After viewing one of my favorite Family Guy clips I began to wonder, exactly how massive would Peter have to be for this to work...

Ignoring Earth's gravity, we can equate the centripetal force of the apple with the gravitational force of Peter on the apple:

m_apple * a_c = m_apple * r_orbit * omega^2 = G * M_Peter * m_apple * r_orbit^-2.

This implies that M_Peter = r_orbit^3 * omega^2 * G ^-1. If we estimate the radius of orbit as about 1m and the orbital frequency as omega = 2*pi / 2s = pi s^-1, we get Peter's mass as 1.5 * 10^11 kg or approximately 160 million tons. Fortunately for the residents of Quahog, this is not massive enough for Peter to create a black hole, his Schwarzschild radius is only 0.1 femtometers.