To calculate the orbital speed and period of a satellite, the gravitational force acting on the satellite must equal the centripetal force required for circular motion. The formula for gravitational force can be equated to the centripetal force to derive the orbital speed. The orbital speed can be calculated using the equation v = √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite. The orbital period can then be determined using the formula T = 2πr/v. Understanding these relationships is essential for solving satellite motion problems.