Calc Diebuster! - Lal'C and Tycho talk with each other from across the Solar System

A minor feat from the end of Diebuster!
Lal'C on Earth talks to Tycho on Pluto. Looking at Endless Mike's Cowboy Bebop calc for a bit of directiong, but this should be pretty straight forward. From the time when Lal'C stops talking and Tycho begins talking.
The timeframe is 11 frames.

T = 1s/24
= 41.6666667ms X 11
= 0.458333334s

The closest Pluto is to Earth is 4,280,000,000km, the furthest Pluto is from Earth is 7,500,000,000km, and on average is 5,187,000,000km away (information from here).

(Low end)
T = 4,280,000,000km/0.458333334s
= 9.3381818e12/299792458
= 31148.8216 C

(Mid end)
T = 5,187,000,000km/0.458333334s
= 1.13170909e13/299792458
= 37749.7519 C

(High end)
T = 7,500,000,000km/0.458333334s
= 1.63636363e13/299792458
= 54583.2154 C

Final Results
Lal'C communicates with Tycho on Pluto (low end) = 31148.822 C
Lal'C communicates with Tycho on Pluto (mid end) = 37749.752 C
Lal'C communicates with Tycho on Pluto (high end) = 54583.215 C