Pluto motion from image 1 to image 13:

image 1:  x1 = 346  y1 = 220
image 13: x2 = 352  y2 = 217

dx = 6 pixels * 1.117"/pixel = 6.702"
dy = 3 pixels * 1.074"/pixel = 3.222"

dr = 7.436"

dt = 12 frames = 7200 sec

--> 5.007e-9 rad/sec

From this, determine how far from Sun Pluto orbits.

acceleration = (G*M_Sun)/r^2 = v^2/r

At opposition, the difference between Earth's, Pluto's velocity determines the angular motion:

d(theta)/dt = (v_Earth - v_Pluto)/(r_Pluto - r_Earth)

let r_Pluto = a*r_Earth

d(theta)/dt = (v_Earth - sqrt(G*M_Sun/r_Pluto)) / (r_Earth*(a-1))

            = (v_Earth - sqrt(G*M_Sun/(a*r_Earth)) / (r_Earth*(a-1))

            = (v_Earth - v_Earth/sqrt(a)) / (r_Earth*(a-1))

            = (v_Earth / r_Earth) * (1-1/sqrt(a)) / (a-1)

let b = d(theta)/dt * r_Earth / v_Earth

      = d(theta)/dt * r_Earth / (2*pi*r_Earth / T_Earth)

      = d(theta)/dt * T_Earth / (2*pi)  (Eq. 1)

Measured value: b = 0.02513

(1-1/sqrt(a)) / (a-1) = b   (Eq. 2)

(sqrt(a) - 1) / (sqrt(a) (sqrt(a)+1) (sqrt(a)-1)) = b

drop a=1 solution,

a + sqrt(a) - 1/b = 0

keeping only sqrt(a)>0 solution (assuming b>0),

sqrt(a) = -1/2 + (1/2)sqrt(1 + 4/b)

a = (1/4) (sqrt(1 + 4/b) - 1)^2

---> a = 33.96 au

Actual value for Pluto:

a = 31.85 in 2010 (actually it varies a lot since the orbit is
   elliptical, but this is the current distance-- Observer's
   Handbook 2010)

:)