Notes on Relativity and Cosmology - Physics Department, UCSB

190 CHAPTER 7. RELATIVITY AND THE GRAVITATIONAL FIELD
from the center of the earth. As a result, their accelerations
have nearly the same magnitude. However, the direction of
the acceleration varies from stone to stone.] How would the
spacetime diagram be different if the stones have an initial velocity
relative to the earth? Take this initial velocity to be the same for all
stones.
x
Stones
Earth
(b) Suppose that three small stones are released from high above the
earth as shown below. Sketch their worldlines on a spacetime diagram
drawn in the reference frame of the middle stone. Use the y direction
(shown below) for the space direction of your diagram. (That is,
sketch the motion in the y, t plane.) How would the diagram be
different if the stones have an initial velocity relative to the earth?
In all cases, assume that the stones pass smoothly through
the earth’s surface – don’t worry about them hitting the
earth.
Stones
y
Earth