I was trying to draw a space-time diagram representing two objects traveling through spacetime, me and the planet Earth. At first I thought I would just draw two straight lines heading upwards some distance, x, apart, seeing as my position relative to the center of the Earth would not be changing over time. I then realized, though, that I am constantly being accelerated outwards from the center of the earth at 9.8 m/s. Therefore, my space-time diagram should show a curved trajectory to the right representing such acceleration. So this is my quandary. Can anyone help me reconcile this? What does this space-time diagram look like?