Do massive objects follow geodesics in the same manner as electromagnetic waves? In my understanding of GR, massive objects and light both follow the geodesic of whatever frame they are in.  But I'm having a hard time understanding this in some specific situations.
On earth, if I throw a ball up in the air, it will reverse direction and return to earth.  If I shine a laser up in the air, it never slows down, it only loses energy in terms of its frequency.  How can they both be following the geodesic of spacetime if they take different paths?
Even if we threw the ball upwards at at the speed of light, and ignored the atmosphere, the ball wouldn't match the same path as the light since it would lose velocity as it gained altitude.
And if we imagine a scenario of a universe with just 1 planet in it, and no expansion, that ball would eventually reverse and fall back to the planet, but the light wouldn't.
Where am I going wrong here?
 A: The mistake you are making is a common one. You are considering only the space through which the object or light pulse moves and since they both start from the same location, you conclude that they follow the same geodesic.  But, you must also include the time dimension.  When you do this you see that the light reaches a certain point in much less time than the object that you threw up.  So, when you plot this in space-time they each follow a different geodesic path and this is why you do not observe them to behave the same way.  Since you cannot throw a ball upward at the speed of light (because it has mass), you can never make the ball and light to follow equivalent geodesics.
A: Before diving into the main part of your question, let me point out that the geodesics do not depend on the frame, but rather are coordinate independent constructions. Think, for example, that given two points $A$ and $B$ on the surface of the Earth, the shortest path between them does not depend on which coordinates you choose to use.
Now for the ball vs. laser "paradox". It is true that free falling objects always travel along geodesics, but there are different sorts of geodesics. While massive objects always travel along timelike geodesics, massless particles always travel along null geodesics (locally, at the speed of light). So a way of answering your question would be to say that light and the ball follow different geodesics.
Let me try to provide some intuition. Since the geodesics are frame independent, we can pick a locally inertial frame of reference to get some intuition from Special Relativity and our conclusions would hold (locally) in any reference frame. If we pick a frame covering a region of spacetime where both the ball and the beam of light are, then, in this frame, the null geodesic followed by the light will be a curve such that $x = ct$, while the ball will follow a curve such that $x = vt$ for constant $v < c$, which, up to signs and other directions which I'm omitting for simplicity, are the general expressions for a null and a timelike geodesic in Minkowski spacetime (notice they are just straight lines through spacetime). By looking in this frame, we see that the condition that massive objects travel along timelike geodesics generalizes the condition from Special Relativity that they can never reach the speed of light (it follows from $E^2 = p^2 c^2 + m^2 c^4 > p^2 c^2$). This restriction forbids them from following the same paths trough spacetime that a beam of light follows, and as a consequence one gets the phenomena you described.
Notice also that one can't make a ball (or any massive object) travel in the speed of light, and hence it will never travel along a null geodesic.
A: The mistake that you are making is to think of geodesics as a property of spacetime alone, and that a particle or wave will mysteriously follow "them".  A geodesic is a property of the spacetime together with a particle or wave; it has no independent existence.
