Well, according to famed cosmologist Albert Einstein, you can try to solve this problem by looking at the subtle bending of starlight as it encounters the immense gravity of a**ther, closer star.*
By measuring that light deflection, you could, in theory at least, weigh out the mass of the target star.
There's only one problem: Einstein never thought that we could actually make this measurement. The legendary scientist said that "there [was] ** hope of observing [that distortion] ... directly," in a 1936 study published in the journal Science.* Read more...