Apply Newton's law of universal gravitation to compute the force between two masses, and explain how gravity supplies the centripetal force for a circular orbit.
Newton's great insight was that the SAME force pulling an apple to the ground also holds the Moon in orbit: every pair of masses attracts each other with F = G*m1*m2/r^2, where G = 6.674x10^-11 N*m^2/kg^2 is a universal constant, tiny compared to everyday forces, which is why gravity between ordinary objects (you and a chair, say) is completely unnoticeable and only becomes obvious when at least one mass is astronomically large, like a planet. Like Coulomb's law (coming in a few weeks), this is an inverse-square law: doubling the distance between two masses cuts the force to one-quarter, not one-half.
For a satellite or planet in a circular orbit, gravity itself IS the centripetal force, with nothing else needed: G*M*m/r^2 = m*v^2/r, which leads to an orbital speed of v = sqrt(G*M/r) and to Kepler's third law, that a larger orbit takes disproportionately longer (T^2 is proportional to r^3 around the same central body). A common misconception is that astronauts in orbit have "escaped" gravity -- they have not; gravity is exactly what keeps them curving around the planet instead of flying off in a straight line. Their apparent weightlessness comes from being in continuous free fall together with their spacecraft, so there is no normal force (nothing pressing them into a floor) to register as weight.
Mastery looks like: They compute the gravitational force between two masses using Newton's law, and explain, in terms of continuous free fall, why orbiting astronauts experience apparent weightlessness.
Common stumbles: Believing gravity effectively "turns off" or becomes negligible in orbit; forgetting to square the distance in the denominator of the gravitation formula.