And Mars bars No Bound...

Certain measurements are more difficult than others.  Orbital distance and orbital period can be accurately measured but not planet mass.

So it is more likely that given average orbital speed and average orbital distance the we have a good estimate of the planet mass, by calculating centripetal force, ${F}_{m}$

${O}_{avg}$ = ( aphelion + perihelion )/2 = ( 249 209 300 +206669000 )/2 = 227939150 km

${F}_{m} = \cfrac{{V}^{2}_{avg}}{{O}_{avg}}$ = ((24.077)^2)/227939150 = 0.00000254 kms^-2

And we move on to orbital speed at the aphelion,

(249 209 300*0.00000254 )^(0.5) = 25.15 kms^-1

Orbital speed at the perihelion,

(206 669 000*0.00000254 )^(0.5) = 22.91 kms^-1

And the orbital speed from considering $\triangle GPE$ alone is,

$v =\sqrt{3{g}_{m}{r}_{m}}$ = (3*0.003711*3390 )^(0.5) = 6.143 kms^-1

The actual Mars orbital speed is measured as 24.077 kms^-1

In a similar way based on the model for Earth where the final orbital velocity is the sum of two rotating velocities, ${V}_{m1}$ and ${V}_{m2}$,  and Mars has a initial velocity ${V}_{i}$ when it was captured by the Sun,

${V}_{m1} - {V}_{m2}$ =  25.15 kms^-1

${V}_{m1} + {V}_{m2}$ =  22.91 kms^-1

${V}_{m1}$ = ( 25.15 + 22.91 )/2 = 24.03  kms^-1  and

${V}_{m2}$ = 25.15 -  24.03 = 1.12 kms^-1

The parallel component of the final orbiting velocity is the sum of the velocity the body would have considering a decrease in GPE alone and the parallel component of the initial approach velocity. To find the parallel initial velocity component,

${V}_{m1}$ = $\sqrt{2*\triangle GPE} + {V}_{ip}$ = 6.143 + ${V}_{ip}$ = 24.03  kms^-1

 ${V}_{ip}$ = 24.03-6.143 = 17.89  kms^-1

The second smaller rotating velocity is the perpendicular component of  the initial velocity, ${V}_{i}$.

${V}_{ir}$ = 1.12 kms^-1

${V}_{i} =\sqrt{{V}^{2}_{ip} + {V}^{2}_{ir}}$ = ((1.12)^2 + (17.89)^2)^(0.5) = 17.92 kms^-1

And the attack angle tan^-1$(\cfrac{{V}_{ir}}{{V}_{ip}}$) = tan^-1(-1.12/17.89) = -3.582 degrees to perpendicular of the orbital line joining Mars and the Sun.

So, Mars approached the Sun with an initial velocity ${V}_{i}$ = 17.92 kms^-1 and was captured by the Sun.