Let me assume that the object has spherical symmetry, however, for solving the present problem it is painted on its surface with different colors. So, imagining a plane section that contains the orbit of the object around the earth. The section of the plane through the object is a circle and we will see different points of the circumference painted in different colors.
At every time during its movement the object has a velocity consisting in two components: the original velocity, and the velocity toward the center of the Earth. So, at each time the object undergoes an inertial translation, as a whole (recall what Einstein said that that an accelerated system can be considered at each time as an inertial system with the instant velocity). Thus, at each instant another color will be in the direction of the Earth.
In the picture, one can see two instanciations of the object that approaches the Earth. The thin black line connects the 1st instanciation with the Earth center. The initial velocity, blue, is $v_0$, the instant velocity towards the Earth is the light-green arrow, and the black arrow is their resultant. Thus the object passes to a 2nd position, as shown in the 2nd instanciation. The dotted black line connects the center of the object with the center of the Earth. If one looks very attentively, one can see that the read segment in the 1st instanciation crosses the line towards the Earth, while in the 2nd instanciation it is completely below the line to the Earth center.
But these are two close instanciations. In continuation, as the object moves, the red segment will get more and more to the left of the line towards the Earth center, and the blue segment will be seen from the Earth. Thus, from the Earth, the colored segments will be all seen, step by step.