The problem with this question is all of the assumptions that go into it. When we're taught physics, we are given analogies that help our understanding, but mislead us when we try to dig deeper.
Firstly, charged particles like electrons are always surrounded by an electromagnetic field. Changes in that field propagate through space at the speed of light and we call it "light" (informally, or "photons", more formally).
Next, electrons do not "orbit". But when their position is measured, they may be detected with certain probability within certain regions around the nucleus called "orbitals" (misleading term). Orbitals are normally not circular or spherical and do not imply the electron orbits the nucleus like a satellite.
Finally, to answer your question directly, when an electron is in the ground state in its orbital, it is in a steady-state which does not cause its electromagnetic field to change, thus no "light" is emitted. However, when an electron is in an excited state, the transition back to the ground state or a lower-energy excited state, does cause its electromagnetic field to change, and we can detect the photons that are emitted and they are contain the same amount of energy that is the difference in energy levels between the two states.