Final answer:
The mass of a satellite does not appear in the formula for its orbital speed because the satellite's mass cancels out during the calculations, leaving the orbital speed dependent only on the mass of the central body around which it orbits and the radius of the orbit.
Step-by-step explanation:
The mass of a satellite is not part of the formula for calculating its circular orbital speed because, in the context of circular orbits around a much larger mass like Earth, all objects accelerate at the same rate due to gravity regardless of their own mass. This is encapsulated in Newton's second law, which combines with the law of universal gravitation to provide a simplified formula for orbital velocity that is independent of the satellite's mass. The formula only requires the mass of the larger body (like Earth) and the radius of the orbit.
For satellites orbiting bodies like Earth, the acceleration towards the center of the planet is provided by the gravitational force, which is the product of the gravitational constant times the masses of the two objects divided by the square of the distance between them. However, since the centripetal force required to keep the satellite in orbit must balance this gravitational force, and centripetal force depends on the satellite's velocity squared divided by the orbital radius, the mass of the satellite cancels out in the computation.
Thus, the orbital velocity is dependent only on the gravitational constant, the mass of the Earth (or other central body), and the orbital radius. The escape velocity is similarly independent of the satellite's mass, being exactly √2 times the orbital velocity.