If a photon has no mass, why is its trajectory still bent when it passes a massive object?

Turns out that light will take the shortest path between two points. For everyday thought the shortest path is a straigt line. But, think of the earth, to get from here to china you cant walk in straight line. You have to follow the curvature of the earth and are really walking a curved path. Thats similar to what happens with light, except it is traveling through space. Space is not just emptiness. It is thought by scientist to be more like a combination of space (Allows for position changes..ie movement) and time (I dont know how to define time). This space-time is not just an idea but it can be manipulated. Specifically when matter interacts with space-time it changes it in a way that can be though of as curving it. All objects moving though space-time now are forced to follow a curved path because there is no such thing as movement outside of space-time (To my knowledge). LIght is no exception. When space time bends/ waprs light must follow this new curved path even though it is not matter. This may be because it is moving, and things that move have to follow the rules...ie move according to how space-times curvature dictates