Final answer:
An orbiting satellite's speed remains constant because gravity acts as a centripetal force, only changing its direction without affecting speed, a consequence of conservation of angular momentum and mechanical energy in a stable orbit free from atmospheric friction.
Step-by-step explanation:
The reason an orbiting satellite's speed remains constant can be best explained by Newton's laws of motion and understanding of gravity. While it's true that satellites change direction as they orbit, the force of gravity, which is directed toward the center of the Earth, only affects the satellite's direction and not its speed when in a stable orbit. This happens because gravity acts as a centripetal force, effectively pulling the satellite inward to keep it in orbit, while the satellite's inertia keeps it moving forward. This results in a constant speed since the force of gravity does not do work on the satellite to change its tangential or orbital speed.
When analyzing the behavior of satellites with respect to their orbits, we observe that their orbital velocity decreases as they move to larger orbits, whereas the change in potential energy increases, which is evidence of the conservation of mechanical energy. The speed is greatest at the periapsis (closest point to Earth) and least at apoapsis (farthest point), as the conservation of angular momentum dictates that the product of radial distance and tangential speed must remain constant.
Satellites in orbit behave in the same way that natural satellites, like the Moon, do. If they are high enough to avoid atmospheric friction, they will maintain their orbits indefinitely without additional energy input, thanks to the balance between gravitational force and their inertial motion.