N$12$M$\mathrm{.}8)$ Some recent space probes have made several hyperbolic passes past the earth to help give them the right direction and speed to go to their final destination. Imagine that one such probe has a speed of $12$ km$.$s at a distance of $650,000$ km from the earth. If the angle that the probe$$s velocity vector v makes with earth. If the angle that the probe$$s velocity vector v makes with its position vector r at that time is $177$ degrees, how near will it pass by the earth at its point of closest approach?