Rarely, there will be sunspots that are big enough to see without a telescope, and apparently the Chinese astronomers recorded these blemishes on the sun from time to time. They travel out in straight lines at the speed of light into the universe. Yes, it involved measuring the Doppler shift in a radio signal reflected off a moving cloud. This tells us the wind speed, and hence gives us a better idea of the pattern of storms. If all objects emit electromagnetic energy, then the earth presumably does.
Objects emit energy because they absorb energy.
The earth absorbs energy from the sun, and so it will start cooling and emit less and less energy when the sun stops heating it. Consider that the universe is made of matter and energy. So saying things move is just saying that some of the energy of the universe manifests itself in the motion of objects. But fifty or a seventy-five years into the future, who can say. Call x 6029, the telephone in the control room at the observatory, if you want to check before you come.