On earth, two parts of a space probe weigh 17300 N and 3260 N. These parts are separated by a center-to-center distance of 19.4 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.

Just plug in

F = Gmm/r^2 = G*(17300/g)(3260/g)/19.4^2
You know G and g, so fill them in.