The gravitational field strength of the Sun at Earth's position is significantly greater than that of the Moon due to the Sun's much larger mass, despite the greater distance. The calculations involve Newton's Law of Gravitation, which indicates that the gravitational force is inversely proportional to the square of the distance between the two bodies. The discussion also includes specific calculations for gravitational field strength halfway between the Earth and the Moon, as well as on Jupiter's surface. Additionally, there is a side conversation about the effects of voltage differences on an electric razor's current when used in Europe. The key takeaway is the importance of mass and distance in calculating gravitational forces.