Answer
$35.9\space GJ$
Since this is a positive value the spacecraft is not bound to the sun.
Work Step by Step
Here we use the equations of kinetic & potential energy to find the total energy consisting of the new horizons spacecraft.
Total energy (E) $=\frac{1}{2}mV^{2}-\frac{GM_{S}}{m}$
Where, m - mass of the spacecraft, V - speed of the spacecraft, $M_{S}$ - mass of the sun, R - distance to the spacecraft from the sun.
$E= 450\space kg\left \{ \frac{1}{2}(51000\times\frac{1000}{3600}m/s)^{2}-\frac{6.67\times10^{-11}Nm^{2}/kg^{2}\times1.99\times10^{30}kg}{6.5\times10^{12}m}\right \}$
$E= 35.9\times10^{9}J= 35.9\space GJ$
