The cancellation of gravitational time dilation and kinematic time dilation at a specific orbital height is a consequence of the interplay between gravitational potential energy and the increase in kinetic energy associated with orbital motion.
In the theory of general relativity, gravitational time dilation occurs because the strength of the gravitational field affects the flow of time. Closer to a massive object, where the gravitational field is stronger, time passes more slowly compared to a location further away.
On the other hand, kinematic time dilation arises due to the relative motion of an object. As an object moves faster, time appears to pass more slowly for it compared to a stationary observer.
In the case of an object in orbit, such as a satellite, the gravitational pull from the Earth decreases with increasing altitude. As the satellite moves away from the Earth's surface, the gravitational time dilation decreases because the gravitational field weakens. However, the orbital velocity of the satellite increases as it moves away from the Earth due to the conservation of angular momentum.
The increase in orbital velocity leads to an increase in the satellite's kinetic energy. According to special relativity, an increase in kinetic energy results in an increase in kinematic time dilation. Therefore, the orbital velocity compensates for the decreasing gravitational time dilation, resulting in a cancellation effect.
At a specific orbital height of around 3,000 km (often referred to as the "Molniya orbit" used by some communication satellites), the gravitational time dilation lost due to the weaker gravitational field is precisely balanced by the kinematic time dilation gained from the higher orbital velocity. This cancellation effect allows the clocks on the satellites to remain synchronized with clocks on the Earth's surface.
It's important to note that the cancellation effect occurs at this specific altitude because it corresponds to the equilibrium between the decrease in gravitational time dilation and the increase in kinematic time dilation. At different orbital heights, the balance between these two effects would not be precisely maintained, and time discrepancies would occur.