Accordingly to the Relativity Theory only the relative speed is important.
In a second part of this exercise three objects are considered.
In order to detect the electromagnetic field we build a gallows on the north pole of the Star. On the gallows hangs, via a rope, an iron ball. The iron ball has a negative charge.
When there is no electric field, normally, the iron ball will hang in a straight line, towards the direction of the center of the Star.
When there is an electric field the ball will point in the direction of the planet. The ball will move in a circle in the same time as the planet will make one revolution.
To describe this problem more accurate and to include time, let us assume it is possible to modulate the charge of the planet.
At the begin of every hour the charge of the planet is positive for a short time and then zero.
In this part 3 objects are involved: A very massive Star (Black Hole) to simulate our Galaxy, one Star and one Planet.
Our Sun, in this configuration, has a speed of 250 km / sec.
The following figure shows this.
<---- Initial Position x O = The Sun x x P = The position of the x x planet now x x p = The position of the planet time t ago x O P - x - x x p x x x ---->The above picture is only correct if you assume that the Sun has no speed.
A correct description is the following:
Suppose at t0 the planet is turned ON and OFF i.e. explodes.
This disturbance propagates in a sphere, and is independent of the speed of the planet.
The Observer will see the explosion when the path of the Sun crosses this sphere.
The direction will be towards the position where the planet was at t0.