00887*4.867E24/(4.867E24+9.942779860e27) = 0.00000434 kms^-2.
                                                         
And the orbital velocity associated with this value is,

v = \(\sqrt{{O}_{v}{F}_{v}}\) = (108208000*0.00000434)^(0.5) = 21.670 kms^-1

Orbital velocity can also be calculated from,

v = \(\sqrt{3{g}_{v}{r}_{v}}\) = (3*0.00887*6052)^(0.5) = 12.69 kms^-1

Both velocity are calculated based on energy concerns, the former on change in PE as Orbs increases and the latter on decrease in GPE at that orbital distance.

At this point we are stuck.  Either surface gravity be adjusted or the relative sun and planet mass be adjusted.  Or we assume that Venus has very little initial velocity when it was captured by the sun.  A check of Venus orbital distance and Sun radius show that gravity due to the Sun,

 \({g}_{s}\)e^(-108208000/696342 ) = \({g}_{s}\)e^(-155.4) is negligible. But still unless the two theoretical values tally up, surface gravity or relative planet mass can both be in error.  Or the theory is in error.

If we assume that the theoretical results should telly up then Venus surface gravity is

\({g}_{v}\) = 21.670^2/(3*6052) = 0.02586  kms^-2.

We check this value with,

\({F}_{v}\)=\(\frac{{M}_{v}}{{M}_{v}+{M}_{s}}{g}_{v}\) = 0.02586*4.867E24/(4.867E24+9.942779860e27) = 0.0000126 kms^-2

which compares well with the calculated value of 0.0000113 kms^-2 , based on orbital measurements.

New Venus surface gravity is 25.86 ms^-2 .