A space-borne optical tweezer apparatus for use with colloidal crystallization experiments has been characterized. The trapping force has been measured as a function of index mismatch between colloidal microspheres and the surrounding fluid and as a function of particle size. This work also presents a method to determine the refractive index of a colloidal microsphere, which is then used to calculate the applied trapping force for the case of an arbitrary background fluid. This is useful for work with dense colloidal suspensions when the usual (e.g., Stokes flow) trap force measurement methods do not apply, as well as microrheological studies of complex soft matter.