In this image of Earth and the Moon from the Sim, what does the circle around Earth represent?

This is the orbit (of the moon around Earth).

An orbit is a circular/oval path that planets, moons, comets, etc follow with a "subject" in the middle. In this case, the circle is the orbit of the moon around Earth.

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.